Research ArticleExperimental Investigation of the Influence for StopingSequence and Granular Grading on Lateral Pressure during theNonpillar Sublevel Caving Mining

Yang Liu1 Rongxing He 1 Fengyu Ren1 Jianli Cao1 Dongjie Zhang2 Yanjun Zhou1

Huan Liu1 Guanghui Li1 and Jing Zhang1

1School of Resources and Civil Engineering Northeastern University Shenyang 110819 China2Institute of Mining and Coal Inner Mongolia University of Science and Technology Baotou 014010 China

Correspondence should be addressed to Rongxing He herongxingmailneueducn

Received 16 December 2019 Accepted 2 May 2020 Published 28 May 2020

Academic Editor Mostafa Sharifzadeh

Copyright copy 2020 Yang Liu et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this study a self-designed scaled physical model was conducted to investigate the variation laws of lateral pressure underdifferent stoping sequences and granular gradings and drawing ore in the experiments was used to simulate the mining processUnder the limiting equilibrium state the values of lateral pressure increased exponentially with the increasing depth of granularmedia and the growth rate of lateral pressure gradually decreased as the depth of granular media increased +en the laboratoryresults indicated that the distribution laws of lateral pressure were divided into three parts namely the drawing influencingregion the upper descending zone and the central growth area As the height of the isolated extraction zone (IEZ) increased thescope of the drawing influencing region and the upper descending zone increased while the range of central growth areadecreased In the case of an invariable height of IEZ more reduction ratio and the scope for drawing influencing region could beappeared in the lower wall Increasing the space between the drawpoints and granular grading were an effective way to control thereduction rate of lateral pressure in the drawing influencing region while the scope of the above parts kept stable Moreover theaverage values of lateral pressure showed an increasing trend as the granular grading decreased at the same number ofdrawing ore

1 Introduction

+e nonpillar sublevel caving mining was usually adopted toextract the underground metal mine which has a highmining intensity consumes little mining costs and usessimple stoping technology [1ndash3] However the surfacesubsidence was inevitably generated in the vicinity of themining operations based on the main characteristic of thismining method +e inaccurate range of the surface sub-sidence could significantly deteriorate recovery ratio the lossof natural resources and operational safety Meanwhile thedistribution laws of lateral pressure were the essential factorto predict the range of surface subsidence induced by thenonpillar sublevel caving mining [4ndash7] Hence it was quiteessential to investigate the distribution laws to control and

avoid the loss of natural resources and jeopardizes surfacesubsidence

Recently many great efforts had made to study thedistribution laws of lateral pressure using physical modelstheoretical analyses and numerical analyses Meanwhile theconventional laws of lateral pressure are based on the theoryof Janssen Coulomb Reimbert Wilfred Airy and Rankineand then the widespread computational formulas of lateralpressure as shown in Table 1 [8ndash19] +e theory of Janssenhad been widely used but the different coefficient of lateralpressure was applied in the different specifications Reimbert[14] studied the equation based on laboratory tests wherethe coefficient of lateral pressure was variable +en Chen[17] reported a formula of lateral pressure with an inclinedangle according to the assumption of the Janssen equation

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8452701 15 pageshttpsdoiorg10115520208452701

Tabl

e1

+econv

entio

nalc

ompu

tatio

nalformulas

ofthelateralp

ressure

+econv

entio

nallaw

sProp

oser

p

cSf

C[1

minuseminus

(f

KCS

)z]

K1

minussin

θ1

+sin

θJanssen[13]

p

cDta

nϕ[1

minus(1

+(

zc

))minus2 ]

c

R4

Kmiddottanϕ

minush

s3K

1

minussin

θ1

+sin

θRe

imbert

[14]

pa

(12)

cz2 K

aK

acos2

(θ

minusε)cos

2 (ε)

timescos(ϕ

+ε)

[1+

sin(ϕ

+θ)

timessin

(θ

minusβ)cos

(ϕ

+ε)

timescos(εminus

β)1113968

]2p

b

(12)

cz2 K

b

Kb

cos2

(φ

+ε)cos

2 (ε)

timescos2

(εminus

δ)[1

minus

sin

(δ

+φ)

timessin

(φ

+β)cos

(εminus

δ)timescos(εminus

β)1113968

]2

Cou

lomb[15]

HDlt15

p

(12)

cz2 (1

tanθ[tanθ

+tanϕ]

1113968+

1+

(tanϕ)

21113969

)2

HDgt15

p

cDta

nϕ

+tanθ(1

minus

1+

(tanθ)

2 (2zD

)(tanϕ

+tanθ)

+1

minustanϕ

timestanθ

1113969

)

WilfredAiry[16]

p

(c

Sf

C)sin

a(1

minus(

fta

na

))[1

minuseminus

(f

KCSsin

a)z

]K

1

minussin

θ1

+sin

θChen[17]

pa

c

zK

aK

a1

minussin

θ1

+sin

θp

b

cz

KbK

b1

+sin

θ1

minussin

θRa

nkine[18]

Notepwas

thelateralp

ressurep a

was

theactiv

elateralp

ressurep b

was

thepassivelateralp

ressureKwas

thecoeffi

ciento

fthe

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ressureKawas

thecoeffi

ciento

fthe

activ

elateralp

ressureKbwas

the

coeffi

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fthe

passivelateralp

ressure

cwas

theun

itweigh

tofg

ranu

larm

ediaS

was

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rizontalprojectedarea

oftheclasssilo

Cwas

theperimeter

ofho

rizontalprojectio

nforthe

classsilo

fwas

frictio

ncoeffi

cientb

etweengranularmediaandclasssilo

ftanϕϕwas

thefrictionangleb

etweengranular

mediaandclasssilo

zwas

theh

eigh

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larm

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nglebetweenclasssilo

andverticallin

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2 Advances in Civil Engineering

which had been used in thin orebody Otherwise the scaledphysical experiments had been widely utilized in the labo-ratory with low cost simpler operation and low timeconsumption Brown et al researched the patterns ofpressures in storage and discharge state with two differentfree-flowing solids [20] Meanwhile Ren et al designed thesetup to study the variation laws of lateral pressure duringthe process of drawing ore [21] With the development ofnumerical simulation technique a mass of number codesincluding ANSYS [22 23] DEM [24 25] and PFC [26] weredeveloped and applied in the models of lateral pressure forgranular media +e PFC3D software was employed tosimulate the distribution laws for internal pressure of thematerial during the coal discharging process [27] and theADINA software was performed to predict the value oflateral pressure in the silo [28] +ese studies had provided acritical understanding including the distribution laws oflateral pressure under the limiting equilibrium state theinfluence on the lateral pressure among materials theinfluencing factors of the geometry for bin shape and thecoefficient characteristic for the lateral pressure and itschanging trend

In nonpillar sublevel caving mining the movement andnonuniform granular conditions of granular media for thecaved rock zone were very common [29 30] +us thedistribution laws of lateral pressure were influenced bymining However most of these studies had focused on thedistribution laws for lateral pressure at the limiting equi-librium and uniform granular conditions Few investigationswere reported for the distribution laws under the drawingore and nonuniform grading conditions Although someimportant factors such as the size of drawpoint the prop-erties of thematerial and the dip and width of orebody couldaffect the lateral pressure the stoping sequence and granulargrading were also vital to analyze the stress states of side wallfor surface subsidence Considering the influence of thestoping sequence and granular grading on the distributionlaws of lateral pressure scaled physical experiments werecarried out and the variation laws of lateral pressure duringdrawing ore were found in this study +is work could notonly help researchers to understand the mechanism ofgravity flow for granular media but also provided a theo-retical tool for predicting the scope of the surface subsidenceinduced by the nonpillar sublevel caving mining

2 Materials and Model

Castro et al [31] reported that the shape of the isolatedextraction zone (IEZ) was not significantly affected by thegeometrical scale using a large 3D physical model To reducethe effect on the operation or flow capability the setupshould be rational and feasible +us some hypotheses ofscaling were applied as follows (1) the geometrical scale of 1 100 was used to simulate for the whole block geometryincluding block dimensions (height and area of draw) thedimensions of drawpoint and the particle size (2) the bulkdensity and the residual friction angle in the model were thesame as those in the field (3) the wall friction angle was

similar to the internal friction angle and (4) the scale oftimes was related to the scale of the length by λt 10012 10

+e equipment was composed of a drawing-ore device adata collection system and a supporting bar for adjusting theorebody dip as shown in Figure 1 As shown in Figure 2 thedrawing-ore device was made up of upper and lower wallsfront and back walls drawpoints and test channels with thesize of 50 cmtimes 25 cmtimes 160 cm (widthtimes lengthtimes height)+egranular media in the drawing-ore device was required tomeasurably stable during the experimental process Hencethe walls of lower and upper were made from steel +enfour drawpoints (the length and width of them were both3 cm) were set in the bottom of the lower wall and theinterval was 76 cm Also the drawpoints were used tosimulate the different stoping sequences To precisely obtainthe values of lateral pressure the upper and lower walls weremade up of 16 panels respectively and the correspondingsize was 50times10 cm (widthtimes length) +en 1ndash8 testchannels were placed in the lower wall and 9ndash16 testchannels were installed in the upper wall and the intervalwas 20 cm in the respective wall 1 and 9 test channels were15 cm away from the bottom of the device and 8 and 16test channels were 5 cm away from the top of the device +etest channels collected information regarding the lateralpressure with different measured heights and the measuredheight of each test channel is shown in Table 2 +en thevalues of lateral pressure with different heights weretransferred from the test channels to the data collectionsystem during the drawing process In the study the stopingsequence and granular grading were investigated as influ-encing factors to possess the distribution laws of lateralpressure during drawing ore Dolomite was used as theexperimental material in the test and was regarded ascohesionless

3 Experimental Process

+e basic operation and theoretical foundation of the iso-lated drawing experiments were provided by Zhang et al[32] A total of 9 physical simulation tests were designed tostudy the influence of the stoping sequence and granulargrading on the distribution laws of lateral pressure Asshown in Tables 3ndash5 three different stoping sequences andthree granular gradings were taken into account in thisstudy According to the geometrical scale and nonpillarsublevel caving mining [1 33] the height of orebody (30 cm)and the drawing mode of nondilution were employed Tokeep the ore flow capabilities consistent with the test ma-terials the ores were obtained directly from the test mate-rials and their size was in accordance with the test material+en the ores were red painted to distinguish them from thetest materials To make the flow velocity of granular mediakeep constant and full similitude of mine conditions thesingle mass of the ores drawn from the drawpoints was about200 g per time and the independent advance of ore breakingwas approximately 15 cm Moreover each experiment wasrepeated 3 times to decrease the influence of randommovements of experimental materials based on the flowbehaviors during the drawing process To avoid the influence

Advances in Civil Engineering 3

on the testing data the drawing-ore device was remainedhorizontal on the ground and the adjusting bar was fixed onthe experimental model

After completing the above steps the drawpoints wereblocked with the elastic materials so as to simulate the realstate without blasting +en the incompact ores were

e data collectionsystem

e drawing-ore device

e drawpoints

Figure 1 +e schematic diagram of the physical model

2

1

3

4

5

6

7

8

9

10

11

12

13

14

15

16

12 3

4

20 cm

15 cm

160 cm

50 cm

25 cm

e lower wall

e upper wall

Figure 2 +e schematic diagram of the drawing-ore device Note 1 2 16 represent the test channels and I II III and V representthe drawpoints

Table 2 +e measured height of each test channel

Test channels+e lower wall +e upper wall

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Measured height (m) 145 125 105 085 065 045 025 005 145 125 105 085 065 045 025 005

4 Advances in Civil Engineering

dropped into the setup with 30 cm and a smooth surface ofthe ores would be obtained Next the surface of the ores wassurrounded by a little waste rock such that each ore granularwas stabilized Otherwise the ore granular in the surfacewould move randomly in the ore loading process therebyaffecting the experimental results Also the other incompactwaste rocks were dropped into the setup so no more ma-terials could be dropped into the experimental model Fi-nally the total internal space of setup was filled with theexperimental materials Additionally the internal frictionangle and friction angle between granular media and thedrawing-ore device were analyzed Meanwhile the totalmass and density of granular media were calculated once theore loading process was terminated Since the internal modelwas filled with the experimental materials the elastic ma-terial blocking the drawpoints was taken off and the ma-terials were then drawn from the drawpoints According tothe above scheme the corresponding drawpoints wereunfolded During the drawing process the flow speed ofgranular media should remain as constant as possible ratherthan fast Hence the single mass of the ore drawn from thedrawpoints was about 200 g each time and the values oflateral pressures and the number of drawing ore wererecorded +en the corresponding drawpoint was termi-nated once the waste rocks were drawn +e interval time of20minutes was employed to simulate the mining conditions+en the next corresponding drawpoints were unfolded andthe previous steps were repeated Consequently the varia-tion laws of lateral pressure could be received once the wasterock reached the last drawpoint

4 Experimental Results

41 4e Relationship between Lateral Pressure and Depth ofGranularMedia Figure 3 presents the relationship betweenthe lateral pressure and depth of granular media under thelimiting equilibrium state +e values of lateral pressureincreased exponentially with the increasing depth of gran-ular media and the growth rate of lateral pressure graduallydecreased as the depth of granular media increased +enthe porosity of granular media increased when the granulargrading increased However the unit weight decreased ac-cordingly Hence the values of lateral pressure showed anincreasing trend as the granular grading decreased for thesame depth of granular media Meanwhile the porosity ofgranular media decreased as the depth of granular mediaincreased and the value of lateral pressure among granulargrading increased with the increasing depth of granularmedia

42 Characteristic of Variation Laws for Lateral Pressure+e relationship between the number of drawing ore and thevalues of lateral pressure with different schemes are shown inFigures 4ndash12 respectively Due to the 20-minute intervaltime the process of drawing ore could be divided into twostages and IEZ induced by two drawing stage was inde-pendent [34] It was suggested that themeasured values from1 and 9 test channels decreased exponentially with anincreasing number of drawing ore in each drawing stage+en the lateral pressure of 2 3 and 10 test channels wasfirstly enhanced and then diminished as the number of

Table 3 Summary of laboratory schemes

Granular gradingStoping sequence

Interval faces From center to end From end to centerGroup 1 Scheme 1 Scheme 4 Scheme 7Group 2 Scheme 2 Scheme 5 Scheme 8Group 3 Scheme 3 Scheme 6 Scheme 9

Table 4 Summary of stoping sequence

Stoping sequence Summary

Interval face(1) Unfold the drawpoints of II and V (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and III (6) repeated the step of (2) and (3)

From center toend

(1) Unfold the drawpoints of II and III (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and V (6) repeated the step of (2) and (3)

From end tocenter

(1) Unfold the drawpoints of I and V (2) recorded the values of lateral pressure during the drawing process (3) blockedthe corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore device sit

for 20minutes (5) unfold the drawpoints of II and III (6) repeated the step of (2) and (3)

Table 5 Summary of granular grading

Granular grading Group 1 Group 2 Group 3+e mass percent () 246 386 368 246 386 368 246 386 368+e granular size (mm) lt2 2sim4 4sim6 lt3 3sim6 6sim9 lt4 4sim8 8sim12

Advances in Civil Engineering 5

Group 1Group 2Group 3

0

400

800

1200

1600

2000

2400

2800

e l

ater

al p

ress

ure (

Pa)

03 06 09 12 1500e depth of granular media

Figure 3 +e relationship between the lateral pressure and depth of granular media under the limiting equilibrium state

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(a)

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(b)

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(c)

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(d)

Figure 4 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 1

6 Advances in Civil Engineering

drawing ore increased in the two drawing stages Meanwhilethe lateral pressure of 8 and 16 test channels had a negativerelationship with the number of drawing ore +e values ofother test channels showed an increasing trend as thenumber of drawing ore rose

In the drawing process the scope of IEZ and isolatedmovement zone (IMZ) increased with an increase in numberfor drawing ore +en the granular media in the IMZ couldbe loosed and that above the IMZ slowly collimation movedand the internal friction angle gradually increased Hencethe lateral pressures were projected to continue decreasingwhile the test channels located in the scope of IMEMeanwhile because of the relatively small scale of IMZ andincrescent internal friction angle in the initial drawing phasethe measured values were augmented while the test channelsabove the scope of IMZ and then the lateral pressuredescended as the IMZ reached the testing range of testchannel Due to the descending surface of granular mediathe value of 8 and 16 test channels tended to gradual

decline As the nondilution ore drawing was used the heightof the IEZ and IMZ was about 30 cm and 738 cm re-spectively Hence the other values were expected to rise asthe test channels were higher than 738 cm

+e variation rates of lateral pressure under differentstoping sequences and granular gradings are exhibited inTable 6 A new standpoint was proposed that the distributionlaws could be divided into three parts One part was drawinginfluencing region which is located in the IMZ and had apositive relationship with the number of drawing ore +eother part was the upper descending zone which is locatedin the surface of granular media and the volume was equal tothe IEZ +e last part was central growth area which wasbetween the previous two parts +en the lateral pressurehad a positive relationship with the number of drawing orein the central growth area As the number of drawing oreincreased the scope of drawing influencing region andupper descending zone increased while the range of centralgrowth area decreased Moreover the reduction rate of

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

1800

1950

2100

2250

2400

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 5 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 2

Advances in Civil Engineering 7

e firstdrawing stage

e seconddrawing stage

1650

1800

1950

2100

2250

e lat

eral

pre

ssur

e (Pa

)

6 12 18 240e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1650

1800

1950

2100

2250

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 6 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 3

0 6 12 18 24 30e number of drawing ore

e firstdrawing stage e second

drawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e l

ater

al p

ress

ure (

Pa)

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

e firstdrawing stage

e seconddrawing stage

6 12 18 24 300e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 7 Continued

8 Advances in Civil Engineering

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

which had been used in thin orebody Otherwise the scaledphysical experiments had been widely utilized in the labo-ratory with low cost simpler operation and low timeconsumption Brown et al researched the patterns ofpressures in storage and discharge state with two differentfree-flowing solids [20] Meanwhile Ren et al designed thesetup to study the variation laws of lateral pressure duringthe process of drawing ore [21] With the development ofnumerical simulation technique a mass of number codesincluding ANSYS [22 23] DEM [24 25] and PFC [26] weredeveloped and applied in the models of lateral pressure forgranular media +e PFC3D software was employed tosimulate the distribution laws for internal pressure of thematerial during the coal discharging process [27] and theADINA software was performed to predict the value oflateral pressure in the silo [28] +ese studies had provided acritical understanding including the distribution laws oflateral pressure under the limiting equilibrium state theinfluence on the lateral pressure among materials theinfluencing factors of the geometry for bin shape and thecoefficient characteristic for the lateral pressure and itschanging trend

In nonpillar sublevel caving mining the movement andnonuniform granular conditions of granular media for thecaved rock zone were very common [29 30] +us thedistribution laws of lateral pressure were influenced bymining However most of these studies had focused on thedistribution laws for lateral pressure at the limiting equi-librium and uniform granular conditions Few investigationswere reported for the distribution laws under the drawingore and nonuniform grading conditions Although someimportant factors such as the size of drawpoint the prop-erties of thematerial and the dip and width of orebody couldaffect the lateral pressure the stoping sequence and granulargrading were also vital to analyze the stress states of side wallfor surface subsidence Considering the influence of thestoping sequence and granular grading on the distributionlaws of lateral pressure scaled physical experiments werecarried out and the variation laws of lateral pressure duringdrawing ore were found in this study +is work could notonly help researchers to understand the mechanism ofgravity flow for granular media but also provided a theo-retical tool for predicting the scope of the surface subsidenceinduced by the nonpillar sublevel caving mining

2 Materials and Model

Castro et al [31] reported that the shape of the isolatedextraction zone (IEZ) was not significantly affected by thegeometrical scale using a large 3D physical model To reducethe effect on the operation or flow capability the setupshould be rational and feasible +us some hypotheses ofscaling were applied as follows (1) the geometrical scale of 1 100 was used to simulate for the whole block geometryincluding block dimensions (height and area of draw) thedimensions of drawpoint and the particle size (2) the bulkdensity and the residual friction angle in the model were thesame as those in the field (3) the wall friction angle was

similar to the internal friction angle and (4) the scale oftimes was related to the scale of the length by λt 10012 10

+e equipment was composed of a drawing-ore device adata collection system and a supporting bar for adjusting theorebody dip as shown in Figure 1 As shown in Figure 2 thedrawing-ore device was made up of upper and lower wallsfront and back walls drawpoints and test channels with thesize of 50 cmtimes 25 cmtimes 160 cm (widthtimes lengthtimes height)+egranular media in the drawing-ore device was required tomeasurably stable during the experimental process Hencethe walls of lower and upper were made from steel +enfour drawpoints (the length and width of them were both3 cm) were set in the bottom of the lower wall and theinterval was 76 cm Also the drawpoints were used tosimulate the different stoping sequences To precisely obtainthe values of lateral pressure the upper and lower walls weremade up of 16 panels respectively and the correspondingsize was 50times10 cm (widthtimes length) +en 1ndash8 testchannels were placed in the lower wall and 9ndash16 testchannels were installed in the upper wall and the intervalwas 20 cm in the respective wall 1 and 9 test channels were15 cm away from the bottom of the device and 8 and 16test channels were 5 cm away from the top of the device +etest channels collected information regarding the lateralpressure with different measured heights and the measuredheight of each test channel is shown in Table 2 +en thevalues of lateral pressure with different heights weretransferred from the test channels to the data collectionsystem during the drawing process In the study the stopingsequence and granular grading were investigated as influ-encing factors to possess the distribution laws of lateralpressure during drawing ore Dolomite was used as theexperimental material in the test and was regarded ascohesionless

3 Experimental Process

+e basic operation and theoretical foundation of the iso-lated drawing experiments were provided by Zhang et al[32] A total of 9 physical simulation tests were designed tostudy the influence of the stoping sequence and granulargrading on the distribution laws of lateral pressure Asshown in Tables 3ndash5 three different stoping sequences andthree granular gradings were taken into account in thisstudy According to the geometrical scale and nonpillarsublevel caving mining [1 33] the height of orebody (30 cm)and the drawing mode of nondilution were employed Tokeep the ore flow capabilities consistent with the test ma-terials the ores were obtained directly from the test mate-rials and their size was in accordance with the test material+en the ores were red painted to distinguish them from thetest materials To make the flow velocity of granular mediakeep constant and full similitude of mine conditions thesingle mass of the ores drawn from the drawpoints was about200 g per time and the independent advance of ore breakingwas approximately 15 cm Moreover each experiment wasrepeated 3 times to decrease the influence of randommovements of experimental materials based on the flowbehaviors during the drawing process To avoid the influence

Advances in Civil Engineering 3

on the testing data the drawing-ore device was remainedhorizontal on the ground and the adjusting bar was fixed onthe experimental model

After completing the above steps the drawpoints wereblocked with the elastic materials so as to simulate the realstate without blasting +en the incompact ores were

e data collectionsystem

e drawing-ore device

e drawpoints

Figure 1 +e schematic diagram of the physical model

2

1

3

4

5

6

7

8

9

10

11

12

13

14

15

16

12 3

4

20 cm

15 cm

160 cm

50 cm

25 cm

e lower wall

e upper wall

Figure 2 +e schematic diagram of the drawing-ore device Note 1 2 16 represent the test channels and I II III and V representthe drawpoints

Table 2 +e measured height of each test channel

Test channels+e lower wall +e upper wall

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Measured height (m) 145 125 105 085 065 045 025 005 145 125 105 085 065 045 025 005

4 Advances in Civil Engineering

dropped into the setup with 30 cm and a smooth surface ofthe ores would be obtained Next the surface of the ores wassurrounded by a little waste rock such that each ore granularwas stabilized Otherwise the ore granular in the surfacewould move randomly in the ore loading process therebyaffecting the experimental results Also the other incompactwaste rocks were dropped into the setup so no more ma-terials could be dropped into the experimental model Fi-nally the total internal space of setup was filled with theexperimental materials Additionally the internal frictionangle and friction angle between granular media and thedrawing-ore device were analyzed Meanwhile the totalmass and density of granular media were calculated once theore loading process was terminated Since the internal modelwas filled with the experimental materials the elastic ma-terial blocking the drawpoints was taken off and the ma-terials were then drawn from the drawpoints According tothe above scheme the corresponding drawpoints wereunfolded During the drawing process the flow speed ofgranular media should remain as constant as possible ratherthan fast Hence the single mass of the ore drawn from thedrawpoints was about 200 g each time and the values oflateral pressures and the number of drawing ore wererecorded +en the corresponding drawpoint was termi-nated once the waste rocks were drawn +e interval time of20minutes was employed to simulate the mining conditions+en the next corresponding drawpoints were unfolded andthe previous steps were repeated Consequently the varia-tion laws of lateral pressure could be received once the wasterock reached the last drawpoint

4 Experimental Results

41 4e Relationship between Lateral Pressure and Depth ofGranularMedia Figure 3 presents the relationship betweenthe lateral pressure and depth of granular media under thelimiting equilibrium state +e values of lateral pressureincreased exponentially with the increasing depth of gran-ular media and the growth rate of lateral pressure graduallydecreased as the depth of granular media increased +enthe porosity of granular media increased when the granulargrading increased However the unit weight decreased ac-cordingly Hence the values of lateral pressure showed anincreasing trend as the granular grading decreased for thesame depth of granular media Meanwhile the porosity ofgranular media decreased as the depth of granular mediaincreased and the value of lateral pressure among granulargrading increased with the increasing depth of granularmedia

42 Characteristic of Variation Laws for Lateral Pressure+e relationship between the number of drawing ore and thevalues of lateral pressure with different schemes are shown inFigures 4ndash12 respectively Due to the 20-minute intervaltime the process of drawing ore could be divided into twostages and IEZ induced by two drawing stage was inde-pendent [34] It was suggested that themeasured values from1 and 9 test channels decreased exponentially with anincreasing number of drawing ore in each drawing stage+en the lateral pressure of 2 3 and 10 test channels wasfirstly enhanced and then diminished as the number of

Table 3 Summary of laboratory schemes

Granular gradingStoping sequence

Interval faces From center to end From end to centerGroup 1 Scheme 1 Scheme 4 Scheme 7Group 2 Scheme 2 Scheme 5 Scheme 8Group 3 Scheme 3 Scheme 6 Scheme 9

Table 4 Summary of stoping sequence

Stoping sequence Summary

Interval face(1) Unfold the drawpoints of II and V (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and III (6) repeated the step of (2) and (3)

From center toend

(1) Unfold the drawpoints of II and III (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and V (6) repeated the step of (2) and (3)

From end tocenter

(1) Unfold the drawpoints of I and V (2) recorded the values of lateral pressure during the drawing process (3) blockedthe corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore device sit

for 20minutes (5) unfold the drawpoints of II and III (6) repeated the step of (2) and (3)

Table 5 Summary of granular grading

Granular grading Group 1 Group 2 Group 3+e mass percent () 246 386 368 246 386 368 246 386 368+e granular size (mm) lt2 2sim4 4sim6 lt3 3sim6 6sim9 lt4 4sim8 8sim12

Advances in Civil Engineering 5

Group 1Group 2Group 3

0

400

800

1200

1600

2000

2400

2800

e l

ater

al p

ress

ure (

Pa)

03 06 09 12 1500e depth of granular media

Figure 3 +e relationship between the lateral pressure and depth of granular media under the limiting equilibrium state

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(a)

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(b)

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(c)

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(d)

Figure 4 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 1

6 Advances in Civil Engineering

drawing ore increased in the two drawing stages Meanwhilethe lateral pressure of 8 and 16 test channels had a negativerelationship with the number of drawing ore +e values ofother test channels showed an increasing trend as thenumber of drawing ore rose

In the drawing process the scope of IEZ and isolatedmovement zone (IMZ) increased with an increase in numberfor drawing ore +en the granular media in the IMZ couldbe loosed and that above the IMZ slowly collimation movedand the internal friction angle gradually increased Hencethe lateral pressures were projected to continue decreasingwhile the test channels located in the scope of IMEMeanwhile because of the relatively small scale of IMZ andincrescent internal friction angle in the initial drawing phasethe measured values were augmented while the test channelsabove the scope of IMZ and then the lateral pressuredescended as the IMZ reached the testing range of testchannel Due to the descending surface of granular mediathe value of 8 and 16 test channels tended to gradual

decline As the nondilution ore drawing was used the heightof the IEZ and IMZ was about 30 cm and 738 cm re-spectively Hence the other values were expected to rise asthe test channels were higher than 738 cm

+e variation rates of lateral pressure under differentstoping sequences and granular gradings are exhibited inTable 6 A new standpoint was proposed that the distributionlaws could be divided into three parts One part was drawinginfluencing region which is located in the IMZ and had apositive relationship with the number of drawing ore +eother part was the upper descending zone which is locatedin the surface of granular media and the volume was equal tothe IEZ +e last part was central growth area which wasbetween the previous two parts +en the lateral pressurehad a positive relationship with the number of drawing orein the central growth area As the number of drawing oreincreased the scope of drawing influencing region andupper descending zone increased while the range of centralgrowth area decreased Moreover the reduction rate of

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

1800

1950

2100

2250

2400

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 5 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 2

Advances in Civil Engineering 7

e firstdrawing stage

e seconddrawing stage

1650

1800

1950

2100

2250

e lat

eral

pre

ssur

e (Pa

)

6 12 18 240e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1650

1800

1950

2100

2250

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 6 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 3

0 6 12 18 24 30e number of drawing ore

e firstdrawing stage e second

drawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e l

ater

al p

ress

ure (

Pa)

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

e firstdrawing stage

e seconddrawing stage

6 12 18 24 300e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 7 Continued

8 Advances in Civil Engineering

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

on the testing data the drawing-ore device was remainedhorizontal on the ground and the adjusting bar was fixed onthe experimental model

After completing the above steps the drawpoints wereblocked with the elastic materials so as to simulate the realstate without blasting +en the incompact ores were

e data collectionsystem

e drawing-ore device

e drawpoints

Figure 1 +e schematic diagram of the physical model

2

1

3

4

5

6

7

8

9

10

11

12

13

14

15

16

12 3

4

20 cm

15 cm

160 cm

50 cm

25 cm

e lower wall

e upper wall

Figure 2 +e schematic diagram of the drawing-ore device Note 1 2 16 represent the test channels and I II III and V representthe drawpoints

Table 2 +e measured height of each test channel

Test channels+e lower wall +e upper wall

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Measured height (m) 145 125 105 085 065 045 025 005 145 125 105 085 065 045 025 005

4 Advances in Civil Engineering

dropped into the setup with 30 cm and a smooth surface ofthe ores would be obtained Next the surface of the ores wassurrounded by a little waste rock such that each ore granularwas stabilized Otherwise the ore granular in the surfacewould move randomly in the ore loading process therebyaffecting the experimental results Also the other incompactwaste rocks were dropped into the setup so no more ma-terials could be dropped into the experimental model Fi-nally the total internal space of setup was filled with theexperimental materials Additionally the internal frictionangle and friction angle between granular media and thedrawing-ore device were analyzed Meanwhile the totalmass and density of granular media were calculated once theore loading process was terminated Since the internal modelwas filled with the experimental materials the elastic ma-terial blocking the drawpoints was taken off and the ma-terials were then drawn from the drawpoints According tothe above scheme the corresponding drawpoints wereunfolded During the drawing process the flow speed ofgranular media should remain as constant as possible ratherthan fast Hence the single mass of the ore drawn from thedrawpoints was about 200 g each time and the values oflateral pressures and the number of drawing ore wererecorded +en the corresponding drawpoint was termi-nated once the waste rocks were drawn +e interval time of20minutes was employed to simulate the mining conditions+en the next corresponding drawpoints were unfolded andthe previous steps were repeated Consequently the varia-tion laws of lateral pressure could be received once the wasterock reached the last drawpoint

4 Experimental Results

41 4e Relationship between Lateral Pressure and Depth ofGranularMedia Figure 3 presents the relationship betweenthe lateral pressure and depth of granular media under thelimiting equilibrium state +e values of lateral pressureincreased exponentially with the increasing depth of gran-ular media and the growth rate of lateral pressure graduallydecreased as the depth of granular media increased +enthe porosity of granular media increased when the granulargrading increased However the unit weight decreased ac-cordingly Hence the values of lateral pressure showed anincreasing trend as the granular grading decreased for thesame depth of granular media Meanwhile the porosity ofgranular media decreased as the depth of granular mediaincreased and the value of lateral pressure among granulargrading increased with the increasing depth of granularmedia

42 Characteristic of Variation Laws for Lateral Pressure+e relationship between the number of drawing ore and thevalues of lateral pressure with different schemes are shown inFigures 4ndash12 respectively Due to the 20-minute intervaltime the process of drawing ore could be divided into twostages and IEZ induced by two drawing stage was inde-pendent [34] It was suggested that themeasured values from1 and 9 test channels decreased exponentially with anincreasing number of drawing ore in each drawing stage+en the lateral pressure of 2 3 and 10 test channels wasfirstly enhanced and then diminished as the number of

Table 3 Summary of laboratory schemes

Granular gradingStoping sequence

Interval faces From center to end From end to centerGroup 1 Scheme 1 Scheme 4 Scheme 7Group 2 Scheme 2 Scheme 5 Scheme 8Group 3 Scheme 3 Scheme 6 Scheme 9

Table 4 Summary of stoping sequence

Stoping sequence Summary

Interval face(1) Unfold the drawpoints of II and V (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and III (6) repeated the step of (2) and (3)

From center toend

(1) Unfold the drawpoints of II and III (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and V (6) repeated the step of (2) and (3)

From end tocenter

(1) Unfold the drawpoints of I and V (2) recorded the values of lateral pressure during the drawing process (3) blockedthe corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore device sit

for 20minutes (5) unfold the drawpoints of II and III (6) repeated the step of (2) and (3)

Table 5 Summary of granular grading

Granular grading Group 1 Group 2 Group 3+e mass percent () 246 386 368 246 386 368 246 386 368+e granular size (mm) lt2 2sim4 4sim6 lt3 3sim6 6sim9 lt4 4sim8 8sim12

Advances in Civil Engineering 5

Group 1Group 2Group 3

0

400

800

1200

1600

2000

2400

2800

e l

ater

al p

ress

ure (

Pa)

03 06 09 12 1500e depth of granular media

Figure 3 +e relationship between the lateral pressure and depth of granular media under the limiting equilibrium state

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(a)

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(b)

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(c)

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(d)

Figure 4 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 1

6 Advances in Civil Engineering

drawing ore increased in the two drawing stages Meanwhilethe lateral pressure of 8 and 16 test channels had a negativerelationship with the number of drawing ore +e values ofother test channels showed an increasing trend as thenumber of drawing ore rose

In the drawing process the scope of IEZ and isolatedmovement zone (IMZ) increased with an increase in numberfor drawing ore +en the granular media in the IMZ couldbe loosed and that above the IMZ slowly collimation movedand the internal friction angle gradually increased Hencethe lateral pressures were projected to continue decreasingwhile the test channels located in the scope of IMEMeanwhile because of the relatively small scale of IMZ andincrescent internal friction angle in the initial drawing phasethe measured values were augmented while the test channelsabove the scope of IMZ and then the lateral pressuredescended as the IMZ reached the testing range of testchannel Due to the descending surface of granular mediathe value of 8 and 16 test channels tended to gradual

decline As the nondilution ore drawing was used the heightof the IEZ and IMZ was about 30 cm and 738 cm re-spectively Hence the other values were expected to rise asthe test channels were higher than 738 cm

+e variation rates of lateral pressure under differentstoping sequences and granular gradings are exhibited inTable 6 A new standpoint was proposed that the distributionlaws could be divided into three parts One part was drawinginfluencing region which is located in the IMZ and had apositive relationship with the number of drawing ore +eother part was the upper descending zone which is locatedin the surface of granular media and the volume was equal tothe IEZ +e last part was central growth area which wasbetween the previous two parts +en the lateral pressurehad a positive relationship with the number of drawing orein the central growth area As the number of drawing oreincreased the scope of drawing influencing region andupper descending zone increased while the range of centralgrowth area decreased Moreover the reduction rate of

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

1800

1950

2100

2250

2400

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 5 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 2

Advances in Civil Engineering 7

e firstdrawing stage

e seconddrawing stage

1650

1800

1950

2100

2250

e lat

eral

pre

ssur

e (Pa

)

6 12 18 240e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1650

1800

1950

2100

2250

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 6 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 3

0 6 12 18 24 30e number of drawing ore

e firstdrawing stage e second

drawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e l

ater

al p

ress

ure (

Pa)

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

e firstdrawing stage

e seconddrawing stage

6 12 18 24 300e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 7 Continued

8 Advances in Civil Engineering

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

dropped into the setup with 30 cm and a smooth surface ofthe ores would be obtained Next the surface of the ores wassurrounded by a little waste rock such that each ore granularwas stabilized Otherwise the ore granular in the surfacewould move randomly in the ore loading process therebyaffecting the experimental results Also the other incompactwaste rocks were dropped into the setup so no more ma-terials could be dropped into the experimental model Fi-nally the total internal space of setup was filled with theexperimental materials Additionally the internal frictionangle and friction angle between granular media and thedrawing-ore device were analyzed Meanwhile the totalmass and density of granular media were calculated once theore loading process was terminated Since the internal modelwas filled with the experimental materials the elastic ma-terial blocking the drawpoints was taken off and the ma-terials were then drawn from the drawpoints According tothe above scheme the corresponding drawpoints wereunfolded During the drawing process the flow speed ofgranular media should remain as constant as possible ratherthan fast Hence the single mass of the ore drawn from thedrawpoints was about 200 g each time and the values oflateral pressures and the number of drawing ore wererecorded +en the corresponding drawpoint was termi-nated once the waste rocks were drawn +e interval time of20minutes was employed to simulate the mining conditions+en the next corresponding drawpoints were unfolded andthe previous steps were repeated Consequently the varia-tion laws of lateral pressure could be received once the wasterock reached the last drawpoint

4 Experimental Results

41 4e Relationship between Lateral Pressure and Depth ofGranularMedia Figure 3 presents the relationship betweenthe lateral pressure and depth of granular media under thelimiting equilibrium state +e values of lateral pressureincreased exponentially with the increasing depth of gran-ular media and the growth rate of lateral pressure graduallydecreased as the depth of granular media increased +enthe porosity of granular media increased when the granulargrading increased However the unit weight decreased ac-cordingly Hence the values of lateral pressure showed anincreasing trend as the granular grading decreased for thesame depth of granular media Meanwhile the porosity ofgranular media decreased as the depth of granular mediaincreased and the value of lateral pressure among granulargrading increased with the increasing depth of granularmedia

42 Characteristic of Variation Laws for Lateral Pressure+e relationship between the number of drawing ore and thevalues of lateral pressure with different schemes are shown inFigures 4ndash12 respectively Due to the 20-minute intervaltime the process of drawing ore could be divided into twostages and IEZ induced by two drawing stage was inde-pendent [34] It was suggested that themeasured values from1 and 9 test channels decreased exponentially with anincreasing number of drawing ore in each drawing stage+en the lateral pressure of 2 3 and 10 test channels wasfirstly enhanced and then diminished as the number of

Table 3 Summary of laboratory schemes

Granular gradingStoping sequence

Interval faces From center to end From end to centerGroup 1 Scheme 1 Scheme 4 Scheme 7Group 2 Scheme 2 Scheme 5 Scheme 8Group 3 Scheme 3 Scheme 6 Scheme 9

Table 4 Summary of stoping sequence

Stoping sequence Summary

Interval face(1) Unfold the drawpoints of II and V (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and III (6) repeated the step of (2) and (3)

From center toend

(1) Unfold the drawpoints of II and III (2) recorded the values of lateral pressure during the drawing process (3)blocked the corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore

device sit for 20minutes (5) unfold the drawpoints of I and V (6) repeated the step of (2) and (3)

From end tocenter

(1) Unfold the drawpoints of I and V (2) recorded the values of lateral pressure during the drawing process (3) blockedthe corresponding drawpoint once the waste rocks were drawn from the drawpoint (4) let the drawing-ore device sit

for 20minutes (5) unfold the drawpoints of II and III (6) repeated the step of (2) and (3)

Table 5 Summary of granular grading

Granular grading Group 1 Group 2 Group 3+e mass percent () 246 386 368 246 386 368 246 386 368+e granular size (mm) lt2 2sim4 4sim6 lt3 3sim6 6sim9 lt4 4sim8 8sim12

Advances in Civil Engineering 5

Group 1Group 2Group 3

0

400

800

1200

1600

2000

2400

2800

e l

ater

al p

ress

ure (

Pa)

03 06 09 12 1500e depth of granular media

Figure 3 +e relationship between the lateral pressure and depth of granular media under the limiting equilibrium state

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(a)

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(b)

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(c)

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(d)

Figure 4 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 1

6 Advances in Civil Engineering

drawing ore increased in the two drawing stages Meanwhilethe lateral pressure of 8 and 16 test channels had a negativerelationship with the number of drawing ore +e values ofother test channels showed an increasing trend as thenumber of drawing ore rose

In the drawing process the scope of IEZ and isolatedmovement zone (IMZ) increased with an increase in numberfor drawing ore +en the granular media in the IMZ couldbe loosed and that above the IMZ slowly collimation movedand the internal friction angle gradually increased Hencethe lateral pressures were projected to continue decreasingwhile the test channels located in the scope of IMEMeanwhile because of the relatively small scale of IMZ andincrescent internal friction angle in the initial drawing phasethe measured values were augmented while the test channelsabove the scope of IMZ and then the lateral pressuredescended as the IMZ reached the testing range of testchannel Due to the descending surface of granular mediathe value of 8 and 16 test channels tended to gradual

decline As the nondilution ore drawing was used the heightof the IEZ and IMZ was about 30 cm and 738 cm re-spectively Hence the other values were expected to rise asthe test channels were higher than 738 cm

+e variation rates of lateral pressure under differentstoping sequences and granular gradings are exhibited inTable 6 A new standpoint was proposed that the distributionlaws could be divided into three parts One part was drawinginfluencing region which is located in the IMZ and had apositive relationship with the number of drawing ore +eother part was the upper descending zone which is locatedin the surface of granular media and the volume was equal tothe IEZ +e last part was central growth area which wasbetween the previous two parts +en the lateral pressurehad a positive relationship with the number of drawing orein the central growth area As the number of drawing oreincreased the scope of drawing influencing region andupper descending zone increased while the range of centralgrowth area decreased Moreover the reduction rate of

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

1800

1950

2100

2250

2400

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 5 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 2

Advances in Civil Engineering 7

e firstdrawing stage

e seconddrawing stage

1650

1800

1950

2100

2250

e lat

eral

pre

ssur

e (Pa

)

6 12 18 240e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1650

1800

1950

2100

2250

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 6 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 3

0 6 12 18 24 30e number of drawing ore

e firstdrawing stage e second

drawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e l

ater

al p

ress

ure (

Pa)

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

e firstdrawing stage

e seconddrawing stage

6 12 18 24 300e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 7 Continued

8 Advances in Civil Engineering

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

Group 1Group 2Group 3

0

400

800

1200

1600

2000

2400

2800

e l

ater

al p

ress

ure (

Pa)

03 06 09 12 1500e depth of granular media

Figure 3 +e relationship between the lateral pressure and depth of granular media under the limiting equilibrium state

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(a)

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(b)

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

2000

2250

2500

2750

8 16 24 320e number of drawing ore

(c)

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

440

880

1320

1760

2200

8 16 24 320e number of drawing ore

(d)

Figure 4 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 1

6 Advances in Civil Engineering

drawing ore increased in the two drawing stages Meanwhilethe lateral pressure of 8 and 16 test channels had a negativerelationship with the number of drawing ore +e values ofother test channels showed an increasing trend as thenumber of drawing ore rose

In the drawing process the scope of IEZ and isolatedmovement zone (IMZ) increased with an increase in numberfor drawing ore +en the granular media in the IMZ couldbe loosed and that above the IMZ slowly collimation movedand the internal friction angle gradually increased Hencethe lateral pressures were projected to continue decreasingwhile the test channels located in the scope of IMEMeanwhile because of the relatively small scale of IMZ andincrescent internal friction angle in the initial drawing phasethe measured values were augmented while the test channelsabove the scope of IMZ and then the lateral pressuredescended as the IMZ reached the testing range of testchannel Due to the descending surface of granular mediathe value of 8 and 16 test channels tended to gradual

decline As the nondilution ore drawing was used the heightof the IEZ and IMZ was about 30 cm and 738 cm re-spectively Hence the other values were expected to rise asthe test channels were higher than 738 cm

+e variation rates of lateral pressure under differentstoping sequences and granular gradings are exhibited inTable 6 A new standpoint was proposed that the distributionlaws could be divided into three parts One part was drawinginfluencing region which is located in the IMZ and had apositive relationship with the number of drawing ore +eother part was the upper descending zone which is locatedin the surface of granular media and the volume was equal tothe IEZ +e last part was central growth area which wasbetween the previous two parts +en the lateral pressurehad a positive relationship with the number of drawing orein the central growth area As the number of drawing oreincreased the scope of drawing influencing region andupper descending zone increased while the range of centralgrowth area decreased Moreover the reduction rate of

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

1800

1950

2100

2250

2400

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 5 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 2

Advances in Civil Engineering 7

e firstdrawing stage

e seconddrawing stage

1650

1800

1950

2100

2250

e lat

eral

pre

ssur

e (Pa

)

6 12 18 240e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1650

1800

1950

2100

2250

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 6 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 3

0 6 12 18 24 30e number of drawing ore

e firstdrawing stage e second

drawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e l

ater

al p

ress

ure (

Pa)

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

e firstdrawing stage

e seconddrawing stage

6 12 18 24 300e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 7 Continued

8 Advances in Civil Engineering

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

drawing ore increased in the two drawing stages Meanwhilethe lateral pressure of 8 and 16 test channels had a negativerelationship with the number of drawing ore +e values ofother test channels showed an increasing trend as thenumber of drawing ore rose

In the drawing process the scope of IEZ and isolatedmovement zone (IMZ) increased with an increase in numberfor drawing ore +en the granular media in the IMZ couldbe loosed and that above the IMZ slowly collimation movedand the internal friction angle gradually increased Hencethe lateral pressures were projected to continue decreasingwhile the test channels located in the scope of IMEMeanwhile because of the relatively small scale of IMZ andincrescent internal friction angle in the initial drawing phasethe measured values were augmented while the test channelsabove the scope of IMZ and then the lateral pressuredescended as the IMZ reached the testing range of testchannel Due to the descending surface of granular mediathe value of 8 and 16 test channels tended to gradual

decline As the nondilution ore drawing was used the heightof the IEZ and IMZ was about 30 cm and 738 cm re-spectively Hence the other values were expected to rise asthe test channels were higher than 738 cm

+e variation rates of lateral pressure under differentstoping sequences and granular gradings are exhibited inTable 6 A new standpoint was proposed that the distributionlaws could be divided into three parts One part was drawinginfluencing region which is located in the IMZ and had apositive relationship with the number of drawing ore +eother part was the upper descending zone which is locatedin the surface of granular media and the volume was equal tothe IEZ +e last part was central growth area which wasbetween the previous two parts +en the lateral pressurehad a positive relationship with the number of drawing orein the central growth area As the number of drawing oreincreased the scope of drawing influencing region andupper descending zone increased while the range of centralgrowth area decreased Moreover the reduction rate of

e seconddrawing stage

e firstdrawing stage

e l

ater

al p

ress

ure (

Pa)

1800

1950

2100

2250

2400

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e l

ater

al p

ress

ure (

Pa)

e seconddrawing stage

e firstdrawing stage

0

475

950

1425

1900

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 5 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 2

Advances in Civil Engineering 7

e firstdrawing stage

e seconddrawing stage

1650

1800

1950

2100

2250

e lat

eral

pre

ssur

e (Pa

)

6 12 18 240e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1650

1800

1950

2100

2250

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 6 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 3

0 6 12 18 24 30e number of drawing ore

e firstdrawing stage e second

drawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e l

ater

al p

ress

ure (

Pa)

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

e firstdrawing stage

e seconddrawing stage

6 12 18 24 300e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 7 Continued

8 Advances in Civil Engineering

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

e firstdrawing stage

e seconddrawing stage

1650

1800

1950

2100

2250

e lat

eral

pre

ssur

e (Pa

)

6 12 18 240e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1650

1800

1950

2100

2250

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

6 12 18 240e number of drawing ore

e firstdrawing stage

e seconddrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 6 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 3

0 6 12 18 24 30e number of drawing ore

e firstdrawing stage e second

drawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e l

ater

al p

ress

ure (

Pa)

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

e firstdrawing stage

e seconddrawing stage

6 12 18 24 300e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 7 Continued

8 Advances in Civil Engineering

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

e firstdrawing stage

e seconddrawing stage

2100

2200

2300

2400

2500

2600

2700

2800

e lat

eral

pre

ssur

e (Pa

)

6 12 18 24 300e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e firstdrawing stage

e seconddrawing stage

0

525

1050

1575

2100

e l

ater

al p

ress

ure (

Pa)

6 12 18 24 300e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 7 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 4

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

450

900

1350

1800

e lat

eral

pre

ssur

e (Pa

)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

1820

1950

2080

2210

2340

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

0

450

900

1350

1800

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

e seconddrawing stage

e firstdrawing stage

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 8 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 5

Advances in Civil Engineering 9

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1600

1800

2000

2200

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drwing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 9 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 6

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

Figure 10 Continued

10 Advances in Civil Engineering

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

e seconddrawing stage

e firstdrawing stage

2000

2200

2400

2600

2800

e lat

eral

pre

ssur

e (Pa

)

8 16 24 320e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

500

1000

1500

2000

e l

ater

al p

ress

ure (

Pa)

8 16 24 320e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 10 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 7

e seconddrawing stage

e firstdrawing stage

1800

1950

2100

2250

2400

2550

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1800

2000

2200

2400

2600

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

380

760

1140

1520

1900

e l

ater

al p

ress

ure (

Pa)

7 14 21 280e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 11 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 8

Advances in Civil Engineering 11

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

lateral pressure showed a declining tendency as the height ofgranular media grew in the drawing influence region

In the case of an invariable mining scheme and the samenumber of drawing ore more reduction ratios and the scopefor drawing influencing region could be appeared in the lowerwall Once the height and mass of the IEZ were identified thescope of the drawing influencing region and the upperdescending zone could be obtained and used to predict therange for the surface subsidence Additionally it was foundthat the stoping sequence and the granular grading both had aprimary influence on the value of lateral pressure

43 4e Relationship between Lateral Pressure and StopingSequence To convenient obtain the influencing effect ofstoping sequences the schemes were divided into threegroups (group 1 scheme 1 scheme 2 and scheme 3 group 2scheme 4 scheme 5 and scheme 6 and group 3 scheme 7scheme 8 and scheme 9) +e different stoping sequenceswould cause the changing of the granular grading after thefirst stage of drawing ore Hence the first stage of drawing

ore in the same group was selected for studying the variationlaws of lateral pressure influenced by stoping sequence so asto reduce the impact of granular grading and the reductionrates of lateral pressure in the first stage for drawing ore areshown in Table 7 It could be noted that the scope of the threeparts was unaffected by the stoping sequence whereas thestoping sequence had an impact on the drawn mass at thesame height of IEZ

Meanwhile the stoping sequence had a remarkableinfluence on the reduction rates of lateral pressure in thedrawing influencing region For the same granulargrading and height of IEZ more reduction rates of lateralpressure were observed with a decrease in the space be-tween the drawpoints For these three different stopingsequences (scheme 1 scheme 4 and scheme 7) with thesame granular grading and height of IEZ (30 cm) thereductive rates of 1 and 9 test channels were 477 and356 675 and 510 and 289 and 259 respec-tively whereas the scope of drawing influencing regionkept stable

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e lat

eral

pre

ssur

e (Pa

)

5 10 15 20 250e number of drawing ore

1 (h = 145m) 2 (h = 125m)

3 (h = 105m)4 (h = 085m)

(a)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

5 (h = 065m)6 (h = 045m)

7 (h = 025m)8 (h = 005m)

(b)

e seconddrawing stage

e firstdrawing stage

1540

1680

1820

1960

2100

2240

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

9 (h = 145m) 10 (h = 125m)

11 (h = 105m)12 (h = 085m)

(c)

e seconddrawing stage

e firstdrawing stage

0

400

800

1200

1600

e l

ater

al p

ress

ure (

Pa)

5 10 15 20 250e number of drawing ore

13 (h = 065m)14 (h = 045m)

15 (h = 025m)16 (h = 005m)

(d)

Figure 12 +e relationship between the number of drawing ore and the values of lateral pressure with scheme 9

12 Advances in Civil Engineering

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

44 4e Relationship between Lateral Pressure and GranularGrading To obtain the effect of granular grading the dif-ferent mining schemes were divided into three groups(group 1 scheme 1 scheme 4 and scheme 7 group 2scheme 2 scheme 5 and scheme 8 group 3 scheme 3scheme 6 and scheme 9) and the relationships between thegranular grading and lateral pressure of reduction rates andaverage values are shown in Table 8 With an increase in thegranular grading the scope of the drawing influencing re-gion had no significant decrease whereas the mass drawnfrom the drawpoints decreased Additionally it was foundthat the granular grading had a primary influence on thevariation rate of lateral pressure in which the reduction rateand reductive ratio in the drawing influencing region wereinconsistent with each other in same stoping sequence andthe reduction rate had a negative relationship with thegranular grading With the same stoping sequence andheight of IEZ the average values of lateral pressure increasedas the granular grading decreased at the same height ofgranular media Because of the more mobility and unitweight of granular media which were generated from themore uniform and smaller size of the granular the morereductive rate and average values of lateral pressure wereobtained For three granular gradings (scheme 4 scheme 5

and scheme 6) with the height of IEZ of 30 cm and the samestoping sequence the reduction rates of 1 and 9 testchannels were 1087 and 865 939 and 700 and770 and 564 respectively and the average values of thelower wall and upper wall were 1696 Pa and 1720 Pa 1428 Paand 1452 Pa and 1336 Pa and 1348 Pa respectively

5 Discussion

In this study the stoping sequence and granular gradingwere chosen as the main influencing factors on the distri-bution laws of lateral pressure induced by nonpillar sublevelcaving mining For calculating the lateral pressure itssuccess mainly depended on the stoping sequence granulargrading the properties of granular media and structuralparameters For instance in terms of the layout of thesublevel parameters used in this test the bigger the height ofsublevel was the bigger the shape of IEZ at the same stopingsequence and granular grading and therefore bigger rangeof drawing influencing region and reductive rate of lateralpressure that would correspondingly be appeared

Research on the variation laws of lateral pressure playedan important role in predicting the scope of surface sub-sidence for theoretical and practical guidance in mine

Table 6 +e variation rates of lateral pressure under different stoping sequences and granular gradings

Test channelVariation rates of lateral pressure ()

Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 Scheme 7 Scheme 8 Scheme 91 h 145m minus 989 minus 846 minus 670 minus 1087 minus 939 minus 770 minus 926 minus 769 minus 6602 h 125m minus 707 minus 557 minus 471 minus 783 minus 650 minus 540 minus 619 minus 520 minus 4403 h 105m minus 294 minus 175 minus 163 minus 343 minus 283 minus 162 minus 277 minus 191 minus 1604 h 085m 320 285 217 176 213 428 294 254 3325 h 065m 275 219 201 317 157 196 269 223 2146 h 045m 212 227 204 315 177 106 251 243 2187 h 025m 322 243 231 383 365 145 273 254 2498 h 005m minus 639 minus 434 minus 561 minus 577 minus 441 minus 428 minus 593 minus 624 minus 5059 h 145m minus 764 minus 618 minus 503 minus 865 minus 700 minus 564 minus 675 minus 549 minus 50010 h 125m minus 531 minus 426 minus 380 minus 674 minus 511 minus 417 minus 495 minus 409 minus 35811 h 105m 149 210 085 173 139 117 178 153 13012 h 085m 241 201 105 201 162 129 234 156 20913 h 065m 176 149 129 133 126 126 179 158 14914 h 045m 362 328 307 395 347 348 363 349 28815 h 025m 208 201 229 310 288 241 266 249 20316 h 005m minus 349 minus 247 minus 39 minus 40 minus 397 minus 316 minus 620 minus 678 minus 640

Table 7 +e reduction rates of lateral pressure in the first stage for drawing ore

Group Scheme+e variation rates of lateral pressure ()

1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m

11 minus 477 minus 394 minus 132 minus 356 minus 3124 minus 675 minus 472 minus 237 minus 510 minus 3817 minus 289 minus 215 minus 084 minus 259 minus 182

22 minus 389 minus 314 minus 103 minus 321 minus 2525 minus 612 minus 404 minus 216 minus 416 minus 3558 minus 282 minus 210 minus 080 minus 234 minus 142

33 minus 295 minus 255 minus 086 minus 261 minus 2026 minus 458 minus 318 minus 108 minus 312 minus 2579 minus 267 minus 159 minus 074 minus 230 minus 144

Advances in Civil Engineering 13

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

production +e main characteristics of the reductive rateand the variation laws for lateral pressure could be refer-enced to propose a method for predicting the failure con-dition of rock mass as well as deeply analyzing themechanisms of rock movement and determining the stopingparameters For instance Li et al tried to predict the range ofsurface subsidence induced by the nonpillar sublevel cavingmining [5] +e distribution laws of lateral pressure were thefoundation of constructing a correct predicting calculationsince the laws intensively reflected the stress characteristicsof rock mass in the caved rock zone

In this study a new standpoint was proposed that thedistribution laws could be divided into three parts and thenthe lateral pressure increased exponentially with increasingdepth of granular media Ren et al [35] and He et al [36]reported the distribution laws of lateral pressure from dif-ferent orebody dip conditions which seemed consistent withthe scope of drawing influencing region but to a certainextent had its variation on the upper descending zone andthe central growth area +ese abovementioned results areunder the invariable width of orebody and the vibration ofblasting is not considered further studies are essential toimprove this simple description to the more comprehensiveresults of complex gravity flow encountered in actual minesIn addition certain parameters such as the width and dip oforebody the size of drawpoint the properties of granularmedia and the shape of wall side could be considered andstudied using a 3D physical model or in situ experiments

6 Conclusions

In this study a laboratory-scaled physical model wasdesigned to investigate the influence of stoping sequence andgranular grading on the lateral pressure during the drawingprocess Under the limiting equilibrium state the values oflateral pressure increased exponentially with the increasingdepth of granular media and the growth rate of lateralpressure gradually decreased as the depth of granular mediaincreased Meanwhile the experimental results showed thatthe distribution laws of lateral pressure were divided intothree parts including the drawing influencing region theupper descending zone and the central growth area +eshape of three parts was virtually identified under differentstoping sequences and granular gradings In addition the

mass drawn or the height of the IEZ could increase the scopeof drawing influencing region and upper descending zoneand could reduce the range of the central growth area Forthe same height of IEZ more reduction ratio and the scopefor drawing influencing region could be appeared in thelower wall +en the influencing laws of granular gradingand stoping sequence on the reduction rates of drawinginfluencing region complemented each other +e reductionrates in the drawing influencing region showed an increasingtrend as the interval of drawpoint and granular gradingdecreased and the scope of these parts was negligibly af-fected by the stoping sequence and granular gradingMoreover the average values of lateral pressure increasedwith a decrease in the size of granular media as the height ofthe IEZ and stoping sequence remain constant

+e experimental results could help to understand thedistribution laws of lateral pressure under stoping sequenceand granular grading and provided an experimental tool topredict the range of surface subsidence

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the Key Program of the NationalNatural Science Foundation of China (no 51534003) theNational Basic Research Program of China (no2016YFC0801601) and the Fundamental Research Funds forthe Central Universities (no N150104006)

References

[1] H Liu P Peng and LWang ldquoComprehensive evaluation andsimulation for large-scale mining using natural cavingmethodrdquo Journal of Central South University vol 46 no 2pp 617ndash624 2015

[2] A Jin H Sun G Ma Y Gao S Wu and X Meng ldquoA studyon the draw laws of caved ore and rock using the discrete

Table 8 +e relationship between the granular grading and lateral pressure of reduction rates and average values

Group Scheme+e variation rates of lateral pressure () +e average values of lateral

pressure (Pa)1 h 145m 2 h 125m 3 h 105m 9 h 145m 10 h 125m +e lower wall +e upper wall

11 minus 989 minus 707 minus 294 minus 764 minus 531 1638 16622 minus 846 minus 557 minus 175 minus 618 minus 426 1482 15003 minus 670 minus 471 minus 163 minus 503 minus 380 1360 1368

24 minus 1087 minus 783 minus 343 minus 865 minus 674 1696 17205 minus 939 minus 650 minus 283 minus 700 minus 511 1428 14526 minus 770 minus 540 minus 162 minus 564 minus 417 1336 1348

37 minus 926 minus 619 minus 277 minus 675 minus 495 1682 19628 minus 769 minus 520 minus 191 minus 549 minus 409 1542 15589 minus 660 minus 440 minus 160 minus 500 minus 358 1330 1338

14 Advances in Civil Engineering

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15

element methodrdquo Computers and Geotechnics vol 80pp 59ndash70 2016

[3] L C Li C A Tang X D Zhao and M Cai ldquoBlock caving-induced strata movement and associated surface subsidence anumerical study based on a demonstration modelrdquo Bulletin ofEngineering Geology and the Environment vol 73 no 4pp 1165ndash1182 2014

[4] Y Wang Technologies for Coordinated Mining of Open-Pitand Underground Mining at Southeastern of GongchanglingIron Mine Northeastern University Shenyang China 2013in Chinese

[5] H Y Li F Y Ren X Y Chen and G H Gong ldquo+e methodfor predicting and controlling the range of surface subsidenceduring deep ore-body miningrdquo Journal of NortheasternUniversity (Natural Science) vol 33 no 11 pp 1624ndash16272012 in Chinese

[6] D L Song F Y Ren J D Qi and M L Dou ldquoDelineationoptimization of incline shaft safety pillar for North miningarea of Xishimen ironrdquo Metal Mine vol 45 no 4 pp 13ndash152016 in Chinese

[7] E T Brown and G A Ferguson ldquoProgressive hanging wallcaving Gathrsquos mine Rhodesiardquo Trans Inst MinMetall vol 88pp A92ndashA105 1979

[8] J R Jahanson ldquo+e use of flow-corrective inserts in binsrdquoJournal of Engineering for Industry vol 88 no 2 pp 224ndash2301966

[9] A W Jenike Storage and Flow of Solids Bulletin of the UtahEngineering Experiment 1980

[10] D M Walker ldquoAn approximate theory for pressures andarching in hoppersrdquo Chemical Engineering Science vol 21no 11 pp 975ndash997 1966

[11] J K Walters ldquoA theoretical analysis of stresses in silos withvertical wallsrdquo Chemical Engineering Science vol 28 no 1pp 13ndash21 1973

[12] P Karasudhi Foundations of Solid Mechanics Kluwer Aca-demic Publishers Dordrecht Netherlands 1965

[13] M Sperl ldquoExperiments on corn pressure in silo cells -translation and comment of Janssenrsquos paper from 1895rdquoGranular Matter vol 8 no 2 pp 59ndash65 2006

[14] M Reimbert and A Reimbert ldquoPressure and overpressurevertical and horizontal silosrdquo in Proceedings of the Interna-tional Conference Design of Silos for Strength and FlowPowder Advisory Cent London England UK 1980

[15] M Ichihara and H Matsuzawa ldquoEarth pressure duringearthquakerdquo Soils and Foundations vol 13 no 4 pp 75ndash861973

[16] W Airy ldquo+e pressure of grainrdquo Minutes of ProceedingsInstitution of Civil Engineers vol 13 no 1 pp 347ndash358 1987

[17] X S Chen ldquoExtension of classical Janssen loose mass pressuretheory and its application in mining engineeringrdquo ChineseJournal of Geotechnical Engineering vol 32 no 2 pp 315ndash319 2010 in Chinese

[18] D Li Study of Lateral Pressure Mechanism between Granularand Bin of Heavy Vehicle Tianjin University Tianjing China2014 in Chinese

[19] A W Jenike ldquoA theory of flow of particulate solids inconverging and diverging channels based on a conical yieldfunctionrdquo Powder Technology vol 50 no 3 pp 229ndash2361987

[20] C J Brown E H Lahlouh and J M Rotter ldquoExperiments ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[21] L Yang F Y Ren R X He and J L Cao ldquoPrediction ofsurface subsidence range based on the critical medium

columnrsquos theory under ore drawingrdquo Journal of NortheasternUniversity (Natural Science) vol 39 no 3 pp 416ndash420 2018in Chinese

[22] P Vidal A Couto F Ayuga and M Guaita ldquoInfluence ofHopper eccentricity on discharge of cylindrical mass flow siloswith rigid wallsrdquo Journal of Engineering Mechanics vol 132no 9 pp 1026ndash1033 2006

[23] M Guaita A Couto and F Ayuga ldquoNumerical simulation ofwall pressure during discharge of granular material fromcylindrical silos with eccentric hoppersrdquo Biosystems Engi-neering vol 85 no 1 pp 101ndash109 2003

[24] M H Sadd G Adhikari and F Cardoso ldquoDEM simulation ofwave propagation in granular materialsrdquo Powder Technologyvol 109 no 1ndash3 pp 222ndash233 2000

[25] W C Paul ldquoDEM simulation of industrial particle flows casestudies of dragline excavators mixing in tumblers and cen-trifugal millsrdquo Powder Technology vol 109 no 1 pp 83ndash1042000

[26] S Bock and S Prusek ldquoNumerical study of pressure on damsin a backfilled mining shaft based on PFC3D coderdquo Com-puters and Geotechnics vol 66 pp 230ndash244 2015

[27] H M Zhen X W Wang and Z J Yang ldquoDistinct elementsimulation on lateral pressure during coal discharging processof coal silo based on PFC3Drdquo Coal Engineering vol S1pp 123ndash125 2013 in Chinese

[28] J B Fu Limit Analysis and Elastio-Plastic Finite ElementAnalysis of Lateral Pressure of Large Silo under ComplicatedConditions Dalian University of Technology Dalian China2013 in Chinese

[29] K V Kuzmin and A V Baranov ldquoPrinciples of research ofmining method of uncontrolled ore caving by physical sim-ulationrdquo Radio Science vol 31 no 2 pp 245ndash261 2009

[30] F Melo F Vivanco and C Fuentes ldquoCalculated isolatedextracted andmovement zones compared to scaledmodels forblock cavingrdquo International Journal of Rock Mechanics andMining Sciences vol 46 no 4 pp 731ndash737 2009

[31] R Castro R Trueman and A Halim ldquoA study of isolateddraw zones in block caving mines by means of a large 3Dphysical modelrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 6 pp 860ndash870 2007

[32] X Zhang G Tao and Z Zhu ldquoLaboratory study of the in-fluence of dip and ore width on gravity flow during longi-tudinal sublevel cavingrdquo International Journal of RockMechanics and Mining Sciences vol 103 pp 179ndash185 2018

[33] C Zhang and S Tu ldquoControl technology of direct passingkarstic collapse pillar in longwall top-coal caving miningrdquoNatural Hazards vol 84 no 1 pp 1ndash18 2016

[34] F Melo F Vivanco C Fuentes and V Apablaza ldquoOndrawbody shapes from Bergmark-Roos to kinematicmodelsrdquo International Journal of Rock Mechanics and MiningSciences vol 44 no 1 pp 77ndash86 2007

[35] F Y Ren L Yang J L Cao et al ldquoPrediction of the caved rockzonesrsquo scope induced by caving mining methodrdquo PLoS Onevol 13 no 8 Article ID e0202221 2018

[36] R X He F Y Ren B H Tan and Y Liu ldquoDistribution law ofgranular lateral pressure in caved ore-rock with limitedwidthrdquo Journal of Northeastern University (Natural Science)vol 40 no 3 pp 108ndash112 2019 in Chinese

Advances in Civil Engineering 15