analytic methods of sinkhole prognosis.pdf

8/11/2019 Analytic methods of sinkhole prognosis.pdf

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7. ALTBERGBAU - KOLLOQUIUM Freiberg 2007

Analytic and numerical methods of sinkhole prognosis.

Krzysztof Tajdu, Anton Sroka

TU Bergakademie Freiberg & IMG PAN, TU Bergakademie Freiberg

ABSTRACT:

Changes in stress around mining excavations can result in changes in the behaviour of therock mass which in turn may lead to damage, failure and collapse of rock mass. Itsleading to create a sinkholes on the surface. The primary objective of the following paperis to present a old and new methods of predicting the sinkholes. The authors present themethods of determine the sinkholes made by shallow underground excavations and theexcavations in fault region. There were made some calculations based on FEM and FDM.

Introduction

Mining excavations cause changes in natural environment. The result of this activity displays as

rock mass movements, causing surface deformation, changes in water conditions and many other

disadvantageous effects. One of the most extraordinarily harmful phenomena, which can appear on

a surface, are sinkholes. This phenomenon can eliminate the land from economic use or stronglydecrease its value. In the subject of mining damages the term sinkholes should be understood as a

brake of surface continuous or very high intensity of local ground movements caused by

underground mining excavations. Commonly the phenomenon of the influence of underground

mining excavations are strictly connected with natural process in rock mass (e.g. mechanical

suffusion), nevertheless exploitation is a primary cause and the suffusion is a secondary cause of

sinkhole deformations.

There can be the following reasons for arising sinkholes (Arkuszewski, 1978):

a. Movements of rock mass caused by shallow excavations,

b. Movements of rock mass caused by excavations near a fault,

c. Reactivations of old goaf,d. Activations of a shaft,

e. The fire in remains seam ling at a small depth,

f. Overlapping excavation edges in a few seams.

The size and range of sinkholes deformations are determined by: depth of excavation, geological

structure, rock mass properties, character of strata, size of underground excavations (specially

width), material of filling the void, number of excavations in different seams, excavations in watery

zone, excavations near the faults which are the cause of open cracks (Saustowicz, 1968). Thecomplex analysis about a reason and effect of creating sinkholes on a surface was presented in the

work of Szwedzicki (1999a, 1999b, 2001, 2003), Grn (1995), Chudek (1980).

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In the above-mentioned paper the authors deal with the problem of arising the sinkholes on a

surface, created by rock mass movements near the shallow excavations (a), and rock mass

movements caused by excavations near a fault (b).

Sinkholes in a region of shallow mining excavations

The main condition of the appearance of sinkholes on a surface are the following: collapses of rock

mass roof into a void and creating a caving zone or a fracture zone (or both), which reaches surface

layers (Szwedzicki, 2003). The caving zone (hz) arises when above the excavation there has

appeared a pressure arch, inside which rock has crushed and collapsed into a void (Fig.1).

Alongside with the increase of excavations volume, the caving zone increases till the moment when

the cracked rock mass pieces fill the void. In situations when the height of the carving zone is

higher than the depth of excavation, the sinkholes will arise on the surface in such forms as surface

collapse or sink funnel (Fig. 2a). In the opposite situations, i.e. when thickness of hard rock mass is

higher than high of caving zone, it means that the fracture zone (hs) will arise above it. The fracture

zone is distinguishing by a very strong fracture, leading to the separate rock mass to the block and

very small rotation of the fracture rock pieces (Fig.1). If the thickness of hard rock mass is smallerthan the height of the fracture zone, then on the surface sinkholes will appear in forms of open

cracks (Fig. 2b) and the surface layers will collapse into rock mass. In the case then the heights of

the carving and fracture zone are smaller than the thickness of rock mass, then on the surface

sinkholes will not appears. The zone between fracture zone and the surface is called the bedding

zone and it is distinguished by bedding of the strata and small fracture.

a) sink funnel

b) open cracks

Fig. 1 Caving, fracture and bedding zone created abovemining face excavations(Mazurkiewicz, Tajduet al.,

1993)

Fig .2 Examples of sinkholes(Ryncarz, 1992)

Analytical methods

The basic factors of determining the area of sinkholes are the following: depth of the seam (H), rock

mass thickness (hn), mechanical parameters of rock mass, seam thickness (g), time of void

existence (t) and others factors which can activate rock mass movements (shift, pits, rock burst,

layers of quicksand). Some of these factors were taken into consideration by the scientists to

determine the height of caving zone (hz).

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Table 1 presents some example equations applied in order to determine the height of caving zone.

Tab.1 : Example equals on high of caving zoneName Equals

Ritter(1879) c

Lhz

16

2

= or

2

2452

8

+=

gctgL

chz

Kommerel(1912)

d

zk

zh =100

Bierbaumer(1913)

For weak rocks

L= ctghz

2

For strong rocks

+

=

2452

245

1

2

tggL

tgtgH

Hhz

Protodiakonow(1930)

For weak rocks

tg

Lhz

2

=

For strong rocks

2

Lhz =

Cymbariewicz(1933)

For granular-cohesiverocks

tg

gctgL

hz2

2452

++

=

For strong rocks

)2

45(2

+=

tggL

hz

Segal(1934)

gLhz =

4

21

Slesariew(1940)

For the weak rocks

=

245

4

2

ctgH

Lhz

For the strong rocks

r

zR

Lh=

16

2

Pokrowski(1948) ( )12

3

=

r

zk

gh

Cytowicz(1951)

2

2452

++

=

tggL

hz

Saustowicz(1968)

22

)1(25,0

2

222gL

p

Rmm

gh

z

r

z

++

=

Ruppeneit(1954)

+

= 1sin2

sin1exp1sin1

2

2

r

zR

HLh

Mohr(1954) ( )

=

12

Lh

z

Gmoszyski(1960)

+

=

2

451

ln5,0

2

tgtg

c

HL

hz

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Example equals on high of caving zone

Orow(1961)

++

=2

4528,0 3 ctggLH

hz

Borisow(1962) ( ) 22 112

7,1

r

rz

RH

RLh

=

Jeranow(1962)

+

=

2452

4

21

tggLh

z

Szirokow(1969)

+

=K

c

c

zK

tggR

HKL

h2

4515,0

Szirokow

(1973)

gghz =

22L5,0

assuming that: 12 c

RH

Jarosz(1977)

+

+=

2

1

1

1

4

3

r

rz

k

kgh

Arkuszewski(1978)

+=

)1(2

)1()1(4

r

rr

zk

kkgh

Labels:

L-width of excavation, H-excavation depth, z - sagging of the lowest uncaved strata, -bulk density, -

friction angle, -Protodiakonows coefficient of rock compact, kd- coefficient of loosen (in %), c- Ritters

coefficient of rock compact,g-excavation thickness, Rr, Rc uniaxial tensile and compressive strength of

rock mass, - Poissons ratio, KC- coefficient of stress compressive concentrations , KK- coefficient of

strength decrease, kr- coefficient of loosen rock, m=1/v,pz- vertical pressure.

As a result of works on the subject of weakness zone creating above the mining excavations, some

equations for the height of fracture zone (hs) had been determined (Saustowicz, 1968; Gajoch andPiechota, 1973; Jarosz, 1977; Arkuszewski, 1978; Kendorski, Roosendaal and Bai, 1995; Das,

2000; Heasley, 2004; Palchik, 2005). The authors below present some examples of equations to

determine the height of fracture zone, for example: Gajoch and Piechota (1973) proposed to define

fracture height as hs=(11,5)g; Arkuszewski (1973) presented it differently, determining the height

of hsas:

( )

214

1

2

2

2

2

2

2

g

tg

b

a

tgb

atggL

b

ahs

+

+

=

(

1)

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where:

a, b- half of the width and height of ellipse with the centre inside the excavations,

shear slip plane angle in the excavation rib.

Heasley (2004) claimed that the zone (hs) reaches 42g-60g (average 50g), but Kendorski,

Roosendaal & Bai (1995) determined it using the following equation (2)

43

100

cgc

ghs+

= (2)

where:

c3i c4 are coefficients depending on strata lithology (table 2).

Tab.2 : Coefficients for average height of fracture zone

Coefficients

Strata lithologyCompressive

strength [MPa]c3 c4

Hard and strong >40 1,2 2

Medium strong 20-40 1,6 3,6

Soft and weak


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depth of sinkhole (wl):

w

hickness,- radius of void.

ory (1951), and

Fe

rams in geomechanics

increased, scientists have tried to find new methods of predicting sinkholes.

umerical methods

rground mining excavations on the rock mass parameters (the value,

di

Flisiak, Cielik, Kowalski, 2006; ReportIT

od, Finite Difference Method, or Boundary Element Method) and also on the

bo

ium based on

Cu

umed that the value of safety factor is equal to 1,7 (it is

more than in both other presented cases).

tgrw ll = 1 assuming tglhw pnl + 1 (6)here:

hn1 - soft clay rocks tlp

The other methods of predicting sinkholes in the region of shallow excavations were presented by:

Sroka & Lbel (2001) this is a method based on empirical analysis of Knothes the

nk (1979) this model describes the way of creating sinkholes in soft clay rocks.

The method and equations presented above were used for many years to predict sinkholes in

shallow excavation areas, but when the popularity of using numerical prog

N

Using the analytical methods, the model of the rock mass needs to be oversimplified. The new

numerical methods allow the engineer working on surface sinkholes to take numerous important

parameters into consideration, having a significant influence on the character and quality of surface

deformation, e.g. lithology and quality of material of strata, parameters of rock mass layers, rock

discontinuity, influence of unde

scontinuity and anisotropy).

As a result of numerous works, different methods have arisen to determine a roof failure of the

underground excavations at the shallow depth, using numerical methods (Kwaniewski, 1998;1999; Meier, 2003; Caa, Jarczyk, Postawa, 2006; Caa,

A/AITES, 2006) and creating sinkholes on the surface.

These methods mainly depend on a selected numerical technique (i.e. Finite Element Method,

Discrete Element Meth

undary conditions.

Some researchers proposed a numerical method based on FDM (Finite Difference Method) using

which the probability of sinkholes appearing on the surface in the region of shallow excavation

could be determined (Caa, Jarczyk, Postawa, 2006). The method is called "shear strengthreduction" and it assumes that the process of rock mass damage above the excavation leads to the

decrease of the value of strength parameters. The method indicates the plane of slip surface in the

place, where the state of equilibrium between shear stress and shear strength appears in the earliest

time. The analysis of stability using shear strength reduction is a simulation, where cohesion (c) andangle of friction () are reducing till the moment of failure. The elasto-plastic med

lomb-Mohr modified plastic conditions was adapted for the sake of this analysis .

This method was widely used in numerous particular instances, such as open pit mines and

building engineering, slope stability analysis etc. In these cases the material of strata is identified in

a better way. That is why, while using this method to calculate stability of the underground mining

excavations at a shallow depth it was ass

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Fig.3 :

Hh

H

Five variants of the calculations (Caa, Jarczyk i Postawa, 2006)

According to the assumptions, the calculations were made (Caa, Jarczyk, Postawa, 2006) forseveral models, during which the process of excavation was in progress. In the model, the seam hadthe thickness of 6m, whereas the number of drifts and goaf was changing. Additionally, calculations

were carried out at different excavations depths ranging from 10m to 130m below the surface.

Figure 3 presents the schematics of numerical calculations simulating underground excavations.

a) this schematic presents a model of a drift with the height g c= 3m and width lc=3m in the

bottom layer of the seam,

b) this schematic presents a drift surrounded by the caving material with the size gz=3m and

lz=9m,

c) this schematic presents three drifts with the same size gc= 3m i lc=3m, and between them

two goaf materials with a size gz=3m i lz=9m are located,d) this variant of the calculations consists of five goaf materials and three drifts in between

(the volume is the same as in previous schematics),

e) this variant of the calculations consists of five drifts and four goaf materials.

The results show that, alongside with the increase of excavation depth, the factor of safety is

reducing.

In order to carry out the analysis of arising sinkholes on the surface, the calculations of Caa,Jarczyk and Postawa (2003) were used and the following conditions to be fulfilled were assumed:

roof layers failure of underground excavation (where, factor of safety is 1.7) (Caa,

Jarczyk, Postawa, 2006) the height of caving zone must be higher than excavation depth z . The height of

the caving zone was calculated using the Saustowicz equation (table 1) for the value ofparameters: L- is depending on calculations variants, H- it is between 10130m, v=0,3,

Rr=3MPa, =25kN/m3, =25, g=3m.

The results of the analysis on arising the sinkholes on the surface are presented in Table 3.

According to the above-presented principles, the sinkholes will arise when the conditions of the

excavations instability and hz are fulfilled. The grey colour and + mark means that the bothconditions are fulfilled and in that case the sinkholes will arise on the surface in the form of either a

sink funnel or a surface collapse.

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Tab.3 : The forecast of sinkholes as the sink funnel or surface collapse.

Variant of calculationsExcavationdepth [m]

a) b) c) d) e)

10 - - + + +

20 - - + + +

30 - - + + +40 - - + + +

50 - - - + +

60 - - - + +

70 - - - - -

80 - - - - -

90 - - - - -

100 - - - - -

110 - - - - -

120 - - - - -

130 - - - - -

Similar analysis was made for the situations of sinkholes in a form of surface cracks (table 4).This situation appears when:

roof layer of underground excavation will failure (factor of safety is 1.7),

the height of caving zone is less than excavation depth ,Hhz the height of fracture zone reaches to the ground on the surface Hhh sz + .

In the purpose of calculating the height of fracture zone the equation 1 (Arkuszewski, 1979) was

used, assuming that the value of parameters are (Saustowicz, 1968):

245 += ( )

+=

z

r

p

Rmm

b

a125,0,

the remaining parameters were equal to the value used in the calculations of caving height.

Tab.4 : The Forecast of sinkholes as the surface cracks

Variant of calculationsExcavationdepth [m]

a) b) c) d) e)

10 - - + + +

20 - - + + +

30 - - + + +

40 - - + + +

50 - - + + +60 - - - + +

70 - - - + +

80 - - - - +

90 - - - - -

100 - - - - -

110 - - - - -

120 - - - - -

130 - - - - -

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According to the presented assumptions the sinkholes will arise when the conditions of instability

of excavation and are fulfilled. The grey colour and + mark means that both conditions are

fulfilled and in that case the sinkholes will arise on the surface in the form of surface cracks.

Sinkholes in the faults region

Many times during the mining excavations near the faults, their activity occur, which leads to

negative effects on the surface like: fault scraps or sink funnels. As the result of analysis we can

single out the three types of deformations disturbance of the surface depending on a localisations of

the point in the surface and localisations of excavations area to the fault cracks:

1) in the case when the dip directions of the normal fault plane are opposite to the directions

of excavations, the form of subsidence trough is distinguishes by the shortening of the

zone of influence in the line of outcrop faults but the reduction of settlements in

subsidence trough above the coal (hanging wall) is compensated by the increase of

subsidence trough settlement in the profile situated above the goaf (footwall) (Fig 4). The

size and range of disturbance are related to the friction force tangent to the fault plane, the

angle of fault (for angle =90 appears only vertical fault scrap) and the filling material inthe fault.

2) in the case when the dip directions of the reverse fault plane are the same as the directions

of excavations, the form of subsidence trough is distinguished by the reduction of

settlements in subsidence trough in the part of the profile place in the hanging wall and

the increase of settlement in the footwall (Fig 5). Particularly negative effects appear in

the region of outcrop faults where the flexure and fault scarps are common. The size and

range of disturbance are related to the fault inclinations gradient (), nevertheless not tothe extent as in the former case (1).

3) in the case when the mining works are executed from both sides of the fault, the size of

deformations depends on excavations parameters like: volume, speed, material of filling

the void etc., the most favourable case is when the same seam is excavated from both

sides at the same time.

Fig 4 Shape of subsidence trough disturbed bythe normal fault with the dip directions opposite

to directions of excavations

Fig 5 Shape of subsidence trough disturbed bythe reverse fault with the dip directions agreed to

the directions of excavations

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( ) ,0u - the constant determining the quotient of fault scrap components.

Another possible method is based on transforming functions method (equation 13) which is

describing the ratio between settlement arisen in the case of influence of active fault to the

settlement of the surface arisen in the same conditions for the region without faults.

( ) ( )( )

0,,, =zxzzxzzx . (13)

This method was described in detail in the work of Tyraa (1979), where the schema of static elasticbeam with an overload and support in defined cases were applied to this analysis.

The methods of analysing the sinkholes arisen by the fault activity have been changing. The

numerical methods allow to describe more precisely, using the mathematic equations, the

behaviour of the rock mass and the behaviour of the fault (Stephansson, Su, 1999).

Numerical methods

Depending from the chosen numerical methods we can model the faults in the different ways

(Stephansson & Su, 1999; Yeung, Sun, Jiang, Blair, 2004; Tajdu& Tajdu, 2005). The authorsfocus on the modelling the faults using finite element analysis. In this method, faults are modelled

as the contact surfaces between two mesh models (Tajdu& Tajdu, 2005).To present this method, several numerical calculations were made for the model, which simulates

the underground excavations in the fault area for both cases (normal and reverse faults) (Figs. 4 and

5). The model with the size 500x1260m consists of 70 000 rectangles elements, which were

modelled in the plane of strain. In this model the exploitation is at the depth of 400m, with a height

g=3m, and length 360m and above it there is a caving zone (hz=7m). Table 5 presents the value of

parameters used during the analysis.

Tab.5 : The value of elastic parameters used in the FEM analysisRock mass layers E [GPa] v

Soil 0,5 0,4

Hard rock mass 3,0 0,3

Coal 1,0 0,3

Cavin zone 0,03 0,3

As it is known from the observations and measurements in the region of the excavations in the fault

area, the range and size of disturbances depend on the vale of frictions force tangent to the fault. In

order to determine the influence of friction on vertical displacement, numerical calculations were

carried out for the exploitation model with normal and reverse faults, changing the value of friction

coefficient on the fault surface from u=0,11,5. The results of the calculations were presented inFigures 6 and 7, where Fig. 6 presents the profile of model settlement for the normal fault, opposite

to the direction of excavation and Fig. 7 presents the profile of model settlement for the reverse

fault agreed with a direction of excavation. It can be noticed that the friction coefficient () has aconsiderable influence on the vale of vertical displacement and on the shape of subsidence trough.

The numerical calculations allows to compare and analyse the subsidence profile for the models

with normal fault and reverse fault (Figs. 4 and 5).

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The results of the vertical displacement for this model agree with the observations and experience:

comparing the profile of subsidence trough disturbed by the normal fault with the profile

of undisturbed subsidence trough it can be seen that (Fig. 8):

o for the disturbed exploitation, the range of mining influence is reduced in the

hanging wall, which is compensated by the increase of vertical displacement in the

footwall,

o in the Figure it can be noticed that the sinkholes arose in the region of fault outcrops. comparing the profile of subsidence trough disturbed by the reverse fault with the profile

of undisturbed subsidence trough it can be seen that (Fig. 9):

o for the disturbed exploitation, the bigger vertical displacements are in the hanging

wall comparing to the undisturbed subsidence trough,

o in the footwall, the vertical displacements for the disturbed subsidence trough are

smaller than in the undisturbed subsidence trough,

o on the surface of the model there appear the sinkholes in the outcrops fault region,

o comparing the sinkholes arisen on the model surface it can be seen that the sinkhole

for the reverse fault is bigger then the one for the normal fault (Fig. 10).

Fig. 6 The influence of friction coefficient on thesubsidence trough profile for the normal fault

opposite to the direction of excavations

Fig. 7 The influence of friction coefficient on thesubsidence trough profile for the reverse fault

agreed to the direction of excavations

Fig. 8 The comparison of the subsidence shapefor the disturbed subsidence made by normal

fault and the undisturbed subsidence trough

Fig.9 The comparison of the shape for the disturbsubsidence made by reverse fault and the

undisturbed subsidence trough

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Fig.10 The comparison of the profile for the disturbed subsidencemade by reverse fault, normal fault and undisturbed profile

Conclusion

Through the years, alongside with the technological progress and the knowledge development in the

subject of strata properties in underground mining regions, the methods of solving the problem of

sinkholes have been changed. At first the prognoses were based only on empirical and analytical

methods, but with time scientists started using numerical analysis, which allowed to take many

other parameters into consideration, which obviously had a serious influence on the character and

quality of deformations such as: lithology, parameters of rock mass layers, natural discontinuities,

and the influence of mining exploitations on strata parameters (value, anisotropy, cracks etc.).

However, in spite of these changes there are still many problems with the proper forecast of the

sinkholes. That is why, the scientists should somehow be able to combine the wisdom andexperiences gathered by the past generations as well as the rapidly developing modern technologies.

References:

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