187155943 determination of residual strength parameters of jointed rock masses using the gsi system

8/12/2019 187155943 Determination of Residual Strength Parameters of Jointed Rock Masses Using the GSI System

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International Journal of Rock Mechanics & Mining Sciences 44 (2007) 247–265

Determination of residual strength parameters of jointed

rock masses using the GSI system

M. Caia,, P.K. Kaisera, Y. Tasakab, M. Minamic

aGeomechanics Research Centre, MIRARCO, Laurentian University, Sudbury, Ont., CanadabDepartment of Advanced Engineering, Tokyo Electric Power Services Company Limited, Tokyo, Japan

cDepartment of Construction, Tokyo Electric Power Company, Tokyo, Japan

Accepted 13 July 2006

Available online 26 September 2006

Abstract

The Geological Strength Index (GSI) system, proposed in 1995, is now widely used for the estimation of the rock mass strength and the

rock mass deformation parameters. The GSI system concentrates on the description of two factors, rock structure and block surface

conditions. The guidelines given by the GSI system are for the estimation of the peak strength parameters of jointed rock masses. There

are no guidelines given by the GSI, or by any other system, for the estimation of the rock mass’ residual strength that yield consistent

results. In this paper, a method is proposed to extend the GSI system for the estimation of a rock mass’s residual strength. It is proposed

to adjust the peak GSI to the residual GSI r value based on the two major controlling factors in the GSI system—the residual block

volume V rb and the residual joint condition factor J rc. Methods to estimate the residual block volume and joint condition factor are

presented. The proposed method for the estimation of rock mass’s residual strength is validated using in-situ block shear test data from

three large-scale cavern construction sites and data from a back-analysis of rock slopes. The estimated residual strengths, calculated

using the reduced residual GSI r value, are found to be in good agreement with field test or back-analyzed data.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Rock mass; Rock mass classification; Geological strength index; Rock failure

1. Introduction

Knowledge of the rock mass strength and deformation

behaviors is required for the design of many engineering

structures in or on rock, such as foundations, slopes,

tunnels, underground caverns, drifts, and mining stopes.

A better understanding of the rock mass strength behavior,

including the peak and residual strengths, will facilitate the

cost-effective design of such structures.The determination of the global mechanical properties of

a jointed rock mass remains one of the most difficult tasks

in rock mechanics. Many researchers have developed

constitutive models to describe the strength and deforma-

tion behaviors of jointed rock masses e.g., [3–5]. Because

there are so many parameters that affect the deformability

and strength, it is generally impossible to develop a

universal model that can be used to a priori predict the

strength of the rock mass. Traditional methods to

determine these parameters include plate-loading tests for

deformation modulus and in-situ block shear tests for

strength parameters. These tests can only be performed

when the exploration adits are excavated and the cost of

conducting in-situ tests is high. Although back-analyses

based on field measurement are helpful in determining the

strength and deformation parameters as a project proceeds,they do not provide design parameters at the pre-feasibility

or feasibility study stages.

Few attempts have been made to develop methods to

characterize the jointed rock mass to estimate the deform-

ability and strength indirectly. The Geological Strength

Index (GSI), developed by Hoek et al. [1], is one of them. It

uses properties of intact rock and conditions of jointing to

determine/estimate the rock mass deformability and

strength. GSI values can be estimated based on the

geological description of the rock mass and this is well

ARTICLE IN PRESS

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E-mail address: [email protected] (M. Cai).

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suited for rock mass characterization without direct access

to the rock mass from tunnels. The GSI system concen-

trates on the description of two factors, rock structure and

block surface conditions. It is a system that provides a

complete set of mechanical properties (Hoek–Brown

strength parameters mb and s, or the equivalent Mohr–

Coulomb strength parameters c and f, as well as the elasticmodulus E ) for design purposes. Recently, a means to

quantify this approach by use of field data, which employs

the block volume (V b) and a joint condition factor (J c) as

quantitative characterization factors, was presented in [2].

Guidelines given by the GSI system are for the

estimation of the peak strength of jointed rock masses. In

general, rock masses, except when highly disturbed, exhibit

strain-softening post-peak behavior, so that the residual

strength parameters are lower than the peak parameters.

Both are required for design. Strain-softening behavior

describes the gradual loss of load-bearing capacity of a

material. For hard rocks, the term ‘‘strength weakening’’

seems more appropriate than the term ‘‘strain-softening’’

because softening refers to reduction of rock stiffness.

At lower confinement levels such as near excavation walls,

most rock masses exhibit some post-peak strength loss, and

when strained sufficiently reach the residual strength. The

peak and residual strengths are respectively the maximum

and minimum stresses of a rock mass that can be sustained

under a given confinement condition. The residual strength

is generally only reached after considerable plastic defor-

mation. There are some guidelines for the estimation of the

rock mass’ residual strength, given by some researchers

[6,7], but upon application of these guidelines, it is often

observed that there are significant inconsistencies in theresidual strengths derived from them. Hence, a new method

has been developed and tested to extend the GSI system for

rock mass’s residual strength estimation. For this purpose,

we propose to adjust the peak GSI value based on the two

major controlling factors in the GSI system, the block

volume V b and the joint condition factor J c to arrive at a

residual GSI –value (GSI r) based on a residual block

volume V rb and residual J rc. The residual GSI r value is

calculated from a relationship involving residual V rb and

J rc. The proposed method for the estimation of rock mass’s

residual strength is then validated using in-situ block shear

test data from three large-scale cavern construction sites

and data from a back-analysis of a rock slope stability

study.

The following definitions for the peak and residual

strength are illustrated in Fig. 1. The residual strength is

defined by the plateau after the peak, in a strain range of

about 5–10 times the strain corresponding to the peakstrength. This level of load bearing capacity is commonly

referred as the ‘‘residual strength’’ in most civil and mining

engineering applications. If straining is allowed to con-

tinue, then, the strength can further decreases and

eventually reaches a lower strength.

2. Influence of the rock’s residual strength on support design

for underground excavations

The post-peak behavior of rocks is important in the

design of underground excavations because it has a

significant influence upon the stability of the excavations.

Rock mechanics test data are available on the strength of

rock masses, especially for intact rocks. A brief review is

presented in the following sub-sections, with focus on the

post-peak behavior of rocks.

2.1. Laboratory tests

Pioneers in experimental study of the complete stress–

strain relations of rocks include Paulding [8], Cook [9],

Hoek [10], Bieniawski [11], Wawersik [12], Wawersik and

Fairhurst [13], and many others. The post-peak behavior of

rocks was studied only after the development of stiff servo-

controlled test machines in the middle of 1960s. In uniaxialcompression, two failure modes are observed [13]. One is

the local tensile or spalling fracture sub-parallel to the

applied load direction and the other is a local and

macroscopic shear fracture. In heterogeneous rocks and

under low confinements, spalling-type failure dominates.

The post-failure behavior of the rocks can be divided into

two classes [13]. Class I behavior is characterized by a

stable fracture propagation. The rocks retain some strength

even when their maximum load-carrying capacity has been

exceeded. Unstable fracture propagation behavior is

characteristic of the Class II behavior.

ARTICLE IN PRESS

Peak

Residual

(a)

S t r e s s

S t r e s s

Peak

Residual

StrainStrain (b)εPeak

5 to 10 εPeak

Fig. 1. (a) Strain-softening of rocks; (b) perfectly brittle failure of rocks.

M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 247–265248



Triaxial test data on marbles by Wawersik and Fairhurst

[13] (Fig. 2) and Rummel and Fairhurst [14] revealed that

peak and residual strengths of rocks increase with

increasing confining pressures. At low confinements, the

loss of the cohesive strength component around peak load

leads to strain localization with significant stress-drop

which is traditionally called strain-softening behavior.

Seeber [15] noticed that if the confining pressure was

greater than one-fifth of the axial stress at failure, strain-

softening was unlikely to occur. For reference, the brittle-

ductile transition limit given by Mogi [16] is s3/s1 ¼ 1/3.4.

Clearly, strain-softening behavior must be expected to

dominate near underground excavations where confine-

ment is reduced.The post-peak behavior of rocks tested in the laboratory

is dependent on the specimen geometry. This is because

that the post-failure curve is altered depending on the

relative stiffness of the machine and the specimen, as well

as the internal confinement profile. With the development

of fractures in the post-peak region, the effective area at the

center of the specimen slowly decreases. The relative

decrease in cross-sectional area is greater for the specimens

of greater height (h) to diameter (d ) ratio (h/d ). Conse-

quently, the post-peak stress strain curves of specimens

with higher h/d ratios are steeper [17].

Besides the uniaxial and triaxial tests, double shear

testing method are utilized by some researchers to study the

complete shear stress–shear displacement relations of rocks

[18,19]. The residual shear strength typically depends on

the applied axial pressure (frictional materials).

The behavior of joints affects the strength and deforma-

tion properties of jointed rock masses significantly. The

shear strength of joints is a major factor in controlling the

strength of jointed rock masses. Early experimental studies

on rock joints were carried out by Patton [20], followed by

Goodman [21] Barton and Choubey [22], Bandis et al. [23],

Barton et al. [24], and others. Conceptually, there are

three modes of failure confirmed from these tests, i.e.,

(a) asperity (roughness) override at low normal stresses;

(b) failure through asperities at elevated normal stresses;

and (c) combinations of asperity override and failure at

intermediate normal stresses.

Barton and Choubey [22] proposed the concept of joint

roughness coefficient (JRC ) to describe the peak strength

of a joint. This concept was further developed incorporat-

ing the mobilized JRC to account the joint surfaceevolution at different deformation stages [23]. The joint

shear strength is known to be dependent on three

components, i.e., the residual or basic frictional compo-

nent, the geometrical component, and the asperity compo-

nent. The asperity and the geometrical components

constitute the roughness strength that has to be mobilized

during shearing of the joint.

One important observation from Barton’s joint model is

that within limited displacements, only an ultimate

mobilized joint roughness coefficient (JRC mob) can be

reached. JRC mob is roughly half of JRC peak when the

displacement is about 10 times of the joint peak strength

displacement (Fig. 3). According to this figure, the residual

strength is only reached when the shearing displacement is

extremely large. In most engineering applications, such

large straining cannot be tolerated. Therefore, the joint

strength at dE10dpeak can be considered as corresponding

to the rock’s residual strength defined in Fig. 1.

2.2. In-situ tests

Strength and deformation properties determined from

the laboratory tests are seldom applicable to field condi-

tions. To overcome this problem, large-scale in-situ tests

have been conducted in some engineering projects. Thetests include in-situ uniaxial compressive tests, triaxial

tests, block shear tests, etc. Uniaxial compressive tests have

been conducted mostly in coalmines to study the stability

of pillars [25]. In-situ block shear tests are often executed in

large civil projects to obtain the shear strength of rock

masses and strengths of bedding or other weakness planes.

The block shear test is often conducted in an underground

gallery or adit. The roof and sidewalls are used to carry the

reaction of the applied normal and shear loads. The rock

blocks are of square base of suitable dimensions in width

and height. The shear stress vs. shear displacement relation

is recorded to identify the peak and residual strengths. It is

observed that the block shear test has a major deficiency

that it provides residual strength of a single shear plane

where in the rock mass, some degree of interlocking is

retained even at its residual state. Thus, in-situ block

shear tests tend to underestimate the residual values. In

addition, the loading system can generally be viewed as a

soft system so that the post-peak stress–displacement

curves may not characterize the strain-softening process

properly for confined states. Most large-scale cavern

designs in Japan, however, employ the residual strength

parameters obtained from these in-situ block shear tests

and utilize post-peak brittle failure models for precautious

design (Fig. 1(b)).

ARTICLE IN PRESS

300

200

100

0 0.10 0.20 0.30 0.40 0.50 0.60 0.70

3.45 MPa

6.9 MPa13.8 MPa

20.7 MPa

27.6 MPa

34.5 MPa

48.3 MPa

0

A x i a l s t r e s s , σ a

( M P a )

Axial stress, a (%) ∋

Fig. 2. Stress–strain curves for Tennessee Marble at different confining

stresses [13].

M. Cai et al. / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 247–265 249



2.3. Need for accurate determination of the residual strength

of rock masses

It is observed that following the strain-softening

behavior of rocks under loading, the residual strength

represents more or less the shear strength along a surface or

shear zone of the fractured rock. In most cases, the residual

strength can be described by the Mohr–Coulomb criterion

with near zero cohesive strength. The post-peak strength

depends on the resistance developed on the failure plane

against further straining. Initially, the fracture orientation,

degree of interlocking, surface irregularity or roughness

will affect the level of resistance. However, as strain

increases, the residual strength will be less. In the field, the

post-peak strength level will be influenced by the boundary

conditions as well. If further straining is constrained, then,

the residual strength level cannot be reached and the rock

mass can thus support a higher load than the residual

strength would suggest.

It is a very challenging and difficult task to correctly

represent the strain-softening behavior of rock masses, due

to a lack of large-scale test data. Most numerical tools

designed for rock engineering application, however,

provide strain-softening constitutive models of varying

sophistication to describe the behavior of jointed rock

masses [26–28]. In these models, the residual strength of the

rock mass and the rate of post-peak strength degradation

play an important role in the determination of the size of

the plastic zones and the associated rock mass deforma-

tion, affecting the final rock support system design. For

example, the current version of Phase2D

[29], an FEMprogram developed by Rocscience, allows the user to define

both peak and residual strength parameters of rock masses.

When the stress of an element has exceeded its peak

strength, it fails in a perfectly brittle manner, switching

directly from peak to post-peak residual parameter values,

with no strain-dependent softening mechanism (Fig. 1(b)).

Although extremely important for these numerical models,

only limited suggestions are given in the user’s manual on

how to determine the residual strength parameters.

If the residual strengths are not determined appropri-

ately, an optimal rock support design can never be

achieved. The influence of the residual strength on the

yielding zone around a 6 m wide tunnel is illustrated in

Fig. 4. The tunnel is located at a depth of about 500 m and

the maximum and minimum in-situ stresses are 12.5 and

4.8 MPa, respectively. The angle between the maximum

principal stress direction and the vertical is 261. Rock mass

peak cohesion, friction angle, dilation angle, and tensile

strength are 3 MPa, 551, 51, and 0.6 MPa, respectively. It is

assumed that after peak strength, the rock mass reaches the

residual strength in a brittle manner. The residual tensile

strength is assumed to be zero and the dilation angle

unchanged from the peak dilation. It should be noted that

constant dilation is an approximation that is clearly not

physically correct. This assumption is made largely because

ARTICLE IN PRESS

J R C m o b / J R C p e a k

Example

1.0

0.5

01.0 2.0 3.0 4.0

START

-0.5

-1.0

-1.5

JRCm=: 15

PEAK

ROUGHNESSDESTROYED

R O U G H N E S

S

M O B I L I Z E D

12·75 10·5

ULT IMAT E

RESIDUAL

(δ / δ PEAK)

M O B I L I Z A T I O N

O F

F R I C T I O N

DILATIONBEGINSATJRCM = 0

EXAMPLE:φpeak

φultimateφresidual

δ

δp

JRCm

JRCp

0

0.3

0.6

1.0

2.0

4.010.0

100.0

0

0.751.0

0.85

0.700.50

0

−φr/i

φr = 30°, i = 15°

JRC = 15, σn = 10.0 MPa.

JCS = 100 MPa

45°

°

30°

15°

0°

i = φp − φr

i = JRC log ( )JCSσn

-2.0 − (φr / i)

Fig. 3. Normalized joint roughness–shear displacement relationship [24].




little is known about how the dilation of a rock mass

changes past peak. Even if the peak strength is the same for

all cases, for different residual friction angles and cohesions

shown in Fig. 4, the yielding zones are drastically different.

The underlying implication is that the residual strength of rock masses has to be properly determined in order to

design appropriate rock support systems.

2.4. Review of existing methods to determine the residual

strength of rock masses

To design underground structures properly, both the

peak and residual strengths of the rock mass are needed.

Much research has been focused on the determination of

peak strengths, and limited attempts have been made to

estimate the residual strength of jointed rock masses.

The existing GSI system only provides guidance for rock

mass peak strength estimation. To address the issue of rock

mass residual strength, Hoek [6,30] suggested elastic-

brittle, strain-softening, and elastic-perfect plastic post-

peak rock mass behavior for very good, average, and very

poor quality rock masses, respectively. Hoek also suggested

that in the case of an average quality rock mass, it is

reasonable to assume that the post failure characteristics

can be estimated by reducing the GSI value from the in-situ

value to a lower value which characterizes the broken rock

mass. The reduction of the rock mass strength from an

undisturbed to a broken state corresponds to the strain-

softening behavior. However, the validity of this assump-

tion is unknown, and new study is needed to understand

the strength reduction mechanism and hence provide a

method for residual strength estimation [6].

Russo et al. [7] proposed to set the residual GSI r value at

36% of the peak GSI value. This empirical relation may

underestimate the residual GSI values for poor-quality

rock masses. On the other hand, for very good-quality rock

masses, it may overestimate the residual GSI r values. Basedon laboratory triaxial test on limestone, Ribacchi [31]

suggested to use the following relations to estimate the

residual strength of jointed rock masses:

mr ¼ 0:65mb; sr ¼ 0:04s or scð Þr ¼ 0:2sc, (1)

where mb and s are the Hoek–Brown peak strength

parameters, the subscript ‘‘r’’ indicates residual values,

and sc is the uniaxial compressive strength of the intact

rock. Taking into account the structure of the tested rock,

these relations may be valid only for rock masses in which

joints are characterized by a thin infilling or slightly

weathered to unweathered joint walls. The corresponding

GSI reduction that would fit such parameters is approxi-mately GSI r ¼ 0.7GSI .

The opinions of several rock mechanics experts on the

post-peak strength parameters were summarized in [32]. It

is generally agreed that the reduction of sc would be

physically and conceptually incorrect because this is a

‘‘fixed’’ index parameter that is determined from intact

rock specimens.

In summary, several attempts have been made to

estimate the residual strength of jointed rock masses. The

reduction of GSI to its residual value is a logical choice,

because the failure of rock masses is associated with the

crushing of intact rock and the wearing of the joint surfaceroughness. Current reduction methods, however, lack

generality and lead to inconsistent results for different

rock masses. Here, a new method is proposed based on the

observation of actual rock mass failure process from

laboratory and in-situ tests, as well as on the understanding

of the rock fracturing process from numerical simulation.

3. Determination of the strength parameters using the GSI

system

3.1. Estimation of peak strength of rock masses using the

GSI system

Two types of strength criteria, i.e., the Mohr–Coulomb

and Hoek–Brown failure criteria, are widely used in rock

engineering. The equivalent Mohr–Coulomb parameters

can be obtained based on the Hoek–Brown envelope and a

chosen range of confinement (s3). In terms of major and

minor principal stresses, s1 and s3, the Mohr–Coulomb

failure criterion can be expressed as

s1 ¼ 2ccosf

1 sinfþ

1 þ sinf

1 sinfs3, (2)

where c and f are the cohesive strength and angle of

friction of the rock mass, respectively.

ARTICLE IN PRESS

(a) (b)

(c) (d)

Fig. 4. Influence of residual strength on the yielding zone around a tunnel.




The generalized Hoek–Brown criterion for jointed rock

masses [33] is

s1 ¼ s3 þ sc mb

s3

sc

þ s

a

, (3)

where mb, s, a are constants for the rock mass, and sc is the

uniaxial compressive strength of the intact rock. The GSIsystem was developed to determine the Hoek–Brown

strength parameters, using the rock structure and joint

surface condition description to describe the rock mass

jointing. To facilitate the use of the system, Cai et al. [2]

presented a quantitative approach that employed the block

volume V b and a joint surface condition factor J c as

quantitative characterization factors. The quantitative

approach was validated using field test data and applied

to the estimation of the rock mass properties at two cavern

sites in Japan. The quantified GSI chart is presented inFig. 5. It provides a means for consistent rock mass

characterization and thus improves the utility of the GSI

system.

ARTICLE IN PRESS

P o t e n

t i a l b

r i t t l e f a i l u

r e z o n e

B r i t t l e

f a i l u

r e z o n e

0.1

1

10

100

1000

10E+3

100E+3

1E+6

10E+6

B l o c k V o l u m e V b ( c m

3 )

Blocky - very well interlocked

undisturbed rock mass consisting

of cubical blocks formed by threeorthogonal discontinuity sets

Joint spacing 30 - 100 cm

Very Blocky - interlocked, partially

disturbed rock mass with multifaceted

angular blocks formed by four or more

discoutinuity sets


Blocky/disturbed - folded and/or

faulted with angular blocks formed by

many intersecting discontinuity sets


Disintegrated - poorly interlocked,

heavily broken rock mass with a

mixture or angular and rounded

rock pieces

Joint spacing < 3 cm

75

50

30

70

65

60

55

45

40

35

25

20

15

10

80

8590

95

Massive - very well interlocked

undisturbed rock mass blocks formed

by three or less discontinuity sets

with very wide joint spacing

Joint spacing > 100 cm

5N/A N/A

Foliated/laminated/sheared - thinly

laminated or foliated, tectonically sheared

weak rock; closely spaced schistosity

prevails over any other discontinuity set,

resulting in complete lack of blockiness


V e r y g o o d

V e r y r o u g h , f r e s h u n w e a

t h e r e d s u r f a c e s

G o o d

R o u g h , s l i g h t l y w e a t h e r e

d ,

i r o n s t a i n e d s u r f a c e s

F a i r

S m o o t h , m o d e r a t e l y w e a t h e r e d o r

a l t e r e d s u r f a c e s

P o o r

S l i c k e n s i d e d , h i g h l y w e a t h e r e d s u r f a c e s w i t h

c o m p a c t c o a t i n g o r f i l l i n g

s o f a n g u l a r f r a g m e n t s

V e r y p o o r

S l i c k e n s i d e d , h i g h l y w e a

t h e r e d s u r f a c e s w i t h

s o f t c l a y c o a t i n g s o r f i l l i n

g s

12 4.5 1.7 0.67 0.25 0.09

Joint Condition Factor Jc

20

30 cm

60

100 cm

40

50

10 cm

708090

5

2

1 cm

3

150

(1 m3)

(1 dm3)

Block Size

Joint or Block Wall Condition

Fig. 5. Quantification of GSI chart [2 ].




In numerical model implementation, it is sometimes

troublesome to refer to a chart for the determination of the

GSI values. Recently, based on the proposed quantitative

chart, and using surface fitting techniques, the following

equation for the calculation of GSI from J c and V b was

developed [34]:

GSI V b; J cð Þ ¼ 26:5 þ 8:79ln J c þ 0:9 ln V b

1 þ 0:0151 ln J c 0:0253 ln V b, (4)

where J c is a dimensionless factor, and V b is in cm3. A

graphic representation of Eq. (4) is presented in Fig. 6. In

other words, the Hoek–Brown strength parameters and

deformation modulus can be directly expressed as afunction of V b and J c:

mb ¼ miexp GSI 100

28 14D

, (5)

s ¼ exp GSI 100

9 3D

, (6)

a ¼ 0:5 þ1

6 eGSI=15 e20=3

, (7)

where D is a factor that depends on the degree of

disturbance to which the rock mass has been subjected by

blast damage and stress relaxation. The D factor wasintroduced in the latest update [35] of the Hoek–Brown

failure criterion.

3.2. Estimation of residual strength of rock masses using the

GSI system

As is demonstrated by the identification and visualiza-

tion of influencing parameters in major rock mass

classification systems, the block volume and the joint

surface condition are the two most important factors that

control the quality and hence the strength and deform-

ability of jointed rock masses [34]. Block volume is affected

by the joint set spacing and persistence. Joint condition is

controlled by joint roughness, weathering, and infilling

material. These are important factors that need to be

characterized for rock mass’s residual strength estimation.

Sjo ¨ berg [36] reported that when using the GSI system to

estimate the rock mass strength at the Aznalcollar open pit

mine in Spain, it was found that by assuming the disturbedrock mass category, good agreement was found between

estimated strength values and back-calculated strengths

from observed slope failures in the footwall. The same

author reckoned that these strength values were probably

conservative and representative of the residual strength of

the rock mass. Although this hypothesis needs to be further

verified by additional data from other slope failures, it

suggests that the reduction of GSI for residual strength

estimation is logical.

To extend the GSI system for rock mass residual

strength estimation, we propose to adjust the original

GSI value based on the two major controlling factors in the

GSI system, i.e., block volume V b and joint condition

factor J c, to reach their residual values.

3.2.1. Residual block volume

Block size, which is determined from the joint spacing,

joint orientation, number of joint sets and joint persistence,

is an extremely important indicator of rock mass quality.

Block size is a volumetric expression of joint density. The

block volume spectrum from ‘‘massive’’ to ‘‘very blocky’’

rock masses ranges from 103 to 107 cm3, and for

‘‘disturbed’’ to ‘‘sheared’’ rock from 0.1 to 103 cm3.

Joints are often of limited length, even in a larger scale

[37]. If the joints are not persistent, i.e., with rock bridges,the rock mass strength is higher and the global rock

stability is enhanced. This effect can be considered using

the concept of equivalent block volume as suggested in [2].

The difference between the peak and residual strength of

a rock mass with non-persistent joints is larger than that

of a rock mass with persistent joints. The implication is

that a drop of GSI from peak to residual values is larger for

rock masses with non-persistent joints. Besides rock

bridges, rock asperity interlocking also contributes to the

difference between peak and residual strengths.

If a rock experiences post-peak deformation, the rock in

the broken zone is fractured and consequently turned into

a poor and eventually ‘‘very poor’’ rock. Hence, the rock

mass properties of a rock mass after extensive straining

should be derived from the rock class of ‘‘very poor rock

mass’’ in the RMR system [38] or ‘‘disintegrated’’ in the

GSI system.

For the residual block volume, it is observed that the

post-peak block volumes are small because the rock mass

has experienced tensile and shear fracturing. After the peak

load, the rock mass becomes less interlocked, and is heavily

broken with a mixture of angular and partly rounded rock

pieces. Numerical simulation using ELFEN [39] and DIGS

[40] revealed that the rock masses in the fracture zone

around underground openings are broken to small blocks.

ARTICLE IN PRESS

Fig. 6. Visualization of the GSI system [34].




ELFEN was also used to simulate the rock failure process

in uniaxial and biaxial loading conditions [41]. The results

indicate that the rock will gradually disintegrate into small

blocks, mostly along the localized shear or kink band zone,

before the residual strength in reached.

Detailed examination of the rock mass damage state

before and after the in-situ block shear tests at some

underground cavern sites in Japan revealed that in areas

that were not covered by concrete, the failed rock mass

blocks are 1–5 cm in size. The rock mass is disintegrated

along a shear zone in these tests.

It can be seen from Fig. 5 that the block volume sizes of

the disintegrated rock masses are in the range of 1–27 cm3,

with an average of about 10 cm3

. This is supported by faultoutcrop observations. The strength of a fault can be

regarded as the lower-bound strength of the rock mass.

Shearing disintegrates and damages the rock mass and

weathering further weaken the fault strength. Another

example of residual block size is presented in Fig. 7, in

which a sheared Flysches in the middle of the picture are

totally disintegrated with a block volume of about 10 cm3.

In summary, the residual block volumes can be

considered independent of the original (peak) block

volumes for most strain-softening rock masses. This is

illustrated in Fig. 8, showing the fractured residual rock

mass will have more or less the same residual block volume

in the shear band for intact rocks, moderately jointed and

highly jointed rock masses. As an estimate, if the peak

block volume V b is greater than 10 cm3, then, the residual

block volume V rb in the disintegrated category can be taken

to be 10 cm3. If V b is smaller than 10cm3, then, no

reduction to the residual block volume is recommended,

i.e., V rb ¼ V b.

3.2.2. Residual joint condition factor

In the GSI system, the joint surface condition is defined

by the roughness, weathering and infilling condition [1,2].

The combination of these factors defines the strength

of a joint or block surface. The joint condition factor is

defined as

J c ¼J WJ S

J A, (8)

where J W, J S, and J A are the joint large-scale waviness

factor, small-scale smoothness factor, and alteration factor,

respectively. The tables for peak J W, J S, and J A are given

in [2].

The failure process affects the joint surface condition,

especially the joint roughness. According to [24], the

difference between peak and residual JRC is large if the

peak JRC value is high. The underlying implication is that

the drop of GSI from peak to residual values should be

larger for rock masses with fresh and rough joints.

The major factor that alters the joint surface condition in

the post-peak region is the reduction of joint surface

roughness, as shown in Fig. 3 for the gradual degradation

of JRC . Peak mobilized roughness angle is given as JRC

log(JCS /sn), where JCS is the joint wall compressive

strength, and sn is the normal stress acting on the joint.

The mobilized joint residual roughness is zero according to

the same figure, which can only be achieved when the joint

experiences a very large shearing displacement. On the

other hand, the concept of ultimate mobilized joint

roughness was suggested by Barton et al. [24]. According

ARTICLE IN PRESS

Fig. 7. Example of sheared Flysches in Greece (photo courtesy of Evert

Hoek).

Residual stateInitial state

Highly jointed

Moderately jointed

Intact

Fig. 8. Illustration of the residual block volume.




to Fig. 3, the joint surface roughness is gradually destroyed

during the shearing process and the ultimate mobilized

roughness is about half of the peak roughness (JRC mob/

JRC peak ¼ 0.5). As stated before, the strain levels in most

civil and mining underground excavation structures are not

large so that the shearing of joints at the displacement level

around 10dp would correspond to the straining of jointedrock masses at the residual strength level defined in Fig. 1.

It is therefore proposed here that the large-scale waviness

and the small-scale smoothness of joints be calculated by

reducing its peak value by half to calculate the residual GSI

value. In a short time period, joint alteration is unlikely to

occur so that the joint alteration factor J A will be

unchanged in most circumstances. However, when water

and clay infill material is involved, the fractured rock

surface can have a lower residual J A.

The residual joint surface condition factor J rc is

calculated from

J rc ¼ J r

WJ r

S

J rA, (9)

where J rW, J rS, and J rA are residual values for large-scale

waviness, small-scale smoothness, and joint alteration

factor, respectively. The residual values are obtained based

on the corresponding peak values. The reduction of J rW and

J rS are based on the concept of mobilized joint roughness,

and the equations are given as

If J W

2 o1; J rW ¼ 1; Else J rW ¼

J W

2 , (10)

If J S

2 o0:75; J r

S ¼ 0:75; Else J r

S ¼

J S

2 , (11)

There is no reduction for J A in the present study.

3.3. Residual GSI value and strength parameters

According to the logic of the original GSI system, the

strength of a rock mass is controlled by its block size and

joint surface condition. The same concept is valid for failed

rock masses at the residual strength state. In other words,

the residual GSI r is a function of residual J rc and V rb, i.e.,

GSI r ¼ f ðJ rc; V rbÞ, (12)

or, applying the explicitly Eq. (4) to rewrite Eq. (12) as

GSI rðV rb; J rcÞ ¼ 26:5 þ 8:79ln J rc þ 0:9 ln V rb1 þ 0:0151 ln J rc 0:0253 ln V rb

. (13)

As for the intact rock properties, fracturing and shearing

do not weaken the intact rocks (even if they are broken into

smaller pieces) so that the mechanical parameters (sc and

mi) should be unchanged. What has changed are the block

size and joint surface condition (especially the roughness).

Therefore, the generalized Hoek–Brown criterion for the

residual strength of jointed rock masses can be written as

s1 ¼ s3 þ sc mr

s3

sc

þ sr ar

, (14)

where mr, sr, ar are the residual Hoek–Brown constants for

the rock mass. It is postulated that these constants can be

determined from a residual GSI r value using the same

equations for peak strength parameters (Eqs. (5–7)). This

simply means that the equations for peak strength

parameter calculation hold true to the residual strength

parameter calculation. This statement is supported by thefact that the rock mass in its residual state represents one

particular kind of rock mass in the spectrum in the GSI

chart (Fig. 5). The rock mass spectrum is defined by the

combination of the block volume spectrum and the joint

surface condition factor spectrum. In fact, the GSI chart

had been expanded from its original spectrum [1] to

account for weak or fractured rocks [42,43].

Once the reduced GSI r is obtained, the residual

Hoek–Brown strength parameters or the equivalent re-

sidual Mohr–Coulomb strength parameters can be calcu-

lated, assuming that other parameters such as sc and mi are

unchanged, i.e.,

mr ¼ miexp GSI r 100

28

, (15)

sr ¼ exp GSI r 100

9

, (16)

ar ¼ 0:5 þ1

6 eGSIr=15 e20=3

. (17)

Because the rock masses are in a damaged, residual state,

D ¼ 0 is used for the residual strength parameter calcula-

tion.

3.3.1. Discussion

When GSI is reduced in the post-peak yielding, the

frictional and cohesive strength components will reduce at

different rates. This can be clearly seen in Figs. 9 and 10.

The frictional strength component, mb, decreases gradually

ARTICLE IN PRESS

0

5

10

15

20

25

0 20 40 60 80 100

GSI

m b

mi=25mi=20mi=15mi=10

mi=10

20

25

Fig. 9. Relationship between mb and GSI.




with decreasing GSI value. The relationships between GSI

and a and s are shown in Fig. 10. For GSI o40, s, the

cohesive strength component, becomes very small and can

be ignored in defining the residual rock mass strength. For

GSI 440, a is approximately 0.5, whereas a is slightly larger

than 0.5 for 20oGSIo40.

Table 1 presents several GSI estimations on the residualstrength parameters of some typical rock masses. For

example, for a strong rock mass whose V b is 12500cm3,

J W ¼ 2, J S ¼ 2, J A ¼ 1, the peak Hoek–Brown strength

parameters are mb ¼ 4.845 and s ¼ 0.012. According to the

proposed method, V rb ¼ 10cm3 and J rc ¼ 1 for the residual

rock mass. The residual GSI r is 30.3, and the corresponding

residual Hoek–Brown strength parameters are: mr ¼ 1.659,

sr ¼ 0. For other rock types, similar strength parameters

can be obtained following our proposed approach. A plot

of the peak and residual Hoek–Brown strength envelops

given by our approach is presented in Fig. 11 for massive

brittle rocks, jointed strong rocks and jointed intermediate

rocks. The methodology described here provides consistent

results for different rock types considered.

The average residual block size of 10 cm3 is suggested for

the determination of the residual GSI value. To evaluate

the influence of the residual block size on the residual

strength, maximum (V rb ¼ 27cm3) and minimum (V rb ¼

1 cm3

) residual block volumes in the disintegrated categoryare used to calculate the equivalent residual Mohr–Cou-

lomb strength parameters. It is seen from the results

presented in Table 2 that the maximum difference in the

friction angle is about 21 and the difference of the residual

cohesion is small if the maximum and the minimum block

ARTICLE IN PRESS

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

GSI

a

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

a s

S

Fig. 10. Relationship between GSI and a and s.

Table 1

Examples of rock mass residual strength parameters of typical rock masses

Massive brittle rocks

(70oGSI o90)

Jointed strong rock

(50oGSI o65)

Jointed intermediate rocks

(40oGSI o50)

Very weak rock (GSI o30)

Peak Residual Peak Residual Peak Residual Peak Residual

J W 3 1.5 2 1 1.5 1 1 1

J S 3 1.5 2 1 1.5 0.75 1 0.75

J A 1 1 1 1 2 2 4 4

J c 9 2.25 4 1 1.125 0.375 0.25 0.1875

V b (cm3) 500,000 10 12,500 10 6000 10 100 10

GSI 82.2 37.4 60.3 30.3 45.2 21.5 21.4 15.1

m 10.591 2.138 4.845 1.659 2.805 1.212 1.208 0.964

s 0.138 0.001 0.012 0.000 0.002 0.000 0.000 0.000

Note: Peak and residual strength parameters are calculated based on sc ¼ 100MPa and mi ¼ 20. We only recommend use of these residual values for

GSI o75. The brittle Hoek–Brown criterion [44,45] is recommended for GSI 475.

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

σ3 (MPa)

σ 1 ( M P a )

Massive brittle rocks (Peak)

Residual

Jointed strong rock (Peak)

Residual

Jointed intermediate rocks (Peak)

Residual

Fig. 11. Peak and residual Hoek–Brown strength envelops for three

typical rock masses.




volumes in the disintegrated category are used. Therefore,

in most applications, it is reasonable to use V rb ¼ 10cm3 to

calculate the residual GSI value and hence the correspond-

ing strength parameters.

For very weak and sheared rock masses such as the

Athens Schist Formation [42] and flysch [43], the peak and

residual block volumes are roughly the same, with anaverage block volume of about 1 cm3 and very poor joint

surface condition. The estimated GSI values are in the

range of 5–15 for this type of rock masses. The volume and

joint surface condition degradation methodology presented

above is able to consistently consider the residual strength

even for the weak rock masses. The validation of the

proposed method using in-situ test data and back analysis

data is presented in the next section.

4. Verification of GSI reduction approach

4.1. Verification from in-situ block shear tests at three

cavern sites in Japan

4.1.1. Kannagawa site

The Kannagawa pumped hydropower project [46] inGumma Prefecture in Japan is now under construction

with a maximum output of 2820 MW. The powerhouse

cavern at 500 m depth has a width of 33 m, a height of

52 m, and a length of 216 m. The cavern excavation was

started in 1998 and the last bench was completed in 2000.

The rock mass at the site consists of conglomerate,

sandstone, and mudstone. The rock masses are classified

into five major groups or domains. Sixty-four uniaxial

compressive tests were conducted to determine the average

strength and standard deviation of each rock type. The

parameter mi for each rock types was obtained from a

limited number of tri-axial tests. A total of 21 block shear

tests were conducted at six test locations. The peak and

residual strength parameters estimated from the GSI

system are given in Table 3, along with the data obtained

from the in-situ block shear tests, for domains CG1, CG2,

FS1 and M1. A residual block volume of 10 cm3 is used in

the calculation. The residual joint surface condition factor

is obtained by degradation of the joint roughness. For

example, J rW ¼ JW =2 ¼ 1:25, J rS ¼ JS =2 ¼ 1 are obtained

for rock CG1. For rock FS1, J rW ¼ 1 instead of J W/2 ¼

0.75 is used because of the minimum constraint on J W is

that it cannot be smaller than 1 according to the rating [2].

GSI r is calculated using Eq. (13), and cr and fr ( ¼ fb+i )

are equivalent residual Mohr–Coulomb strength para-meters calculated from the Hoek–Brown strength para-

meters for a s3 range of 0–5 MPa. The predicted residual

strength in terms of cohesion and friction angle for CG1,

CG2 and FS1 are comparable to the results obtained from

the in-situ block shear tests. For M1 rock mass, the GSI

estimation underestimates the field residual friction angle.

ARTICLE IN PRESS

Table 2

Comparison of residual strength parameters for different residual block

sizes

Residual J c Residual block

volume V b(cm3)

GSI r Residual strength

parameters

fr cr (MPa)

2.25 Max. 27 39.4 51.4 1.10

Average 10 37.4 50.9 1.04

Min. 1 33.2 49.8 0.92

1 Max. 27 32.1 49.4 0.90

Average 10 30.3 48.9 0.85

Min. 1 26.5 47.6 0.77

0.375 Max. 27 23.1 47.1 0.57

Average 10 21.5 46.3 0.55Min. 1 18.1 44.7 0.51

0.1875 Max. 27 16.6 43.9 0.48

Average 10 15.1 43.1 0.46

Min. 1 12.1 41.3 0.41

Note: The calculation of the residual strength parameters is based on

sc ¼ 100MPa and m i ¼ 20.

Table 3

Characterization of the rock mass peak and residual strengths at the Kannagawa site using the GSI system

Rock zone CG1 CG2 FS1 M1

Peak Residual Peak Residual Peak Residual Peak Residual

GSI system J W 2.5 1.25 1.5 1 1.5 1 1.5 1

J S 2 1 1.5 0.75 1.5 0.75 1.5 0.75

J A 1 1 1 1 1 1 2 2

J c 5 1.25 2.25 0.75 2.25 0.75 1.125 0.38

V b (cm3) 309,000 10 303,000 10 295,000 10 110,000 10

GSI 73.8 32.3 64.9 27.8 64.8 27.8 53.6 21.5

sc

(MPa) 111 111 162 162 126 126 48 48

mi 22 22 19 19 19 19 9 9

c (MPa) 4.1 1.1 3.7 0.96 3 0.96 1.1 0.35

f ¼ fb+i (degree) 58 51.8 57.8 51.0 56.6 49.3 42 33.2

Block shear test c (Mpa) 5.2 1.3 3.4 1.3 3.4 0.5 1.9 0.5

f ¼ fb

+i (degree) 57 52.8 57 52.8 57 49 40 40




The residual strength estimated from the GSI system

roughly represents the lower bound of the field test data for

M1 rock mass. Note that the peak and residual strength

parameters determined from the in-situ block shear test

have been used in the cavern design. The displacement and

yielding zone predicted by the FEM analysis agree well

with the field monitoring data [46].

A comparison of the GSI estimate and the field test data

for FS1 rock mass is presented in Fig. 12. The average

residual strength estimated from the GSI system is slightly

lower than the field data average, but is well within the data

variability shown in the field test data [41].

4.1.2. Kazunogawa site

Kazunogawa power station [47], located in Yamanashi

Prefecture, Japan, at about 500 m depth, has a generating

capacity of 1600 MW. The cavern dimensions are: width

34 m, height 54 m, and length 210 m. The cavern excavation

was started in 1994 and the last bench was excavated in

1996.

The rock mass consists of sandstone and composite

rocks of sandstone and mudstone, described as two groups

(CH and CM) of rock mass types based on the Denken rock

mass classification system [48]. Three joint sets are

observed at this site. The joint spacing of the major joint

set (JEW-h) is in the range of 1–20 cm. The average joint

spacings of the other two joint sets are 25 and 50 cm,

respectively. Joints are fresh, have small undulation and

are rough. Rough joint surface assessment can also be

indirectly obtained from joint profiles in previous labora-

tory joint test. The block sizes are basically controlled by

the joint frequency of the major joint set. From the joint

density distribution graph, it is seen that the average joint

spacing is about 10 cm for CH rock mass.

Seventy-five uniaxial compressive tests were conducted

to determine the strength parameters of the intact rocks.The peak and residual shear strengths of the rock mass

were obtained from 12 in-situ block shear tests. The peak

and residual strength parameters of CH rock mass

estimated from the GSI system are given in Table 4,

along with the data obtained from the in-situ block shear

tests. A method similar to the Kannagawa case is

employed to determine the residual block volume and

joint surface condition factor. The residual GSI r is about

half of the peak GSI value. The predicted residual

strength in terms of cohesion and friction angle is

comparable to the results obtained from the in-situ

block shear tests. A comparison the GSI estimate to the

field test data is presented in Fig. 13. The GSI system

approach slightly overestimates the cohesion of both

peak and residual strengths.

4.1.3. Okawachi site

Okawachi powerhouse, which is about 280 m deep

underground, has a generating capacity of 4

320,000 KW. The cavern dimensions are: width 24 m,

height 46.6 m, and length 134.5 m. The cavern excavation

was started in 1988 and the last bench excavation was

completed in 1991. Detailed information about the cavern

construction can be found in Harada et al. [49].

ARTICLE IN PRESS

0

5

10

15

20

25

0 10

Normal stress (MPa)

S h e a r s t r e s s ( M P a )

GSI (peak)

Test data (peak)

GSI (residual)

Test data (residual)

2 4 6 8

Fig. 12. Comparison of peak and residual strength calculated from the

GSI system and field test data (FS1).

Table 4

Characterization of the rock mass peak and residual strengths at the

Kazunogawa site using the GSI system

CH rock mass

Peak Residual

GSI systemJ W 2 1

J S 2 1

J A 1 1

J c 4 1

V b (cm3) 12,500 10

GSI 60.3 30.3

sc (MPa) 108 108

mi 19 19

c (MPa) 2.29 0.87

f ¼ fb+i (degree) 54.7 49

Block shear test

c (MPa) 1.5 0.47

f ¼ fb+i (degree) 58 50.3




Rock mass around the cavern is porphrite with anaverage uniaxial compressive strength of 237 MPa. Three

sets of joints exist at the site with an RQD value that varies

in the range of 60–70. Joints are fresh and rough. In-situ

block shear tests were conducted to obtain the peak and

residual shear strength of the jointed rock masses. Plate

loading tests were also conducted to determine the in-situ

deformation modulus of the rock masses. The average

deformation modulus obtained from the field test is

24.1 GPa, which roughly corresponds to a peak GSI value

of 63.

The peak block volume shown in Table 5 was calculated

using the relationship between the V b

and RQD [50], i.e.,

V b ¼ b ((115-RQD)/3.3)3, where RQD ¼ 70 and b ¼ 35.

The large-scale roughness (J W ¼ 2.5) is determined based

on the data fitting by matching the peak strength

parameters of the GSI estimate to the peak strength

parameters from the in-situ tests. This matching excise is

also supported by the good agreement between the

deformation moduli obtained from the GSI system

(21.1 GPa) and the field test (24.1 GPa). The peak and

residual GSI values are about 63 and 32, respectively. As

can be seen from Table 5 and Fig. 14, the predicted residual

strength in terms of cohesion and friction angle is

comparable to the result obtained from the in-situ block

shear tests.

4.2. Verification from a slope stability back-analysis

Back-analysis of the strength and deformation para-

meters of the rock mass has been applied to many

ARTICLE IN PRESS

0

2

4

6

8

10

12

14

16

18

20

0 10

S h e a r s t r e s s ( M P a )

GSI (peak)

Test data (peak)

GSI (residual)

Test data(residual)

Normal stress (MPa)

8642


GSI system and field test data at the Kazunogawa site (CH).

Table 5


Okawachi site using the GSI system

CH rock mass

Peak Residual

GSI systemJ W 2.5 1.25

J S 2 1

J A 1 1

J c 5 1.25

V b (cm3) 13,352.9 10

GSI 62.8 32.3

sc (MPa) 236.7 236.7

mi 19 19

c (MPa) 4.45 1.32

f ¼ fb+i (degree) 59.2 54.8

Block shear test

c (MPa) 4.53 1.23

f ¼ fb+i (degree) 60.9 55.1

0

2

4

6

8

10

12

14

16

18

20

0 10

Normal stress (MPa)

S h e a r s t r e s s ( M P a

)

GSI (peak)

Test data (peak)

GSI (residual)

Test data (residual)

2 4 6 8


GSI system and field test data at the Okawachi site (CH). Note that the

measured and predicted residual strength envelopes are overlapping.




engineering projects [51]. It is especially useful when failure

has occurred and reached to the residual state as is in the

case of slope instability. It is tempting to consider the

possibility of back analyzing existing slope failures in order

to determine the shear strengths that must have been

mobilized in the full-scale rock mass at the time of the

failure. In fact, back-analysis of slope failures can be a veryimportant source of shear strength data [52].

In back-analysis of slope stability, the shear strength

parameters, c and f are adjusted till the factor of safety is

unity (1.0) as a prerequisite for failure in a limit equilibrium

analytical model. This pair of parameters can be considered

as the residual strength parameters. This is so because it is

generally required that the rock mass must experience a large

deformation in excess of that required to mobilize the peak

strength. Thus, the resistance mobilized by reactivated

landslides is equal to the residual strength of the material

within the slip zone. This is, however, only valid for rotational

or sliding failure involving the entire failure volume, not for

progressive failures. Thus, a back-analysis using limit

equilibrium method or FEM/DEM employing strength

reduction method can obtain residual strength parameters.

Fig. 15 presents the relationship between the friction

angles and cohesive strengths mobilized at failure for some

slopes [52]. Cohesion is generally small (o 0.2 MPa) and

the friction angle varies between 201 and 451 for most

cases. It is interesting to note that for ‘‘undisturbed hard

rock masses,’’ (f ¼ 40–451 in Fig. 15) the cohesion is in the

range of 0.3–0.5 MPa. Based on our experience, weconsider the back-analyzed c and f values representative

of the residual strength parameters.

Sjo ¨ berg [36] used the Hoek–Brown strength criterion to

estimate the strength of the rock mass at the Aznalcollar

open pit mine located in southern Spain. The dominant

footwall rock types are slates and schist with well-

developed cleavage. At the end of mining, the pit was

approximately 1300 700 m in area and 270 m deep with

an overall slope angles varied from 301 to 381. Despite the

relative moderate slope, the mine has suffered several large-

scale failures of the footwall slope. Failure was not

structurally controlled but rather stress controlled. The

failure surfaces were identified from the slope monitoring

using techniques such as surfaces displacement stations and

inclinometers.

ARTICLE IN PRESS

0 5 10 15 20 25 30 35 40 45 50

Friction angle - degrees

0.0

0.1

0.2

0.3

0.4

0.5

C o h e s i o n - M P a

R e s i d u a l s t r e n g t h o f

s l i c

k e n s i d e d s u r f a c e s

c o a

t e d w i t h h i g h c l a y

m i n

e r a l c o n t e n t m a t e r i a l s

D i s

t u r b e d m a t e r i a l w i t h

r o u

n d e d w e a k l y c e m e n t e d

p a r t i c l e s a n d a p p r e c i a b l e

c l a

y m i n e r a l c o n t e n t

U n

d i s t u r b e d s o i l a n d

j o i n t e d r o c k m a s s e s

w i t h r e l a t i v e l y l o w

c l a

y m i n e r a l c o n t e n t

R o c k m a s s e s o r d u m p s

c o n t a i n i n g h a r d c l e a n

a n g u l a r i n t e r l o c k i n g

p a r t i c l e s a n d b l o c k s

Undisturbed hard rock masses with no major structrural patterns dipping towards slope

Undisturbed hard rock masses with no through- going structures dipping towards slope

Undisturbed rock masses with a few structures dipping towards slope

Soft rock masses or jointed hard rock disturbed by blasting or excess loading

Weatherd soft rock or discontinuities in hard rock

Clay Soil

Sand

Fig. 15. Relationship between the friction angles and cohesive strengths mobilized at failure for the some slopes [52].




Because failures were not structurally controlled, the

continuum numerical tool FLAC was used to simulate the

slope failure by using a perfectly plastic material model

[36]. It was found that by assuming disturbed rock mass

parameters, good agreement could be achieved between

estimated strength values and back-calculated strengths

from observed slope failures in the footwall. The presence

of the stiff and strong pyrite prevented the failure to initiate

at the toe. The failure was developed rather inside the

slope. At the stage when the toe buttress zone reachedcritical state, the post failure state was probably reached

and hence the calibrated strength values were representa-

tive of the residual rock mass strength.

No direct joint spacing and surface condition were

available in the report by Sjo ¨ berg [36]. However, peak GSI

values, inferred from the RMR values, were given. The

representative GSI values for slate and schist-foliation are

61 and 58, respectively. As listed from Table 6, the GSI

values can be estimated by using the good and fair joint

surface condition for slate and schist and their correspond-

ing block volume (back-fitted from known GSI value),

respectively. Using the method developed in this study, we

can estimate the peak and residual strength of the rock

masses. From the back-analysis, the residual cohesion for

the slate is found in the range of 0–0.3 MPa and the

residual friction angle in the range of 25–351. The estimated

cohesion and friction angle for the same rock mass, using

the GSI reduction approach, are 0.39MPa and 301,

respectively. As can be seen from Fig. 16, the estimated

residual strength of the slate is well within the lower and

upper bounds indicated from the back-analysis.

Back-analysis data from slope stability provides excel-

lent in-situ data for method validation. As more data

becomes available, the proposed method for rock mass

residual strength estimation can be further validated.

4.3. Discussion of results

Traditionally, the determination of mechanical proper-

ties of jointed rock masses in Japan and other countries is

achieved through well planned and executed in-situ blockshear test and plate-loading test. Such tests are expensive

and time consuming. Most importantly, results only

become available once underground access has been

established. An alternative to the test approach is the use

of a rock mass classification system such as the GSI system

to provide design parameters early in the design phase and

reduce the need for extensive in-situ testing. Nevertheless,

in-situ tests can be used to verify the GSI prediction or the

observational (back-analysis) method [53] will be required

to confirm the GSI predictions.

The quantitative approach uses the block volume and

joint surface condition factor to determine both the peak

and residual GSI values. These input parameters in the

validation examples were obtained from field mapping and

from borehole logging data. The strength and deformation

parameters estimated from the GSI system are very close to

those obtained from in-situ tests or back analysis,

indicating that the GSI system can be effectively applied

to the design of underground caverns and rock slopes.

The degradation of the block volume and the joint

surface condition for CG2 rock mass at the Kannagawa

site is graphically presented in Fig. 17. GSI is reduced from

a peak value of 64.9 to a residual value of 27.8. The gradual

decrease of the GSI value can be linked to the post-peak

strain softening of the rock mass (see Fig. 1(a)). Future

ARTICLE IN PRESS

Table 6


Aznalcollar open pit mine footwall using the GSI system

Slate Schist-foliation

Peak Residual Peak Residual

GSI systemJ W 1.5 1 2 1

J S 1.5 0.75 1.5 0.75

J A 1 1 2 2

J c 2.25 0.75 1.5 0.375

V b (c m3) 100,000 10 150,000 10

GSI 61.0 27.8 57.9 21.5

sc (MPa) 25 25

mi 9 8

c (MPa) 0.97 0.39 0.87 0.27

f ¼ fb+i (degree) 38.8 30.1 37 27.2

Back-analysis using limit equilibrium method [36]

c (MPa) 0–0.3 0–0.12

f ¼ fb+i (degree) 25–35 22–30

0

1

2

3

4

5

6

7

8

0

Normal stress (MPa)

S h e a r s

t r e s s

( M P a

)

GSI (peak)

GSI (residual)

Back analysis (lower bound residual)

Back analysis (higher bound residual)

GSI (peak)

GSI (residual)

Back analysis (average)

8642

Fig. 16. Comparison of the residual strength calculated from the GSI

system and back calculated data at the Aznalcollar open pit mine footwall

(slate).




research will address the issue of the rate of GSI value

decrease associated with the plastic strain.

The ratios of residual GSI r

to peak GSI depend on the

peak GSI values, as shown in Fig. 18. The investigated case

histories have peak GSI values between 40 and 80 and the

GSI r/GSI ratios vary from 0.37 to 0.51. The point with

a low GSI value of 21 is adopted from Table 1 with the

GSI r/GSI ratio obtained by our proposed method. For

very weak rock masses, the residual GSI r is equal to the

peak GSI . If a trend line is drawn, it should pass through

the point (0,1). A trend line by forcing it to pass through

point (0,1) is hence obtained (as shown in Fig. 18). The

residual GSI r value can then be empirically expressed as a

function of the peak GSI value as

GSI r ¼ GSI e0:134GSI. (18)

Russo et al. [7] suggested that the residual GSI r value is

36% of the peak GSI value. This is represented as a

horizontal line in Fig. 18. It is observed that their

suggestion may underestimate the residual GSI r values

ARTICLE IN PRESS

0.1

1

10

100

1000

10E+3

100E+3

1E+6(1m3)

10E+6

B

l o c k V o l u m e V b ( c m

3 )

Blocky - very well interlocked

undisturbed rock mass consistingof cubical blocks formed by three

orthogonal discontinuity sets


Very Blocky - interlocked, partially

disturbed rock mass with multifaceted

angular blocks formed by four or morediscoutinuity sets


Blocky/disturbed - folded and/or

faulted with angular blocks formed by

many intersecting discontinuity sets


Disintegrated - poorly interlocked,

heavily broken rock mass with amixture or angular and rounded

rock pieces


75

50

30

70

65

60

55

45

40

35

25

20

15

10

80

8590

95

Massive - very well interlocked

undisturbed rock mass blocks formed

by three or less discontinuity sets

with very wide joint spacing

Joint spacing > 100 cm

5N/A N/A

Foliated/laminated/sheared - thinly

laminated or foliated, tectonically shearedweak rock; closely spaced schistosity

prevails over any other discontinuity set,

resulting in complete lack of blockiness


V e r y g o o d

V e r y r o u g h ,

f r e s h u n w e a t h e r e

d s u r f a c e s

G o o d

R o u g h , s l i g h t l y w e a t h e r e d ,

i r o n s t a i n e d s u r f a c e s

F a i r

S m o o t h , m o d e r a t e l y w e a t h e r e d o r

a l t e r e d s u r f a c e s

P o o r

S l i c k e n s i d e d ,

h i g h l y w e a t h e r e

d s u r f a c e s w i t h

c o m p a c t c o a t i n g o r f i l l i n g s o f

a n g u l a r f r a g m e n t s

V e r y p o o r

S l i c k e n s i d e d ,

h i g h l y w e a t h e r e

d s u r f a c e s w i t h

s o f t c l a y c o a t i n g s o r f i l l i n g s

12 4.5 1.7 0.67 0.25 0.09

Joint Condition Factor Jc

20

30 cm

60

100 cm

40

50

10 cm

7080

90

5

2

1 cm

3

150

(1 dm )3

Block Size

Joint or Block Wall Condition

Degradation of joint surface condition

D e gr a d a t i on of b l o c k v ol um e

Residual

Residual

Peak

D e g

r a d a t i o

n o f G

S I

Peak

σ

Fig. 17. Degradation of the block volume and joint surface condition of CG2 rock mass from peak to residual state.




for poor quality rock masses (e.g., GSI o40). For very

good quality rock masses (GSI 480), their suggestion may

overestimate the residual GSI r values.

To obtain reliable results of the residual GSI r value, the

method proposed in Section 3.2 should be followed, i.e., by

obtaining the residual block volume and joint surface

condition factor and using the GSI chart or Eq. (13) to

calculate the residual GSI r. For quick estimates, Eq. (18)

can also be utilized if the peak GSI value is known.

Because very large straining is needed to reach the true

residual state, the residual GSI r value discussed here refers

to the post-peak strength in a limited straining range. In

the design of underground structures, most residual

strength parameters utilized are in fact the residual post-peak strength parameters representing limited post-peak

deformation.

The residual strength of intact rocks, as interpreted from

the triaxial test, is at the same level as the residual strength

of the jointed rock mass. In the low confinement range, the

residual cohesion and friction angle of the Tennessee

Marble are 2.4 MPa and 51.61, respectively. As can be seen

from Table 3 and Table 5, the residual strengths of some of

the hard jointed rock masses (CG1 conglomerate and CH

porphrite) are roughly at the same level of the residual

strength of intact rocks (Tennessee Marble), suggesting

that our assumption of the independence of the residual

block volume on the original jointing state is valid.

As stated previously, if the peak block volume is small

(o10cm3), the residual block volume is equal to the peak

block volume and the same approach outlined above can

be applied to the estimation of the strength parameters. In

this fashion, consistent estimation of the both peak and

residual strength parameters can be obtained.

The proposed method is applicable to most rock types

when failure is dominated by shear failure. Care must be

given for brittle failure of massive rocks involving spalling

failure and very weak rocks that have been ‘‘over

consolidated’’ or ‘‘re-bonded.’’ In such a case, special

failure criteria such as brittle Hoek–Brown failure criterion

[44] should be used and proper test program be planned for

the determination of the residual strengths. Furthermore, if

the rock mass fails by block rotation and local crushing,

probably a different analysis approach such as UDEC or

3DEC should be considered instead of a continuum

analysis. The users must be aware of the limitations when

applying the GSI system and the methodology fordetermining the peak and residual strength parameters

using this quantitative approach.

5. Conclusions

It is observed from laboratory and field test data that

following the strain-softening behavior of rocks under

loading, the residual strength represents more or less the

mobilized shear strength along a surface or shear zone of

the fractured rock. The post-peak strength depends on the

resistance developed on the failure plane (zone) against

further straining. Initially, the fracture orientation, degree

of interlocking, surface irregularity or roughness will affect

the post-peak load level. However, as the straining

continues, the residual strength is less dependent on these

factors.

The Geological Strength Index (GSI) system is a

universal rock mass classification system. It is a rock mass

classification system that is directly linked to engineering

parameters such as Mohr–Coulomb or Hoek–Brown

strength parameters or rock mass modulus. The current

GSI system guidelines, however, are for the estimation of

the peak strength and do not include guidelines for the

estimation of the rock mass’ residual strength that yield

consistent results. A new method is proposed here toextend the GSI system for the estimation of rock mass’s

residual strength. The peak GSI value is reduced based on

the reduction of the two major controlling factors in the

GSI system, i.e., residual block volume V rb and residual

joint condition factor J rc, to obtain the residual GSI r value.

The residual block volume is found to be in the category of

the ‘‘disintegrated’’ rocks in the GSI chart, characterized

by the facts that the failed rock masses at the residual

strength level are poorly interlocked, heavily broken with a

mixture of angular and rounded rock pieces. The average

block size of 10 cm3 is suggested for the residual GSI r value

estimation. For joint surface condition, the major factor

that alters the condition in post-peak region is the

reduction of joint surface roughness. The actual degrada-

tion of the joint surface is based on the concept of

mobilized residual joint roughness suggested by Barton

et al. [24]. The large-scale waviness and the small-scale

smoothness of joints can be calculated by reducing their

peak values by half with conditions to meet the minimum

values. The joint alteration factor J A is assumed un-

changed. The residual GSI r value is calculated from the

relationship between GSI r and V rb and J rc.

It has also been assumed that the intact rock properties

such as sc and mi remain unchanged as the rock mass

changes from its peak to residual state. Hence, the residual

ARTICLE IN PRESS

GSIr / GSI = e

-0.0134GSI

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

GSI

G S

I r / G S I

GSIr = 0.36GSI

Fig. 18. Relationship between GSI r/GSI ratio and GSI .




strength parameters are calculated using the same form of

the generalized Hoek–Brown strength criterion. The

equivalent Mohr–Coulomb strength parameters are calcu-

lated based on the Hoek–Brown strength parameters.

The proposed method for the estimation of rock mass

residual strength is validated using in-situ block shear test

data from three large-scale cavern construction sites andthe data from the back-analysis of a rock slope stability.

The estimated residual strengths, calculated using the

residual GSI r value, are in good agreement with field test

data or back analyzed data. The proposed method for

residual strength estimation extends the GSI system and

adds quantitative means to determine the complete set of

rock mass properties needed for design.

When applying the GSI system to a numerical simula-

tion, the users must be aware of the limitation of the

approach related to quantifying a discontinuous rock mass

in a continuum-modeling framework. In certain circum-

stances, a discontinuous analysis tool, rather than con-

tinuum models with parameters obtained by the GSI

system, should be used. In addition, one needs to be aware

of the mechanical instability problem associated with

strain-softening materials in continuum elasto-plastic

analyses. The simulation results could be highly dependent

on the mesh size and slight change of material parameters;

hence the uniqueness of a solution can often not be

guaranteed. Although the paper provides a contemporary

method for rock mass’s peak and residual strength

parameter determination, its successful application relies

heavily on the professional judgment, as is typically the

case in rock mechanics and rock engineering.

Acknowledgements

This study was funded by Tokyo Electric Power Services

Co. Ltd (TEPSCO). The authors wish to thank Tokyo

Electric Power Company (TEPCO) for providing access to

test sites and test data and permitting to publish the results.

The authors also thank Evert Hoek for his valuable

comments and suggestions during the preparation of the

manuscript.

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