Peng S., Zhang J., Engineering Geology for Underground Rocks

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4.6 Rock failure criteria 95

tan129

tan



(4.31)

tan129



(4.32)

Fig.4.19. The Mohr-Coulomb yield surface and different possibilities for corre-

sponding Drücker-Prager yield conditions.

When the external pyramid envelope is used, the conversion formulae

for the material parameters from the Mohr-Coulomb criterion to the

Drüker-Prager criterion are as follows:

)sin3(3

sin2



(4.33)

)sin3(3

cos6



(4.34)

96 4 Rock strength experiments and failure criteria

When the internal cone envelope coincident at

= S/6 is used, the con-

version formulae for the material parameters from the Mhor-Coulomb cri-

terion to the Drüker-Prager criterion become:

)sin3(3

sin2



(4.35)

)sin3(3

cos6



(4.36)

4.6.5 Modified Lade criterion

The modified Lade criterion was proposed by Ewy (1998) based on Lade

strength criterion (Lade 1984). In this criterion the three effective principal

stresses were considered, and this criterion finds applications in petroleum

engineering for wellbore stability and sand production. The modified Lade

can be expressed as follows:

 27

)(

(4.37)

where

)'()'()'(

321

SSSI 

VVV

)')(')('(

321

SSSI 

VVV

tan

sin1

)sin79(tan4



Modified Lade criterion considers the influence of intermediate princi-

pal stress on rock failures. The failure predicted by this criterion is less

failure/conservative than the Mohr-Coulomb criterion because the latter

ignores the influence of intermediate principal stress (

). The modified

Lade predicts more failure/aggressive than the Drüker-Prager criterion, be-

cause the latter predicts a greater strengthening effect from

4.6 Rock failure criteria 97

4.6.6 Hoek-Brown criterion

Through study of the experimental results of a wide variety of rocks, Hoek

and Brown (1980) presented the following empirical rock failure criterion

for jointed rock masses:

sUCSmUCS )/'(''

331



VVV

(4.38)

where

are the maximum and minimum effective principal stresses,

respectively; m and s are the constants depending on the properties of the

rock and on the extent to which it has been broken before being subject to

the stresses; a is the constant depended upon the rock mass characteristics;

m ranges from 0.001 (extremely week rock) to 25 (extremely strong rock)

and s = 1 for intact rock; s < 1 for previously broken rock.

For intact rocks that make up the rock mass, Eq. 4.38 simplifies to:

331

''' sUCSmUCS 

VVV

(4.39)

For clastic sediments, Hoek and Brown (1997) suggested using the

following values for m:

m = 22 for conglomerate; m = 19 for sandstone; m = 9 for siltstone; and

m = 4 for claystone.

The uniaxial compressive strength of the rock mass (

) is obtained by

setting

= 0 in Eq. 4.38 (Hoek 2007):

UCSs

(4.40)

The tensile strength of the rock mass (

) can be obtained from the fol-

lowing equation:

msUCS

/

(4.41)

The constant a, s, and m can be expressed as the follows:

)(

3/2015/ 

 eea

GSI

(4.42)



GSI

1428

100

exp

(4.43)



GSI

100

exp

(4.44)

98 4 Rock strength experiments and failure criteria

where m is the material constant for the intact rock; D is the disturbance

factor depended on the degree of disturbance to which the rock mass has

been subjected by blast damage and stress relaxation. It varies from 0 for

undisturbed in-situ rock masses to 1 for very disturbed rock masses; GSI is

the Geological Strength Index introduced by Hoek (1994). GSI varies from

0-100 and can be estimated from Fig. 4.20 (Hoek 2007).

Fig. 4.20. Estimate of Geological Strength Index (GSI) based on geological de-

scriptions (after Hoek 2007).

References 99

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gested methods. Pergamon Press, Oxford

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moduli on stresses and strains around axisymmetric boreholes. Rock Mech

Rock Engng 22:189-203

Ewy RT (1998) Wellbore stability prediction using a modified Lade criterion.

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way

Drüker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design.

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US National Congress of Appl Mech Proc p1015-1021

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chanical properties of clastic rocks. Environ Geol 51:113-120

100 4 Rock strength experiments and failure criteria

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phys Res 76:1255-1269

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axial stress and the effect of pore pressure on the criterion. Proc 5

Rock

Mech Symp in Rock Mechanics Fairhurst C (ed), Pergamon p563-577

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Young scientists, China Sci

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in Mining. West Virginia University, pp 362-371

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5 Sedimentary rock masses and discontinuities

5.1 Rock mass and discontinuities

5.1.1 Introduction

One of the most prominent features of the earth’s upper crust is the pres-

ence of joints and fractures at all scales. The fractures and joints usually

are named to be discontinuities. A rock mass consists of both rock blocks

and discontinuities. A rock block/matrix and a rock mass have significant

differences in geomechanical behaviors. Nearly every physical property of

sedimentary rock (such as mechanical properties; hydraulic, thermal, and

electrical conductivities; and acoustic properties) is determined to some

extent on the fractures and the fluids they contain. The success of many

applications such as efficient recovery from fractured reservoirs, hazardous

waste disposal, and geothermal energy extraction depends on a thorough

understanding of fracture behavior. Many petroleum reservoirs and coal

seams are situated in fractured porous formations. Thus, prior to any rock

engineering it is necessary to determine the geometrical and mechanical

properties of the fractures and rock mass from lab and the field. For in-

stance, the geometry, locations, orientation, aperture variations and fluid-

mechanical properties of fractures and rock mass are needed to be deter-

mined.

The discontinuities can be the single most important factor governing

the deformability, strength, and permeability of the rock mass. Moreover, a

particularly large and persistent discontinuity could critically affect the

stability of any underground excavation (Hudson and Harrison 1997). For

these reasons, it is necessary to develop a thorough understanding of the

geomechanical properties of discontinuities and rock mass and understand

the way in which discontinuities affect geological engineering.

102 5 Sedimentary rock masses and discontinuities

5.1.2 Discontinuities

Bedding

There are different kinds of discontinuities in rock formations. Bedding is

one of the most common geologic phenomena in sedimentary rocks. The

bedding plane or interface between two layers in the sedimentary rock

mass represents geologically the transitive interface from one sedimentary

environment to another, and it also represents an interruption of sedimen-

tary planes. A bedding plane is a weak plane, usually consisting of plant

detritus, mica, and other weak minerals. Therefore, it is usually treated

mechanically as a weak plane.

Unconformity

Unconformity plane is a surface that represents a break in the geologic re-

cord, with the rock unit immediately above it being considerably younger

than the rock beneath. There are three major aspects to consider:

1. Time. An unconformity develops during a period of time in which

no sediment is deposited.

2. Deposition. Any interruption of deposition or breaks in sedimenta-

tion is an unconformity.

3. Structure. Structurally, unconformity may be regarded as planar

structures separating older rocks below from younger rocks above.

A plane of unconformity may be a surface of weathering, erosion, or de-

nudation, or a surface of non-deposition, or possibly some combination of

these factors. It may be parallel to the upper strata, make an angle with the

upper strata, or be irregular. Subsequent Earth movements may have

folded or faulted it. Therefore, rock mechanical behaviors are very differ-

ent cross the unconformity plane.

Weak layer

A weak layer in the sedimentary rock mass is the layer with very low

strength. Rock construction is most likely to fail in this layer. Therefore,

the weak plane plays a key role in stability of rock engineering.

Tectonic structural plane

Tectonic structural plane includes faults, fractures, and other discontinui-

ties induced by tectonic activities.

5.2 Mechanical characteristics of clastic rocks 103

5.2 Mechanical characteristics of clastic rocks

The mechanical properties of clastic rocks are not only affected by the ex-

ternal factors, such as the state of stress and surrounding geological envi-

ronment, but also strongly dependent on the depositional and sedimentary

environments, including components, textures, and structures of the rocks.

It is of importance to study the mechanical properties of clastic rocks for

energy industry, because oil and gas, as well as coal, are situated in these

rocks (Peng and Meng 2002). Until now, most research on the microstruc-

ture of the rock and its deformation and strength behaviors mainly focuses

on granites and other hard rocks. Therefore, relations between the sedi-

mentary characteristics and mechanical properties of clastic rocks need to

be addressed, particularly those of soft rocks such as mudstone and shale

(Peng 1998).

The formations of coal measures are primarily composed of clastic rocks

and coal seam. The rocks in coal measures mainly consist of sandstones,

siltstones, and mudstones. For example, coal measures of the Permian pe-

riod in the Huainan coalfield in China were formed from a delta plain envi-

ronment (Peng and Meng 2002), which contains 33.66% of sandstones,

8.7% of siltstones, 50.38% of mudstones, and 7.23% of coal seams. Sedi-

mentary rocks in coal measures originated in shallow crust, and their for-

mation and existing environments are distinctly different from those of ig-

neous or metamorphic rocks. Because of their lithological characteristics,

complex components, and textures, clastic rocks differ considerably from

other rocks in mechanical properties. Therefore, it is important to establish

the qualitative and quantitative relations between sedimentary parameters

and mechanical properties in clastic rocks for recognizing the mechanical

properties in different sedimentary rocks, revealing deformation and fail-

ure mechanisms of clastic rocks, and solving the related engineering prob-

lems (Meng et al. 2006). The following sections present lab experiments to

determine clastic rocks mechanical properties.

5.2.1 Sample preparation and test methods

The rock samples were obtained from the roof and floor strata of the pri-

mary coal seams in the Permian coal measures in the Xinji coal mine, the

Huainan coalfield in China. In order to make the testing results conform as

much as possible to the natural status, the rock samples were promptly

packaged and fully waxed after they were picked up. The lab experiments

are conducted to test the mechanical properties, observe the microstruc-

tures of rock slices by using optical microscope, and analyze the mineral

104 5 Sedimentary rock masses and discontinuities

and chemical components for 55 samples. The quantitatively statistical

analyses are conducted for these experimental results.

The mechanical properties of rocks are tested in the servo-controlled

testing system (MTS 815.02). Using the optical microscope, the sedimen-

tary parameters such as the component, grain size, intersertal material, ce-

mentation type, and structural support type in all samples of clastic rocks

are observed and analyzed statistically. In the process of quantitative

analyses of the granularity of the rock slices, the object glass desk of the

microscope is moved in both horizontal and vertical directions to deter-

mine the size of detritus grain (lattice number) of the sample slice lying in

the cross-line in the microscope. In each rock slice 500 points are meas-

ured; then the grain diameter can be obtained by multiplying the measured

lattice numbers by the value of the actual size (in mm). The value of the

actual size for each lattice is measured using the standard micro-ruler. The

rock grain size is measured by the Phi (

) scale as a log transformation of

the grain diameter in millimeters in order to simplify computation of statis-

tical parameters. Because the

scale is now used almost exclusively for

computation and is gradually replacing the millimeter scale, it is used in

the ongoing analyses. The following expression is used to calculate the

standard grain-size scale:

log

(5.1)

where:

is the grain-size scale; D is the diameter of the grain in mm. It can

be seen that the larger diameter of the grain size has a smaller

scale.

The average grain size in the

scale can be calculated by the following

equation:

)(

845016

III



)

(5.2)

where:

)

is the average grain-size

scale

䯸

which reflects the hydrody-

namic performance during deposition of terrigenous clasts

䰇

䫺

and

are the corresponding grain sizes of the cumulative contents of

16%

䯸

50%

, and 84% in the cumulative curve of the clastic grains, respec-

tively.

5.2.2 Clastic rock contents versus rock mechanical properties

Statistical analyses of experimental results show that the mechanical prop-

erties are highly related to the content of the clastic grains and quartz in

clastic rocks. In this research, the clasts whose grain diameters are more