SHEAR STRENGTH CRITERIA OF ROCK JOINTS

By,V.GOUTHAM

13MI60R09MINING ENGINEERING

INTRODUCTION

The term "rock-joint" is used to describe the mechanical discontinuities of geological origin, that intersect near-surface rock masses.

The surface roughness of rock joints depends on their mode of origin, and on the mineralogy of the rock.

Roughest joints are those that formed in intrusive rocks in a tensile brittle manner, and smoothest the planar cleavage surface in slates.

CHARACTERISTICS OF ROCK JOINTS: Joint Sets and Length: Joints and Fractures, Set Number, and Persistence Joint Orientation: Joint Plane Orientation and Representation Joint Spacing: Joint Spacing, Frequency, Block Size, and RQD Joint Surface and Opening: Roughness, Matching, Aperture and Filling

MECHANICAL PROPERTIES: Normal Stiffness and Displacement Shear Strength of Rock Joints and Fractures

FACTORS AFFECTING Range of normal stress Mode of failure Influence of roughness

COMPONENTS OF SHEAR STRENGTH FOR NON-PLANAR JOINTS

Newland and Allely (1957) equation for low σn based on the observed dilatant behaviour of granular material such as sand The strength components φ b and i are usually termed the "basic angle of friction" and the "effective roughness”.

At high normal stresses The real slope problem involves many different i values.

dn is the peak dilation angle

sn is the shear component

MECHANISM OF SHEAR FAILURE

DEVELOPMENT OF PEAK STRENGTH CRITERION FOR ROUGH UNDULATING JOINTS

The results of direct shear tests performed on a wide variety of model tension fractures with few assumptions of values gives following relations:

The strength component 2dn is stress dependent basic friction angle φb for the model materials ranges from 28.5 ° to 31.5 °

The proposed peak strength criterion for rough-undulating joints:

A rapid estimate of shear strength and the overall shape of the curves for different values of σ c (or JCS) can be obtained from Figure.

The uncertainty connected with high values of normal stress (> %) is due to the negative values of peak !dilation angle, dn,.

ESTIMATION OF SHEAR STRENGTH AT VERY LOW NORMAL STRESSES

The following curvilinear envelope is most suitable:

ignoring the shearing component at low normal stress. Maximum value of arctan(Ƭ/σn) in the region is of 70 °.

A shear strength envelope for rough joints having a vertical tangent at or close to the shear stress axis instead of a 'cohesion‘ intercept is inherently satisfying as a limiting condition. The use of a 'cohesion‘ intercept for rock joints is inherently dangerous.

ESTIMATION OF SHEAR STRENGTH AT HIGH NORMAL STRESSES

If the effective normal stress is high, or if the unconfined compression strength of the rock is low, the dimensionless ratio (σn / σc) reduces towards unity, and the resultant shear strength theoretically approaches Ƭ=σn tan φb.

There is an increasing error between prediction and test results if if the effective normal stress) exceeds the rock's unconfined compressive strength.

JCS=σ1-σ3

σ1=axial stress at failureσ1-σ3=effective confining

pressure

Detailed review of experimental data Experimental predicted

The most obvious reason for the low predicted shear strength for the faults in the Solenhofen and Oak Hall limestones is the ductility. Mogi [4] observed that the fracture behaviour of rocks changes from brittle to ductile with increasing confining pressure, the transition pressure being higher for stronger rocks, and appreciably lower for weaker marbles and limestones.

THE PROBLEM OF JOINT WEATHERING The depth of penetration of weathering into joint walls depends largely on

the rock type, and in particular on its permeability. The present problem is to estimate the effective JCS value.

Two cases possible:1. rock mass and rock blocks are collectively weathered or altered to a

uniformly low strength.2. the joint walls are only weathered to a limited depth. As a direct result of surface weathering processes the walls of water

conducting joints become weaker than the surrounding rock if the latter is relatively impermeable. Secondly,both JCS and σc are greatly reduced

THE STRENGTH OF WEATHERED JOINTSThe unconfined compressive strength of the unweathered rock was

measured, and the value of JCS was obtained from "back-analysis" of the strength exhibited at failure. This represents a realistic approximation for obtaining a safe (lower-bound) estimate of shear strength, when using the peak strength criterion described earlier. In general JCS/σ c =1/4.

NON-PLANAR JOINTS OF REDUCED ROUGHNESSSmooth but undulating sheeting, foliation, and bedding joints would probably

be amongst the intermediate class, grading down to smooth and nearly planar foliation, bedding and shear joints.

There exists much reduced dilation, dn, and in particular, little or no shear component, Sn. The smooth surfaced undulations would tend to slide over one another. Three broad classes of non-planar surfaces have been "defined" in Figure below. The joint roughness coefficients: 20, 10 and 5 for classes A, B and C are purely empirical

EFFECT OF SCALE ON THE SHEAR STRENGTH OF JOINTS

Shear strength developed is strongly dependent on the compressive (or tensile) strength of the rock, which is itself scale dependent.

The larger asperities that are sheared at high normal stress will be fundamentally weaker (in units of stress) than the small ones sheared at low normal stress.

Both void spaces and contact areas were larger on an in situ scale for any given normal stress.

When extrapolating σn or JCS to the in situ scale some reduction might be involved in practice, and this should be allowed for by some form of safety factor.

JRCn =JRCo (Ln /Lo )-.02JRC

JCSn =JCSo (Ln /Lo )-.03JRC

SHEAR STRENGTH CRITERION FOR INNTACT ROCK, FRACTURED ROCK, ROCK KOINTS, ROCK FILLS

• The non-linear Hoek–Brown (H-B) criterion for intact rock was eventually adopted, and many have also used the non-linear shear strength criterion for rock joints, using JRC, JCS. The actual shear strength of rock masses, meaning the prior failure of the intact bridges and then shear on the fractures and joints at larger strains.

CRITICAL STATE FOR ROCK When effective normal stress mobilized on a potential failure plane finally

reaches the level of the confined compression strength (σn=σ1-σ3), the one-dimensional dilation normally associated with shearing will be suppressed.

. The critical state is the stress condition under which the Mohr envelope of peak shear strength reaches a point of zero gradient.

This represents the maximum possible shear strength of the rock.

It will be seen that the ultimate shear strength represented by point C is equal to the critical effective confining pressure (σ3) required to reach the critical state. The normal stress is equal to 2σ3.

An extensive recent study by Singh et al.(2011) in Roorkee University has revealed that σc=σ3 (critical) for the majority of rock types

SHEAR STRENGTH OF ROCK JOINTS AND SOME PROBLEMS

Figure below illustrates the form of the third strength criterion It will be noted that no cohesion intercept is intended. It will also be noted

that subscripts have been added to indicate scale-effect. It will be noted that the peak dilation angles vary significantly. This is

important when transforming principal stresses to normal and shear stresses that act on a plane.

ISRM suggested methods for shear testing rock joints have suggested multi-stage testing of the same samples.

Since there will be a gradual accumulation of damage, there is already a ‘built-in’ tendency to reduce friction (and dilation) at higher stress, and therefore to increase the apparent cohesion intercept (if using M-C interpretation).

Problems identified also include continued use of φb in place of φr. These problems are accentuated if JRC is high, and JCS low.

Barton (2007) (following Barton, 1971) showed that this causes over-closure, and higher resulting shear strength, especially in the case of rough joints.

The multi-stage testing procedures for rock joints has prolonged the artificial life support of cohesion, affecting numerical modelling and countless thousands of consultants’ reports and designs.

NUMERICAL MODELLING OF JOINTS Rock masses are the most complex engineering materials utilized by man. road, rail and water transport tunnels, dam site location, oil and gas

storage, food storage and sports facilities in caverns, and we are heading for final disposal of high-level nuclear waste.

The complexity may be due to variable jointing, clay-filled discontinuities, fault zones, anisotropic properties, and dramatic water inrush and rock-bursting stress problems

When modelling a rock mass in a 2Drepresentation, the deformation modulus, Poisson’s ratio, shear and tensile strengths, and density will figure as a minimum in both models

In the case of the additional representation of the jointing, one will in the case of UDEC-BB also specify values of JRC, JCS and φr for the different joint sets, the spacing of cross-joints and block sizes Ln are specified

Attempts to model ‘break-out’ phenomena are not successful with standard M-C or H-B failure criteria, because the actual phenomena are not following in ‘c plus σntan φr’. The reality is degradation of cohesion at small strain and mobilization of friction

Rock masses actually follow a complex progression to failure, as suggested in Barton and Pandey (2011), who recently demonstrated the application of a similar ‘c then σn tanϕ’ modelling approach and applied it in FLAC3D, for investigating the behaviour of multiple mine-stopes in India

A demonstration of the simpler, Q-based continuum-model ‘cohesive component’ (CC) and ‘frictional component’ (FC) for a variety of rock mass characteristic. Low FC needs more bolting, while low CC needs more shotcrete, even local concrete linings.

They already exist in the Q-parameter logging data, and the effect of changed conditions such as clay-fillings

UDEC-MC and UDEC-BB modellers often exaggerate the continuity of modelled jointing .

FUNDAMENTAL GEOTECHNICAL ERROR The subject of concern is the transformation of stress from a principal (2D)

stress state of σ1 and σ2 to an inclined joint, fault or failure plane, to derive the commonly required shear and normal stress components ז and σn.

If the surface on to which stress is to be transformed does not dilate, which might be the case with a (residual-strength) fault or clay-filled discontinuity, then the assumption of co-axial or co-planar stress and strain is valid

. If on the other hand dilation is involved, then stress and strain are no longer co-axial. In fact the plane onto which stress is to be transferred should even be an imaginary plane

. Bakhtar and Barton (1984) were attempting to biaxially shear diagonally fractured 1m3 samples of rock. The sample preparation was unusual because of principal stress (σ1) driven controlled-speed tension fracturing. This allowed fractures to be formed in a controlled manner.

The conventional and dilation corrected stress transformation equations can be written as

CONCLUSIONS In the majority of publications the results of shear tests on rock joints are

reported in terms of linear c and φ Coulomb parameters. The use of a cohesion intercept at low or zero normal stress is inadmissible.

An empirical non-linear equation of peak shear strength which is sensitive both to JCS and JRC

The presence of water in rock joints reduces effective stress. Rough joints suffer a reduction in shear strength due to the adverse effect of moisture on the compressive and tensile strength of rock. The effect of the compressive strength reduction is less for smoother joints.

Any process that causes a reduction in this compressive strength should result in reduced peak shear strength. Increased weathering, saturation, time to failure, and scale, reducers the compressive strength of rocks. According to the proposed equation of peak shear strength, rough--undulating joints will be most affected, and smooth--nearly planar joints least of all.

At very high stress levels the shear stress required to fracture intact rock is no greater than the shear strength of the resulting fault. This important condition, known as the brittle-ductile transition is found to be dependent on the basic friction angle.

Large scale rock mechanics tests designed to investigate the effect of scale on the compression strength and frictional strength of rocks have been analysed using the empirical theory of frictional strength. However, it is possible that these scale effects may be absent or much reduced under the influence of high confining pressures in the Earth's crust, if pore and flaw volumes are significantly reduced.

A simple critical state concept for rock, and thereby delineate the necessary deviation from linear M-C criterion, in order to model correct curvature of the strength envelope. The reality is high friction, no cohesion and strong dilation at low stress.

The critical confining pressure σ3 (critical) required to achieve maximum possible shear strength, where the Mohr envelope becomes horizontal, is approximately the same as the UCS for the case of most rock types. Thus σ1maximum =3σ3(critical) ≈3σc. Triaxial tests only need to be performed at low confining pressures, in order to give the complete strength envelope.

Current multi-stage testing routines for rock joints tend to exaggerate cohesion and reduce friction. The error of recommending ϕb in place of ϕr may represent several degrees different strengths if joints are

weathered, and results in incorrect back-calculated JRC values. It has been recognized that cohesion (if existing) is broken at small strain,

while friction is mobilized at much larger strain and is the remaining shear strength if displacement continues i.e., degradation of cohesion followed by the mobilization of friction.

Numerical modelling with the discrete addition of rock joints in UDEC and 3DEC represents a big step in the direction of more realistic modelling of excavation effects in rock masses, for the purpose of deformation prediction and support design.

Exaggerating joint continuity, especially in 2D UDEC models, may cause at least a ten-times exaggeration of deformation in comparison to measured results of e.g. cavern deformation response. It is wise to check numerical model predictions of displacement with empirical Q-based formulae.

REFERENCES:

1. Barton, N., 1973. Review of a new shear-strength criterion for rock joints. Eng. Geol.,7: 287--332.

2. N. Barton.,1976. The Shear Strength of Rock and Rock Joints, Int. J. Rock Mech. Min. $ci. & Geomech. Abstr. VoL 13, pp. 255- 279.

3. Nick Barton., Shear strength criteria for rock, rock joints, rockfill and rock masses: Problems and some solutions.,Journal of Rock Mechanics and Geotechnical Engineering 5 (2013) 249–261.

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