ROCK MECHANICS

TRIAXIAL TEST

Conventional triaxial testing apparatus is often expensive and slow to operate. Twenty or more triaxial tests may be required to predict the strength of a rock sample with satisfactory accuracy, the number of tests depending on the homogeneity of the sample and the scatter of the data. A simpler design of cell was developed (Hoek and Franklin,1968), primarily to speed up the testing procedure(Hoek&Franklin 1970).

TRIAXIAL TESTThis cell applies a confining pressure only, and is used in conjunction with a conventional compression testing machine to apply axial force to thespecimen.

The axial force is applied via two spherically seated platens in order tominimise bending stresses.

The main feature of the cell design is a one-piece synthetic rubber sleeve that retains an annulus of fluid while the specimen is inserted, tested to failure and then extruded. (Hoek&Franklin1970)

Hoek&Brown 1980

TRIAXIAL TESTThe cell body, weighing only 5 kg.

The version used for the current series of tests was designed to accept 38 mm diameter specimens with a length : diameter ratio of 2 : 1.

Different sizes of cell are required to test different sizes of core, and a range of sizes are now in commercial production (maximum diameter of specimens: 54 mm).

The cell is designed to apply confining pressures of up to 70 MPa,selected as the maximum likely to be encountered in engineering practice since it is approximately equivalent to the vertical stress under 3000 m of overburden.

Cell pressure is provided from a hydraulic pump connect to an oil inlet in the cell wall.(Hoek&Franklin 1970)

TRIAXIAL TESTThree different types of triaxial compression test are described. The tests are intended to measure strength of cylindrical rock specimens as a function of confining pressure. The three test types differ from each other in the manner by which the strength envelope is produced.

Test type I (individual test), individ- ual points on the failure (peak strength) envelope are obtained from several tests.

Test type II (multiple failure state test) and the envelope is produced with a single test employing a stepwise procedure.

Test type III (continuous failure state test) the envelope is produced with a single test employing a continuous procedure.

The information obtained from a single specimen increases thus from type I to type III.(ISRM 1983)

TRIAXIAL TEST

Type Iindividual test

Type IImultiple failure

state test

ISRM 1983

Type IIIcontinuous

failure state test

TRIAXIAL TEST

Axial strain Axial stress curve

Type II (multiple failure state test)(ISRM 1983)

Confinning Pressure Axial stress curve

TRIAXIAL TEST

Axial strain Axial stress curve

Type III (continuous failure state test)(ISRM 1983)

Confinning Pressure Axial stress curve

FAILURE CRITERION

Mohr-Coulomb Failure criterion (linear failure envelop)(Hudson&Harrison 2007)

FAILURE CRITERION

Mohr-Coulomb Failure criterion (parabolic failure envelop)(Hoek&Brown 1980)

FAILURE CRITERION

Mohrs hypothesis:Nonlinear failure curve (parabolic), defined as the envelope of all Mohr circles that cause failure

FAILURE CRITERION

Minor principal stress Maximum principal stress curve(Hoek&Brown 1980)

FAILURE CRITERION

Hoek-Brown empirical failure criterion(Hoek&Brown 1980)

5,02331 )( cc sm ++=

1: major principal stress3: minor principal stressc: compressive strength

m: material constant dependson the rock type and itsmechanical quality

s: material constant representsthe cohesion of the rock

FAILURE CURVE: TRIAXIAL TESTS

Failure curve of granite (red: linearapproximation, blue: parabolic failure curve)

(Hoek&Brown 1980)

Determination of failure curve withindividual triaxial

tests (Type I)

Differencesbetween linearand parabolicfailure curve.

Failure curve of sandstone (red: linearapproximation, blue: parabolic failure curve)

(Hoek&Brown 1980)

FAILURE CURVE: TRIAXIAL TESTS

ESTIMATION OF FAILURE CURVE

Mohrs hypothesist

c

t

t

t

B

acB

b

Ba

acab

=+==

=

+=

)(3

32

)( 22

Estimation of the parabolic failure curve from the results of compressive and tensile

strength tests

This tests measures peak and residual direct shear strength as afunction of stress normal to the sheared plane.

The results of it useful for example: limiting equilibrium analyses of slope stability problems stability analyses of dam foundations.

A shear strength determination should preferably comprise at least five tests on the same test horizon with each specimen tested at a different but constant normal stress.(ISRM 1974)

DIRECT SHEAR STRENGTH TEST

DIRECT SHEAR STRENGTH TEST

Arangment of direct shear test in laboratory (shear box)(ISRM 1974)

DIRECT SHEAR STRENGTH TEST

Arangment of direct shear test in laboratory(ISRM 1974)

The first stage of the test is the consolidation stage, when only the normal stress applied to the specimen. The consolidation stage allow pore water pressures in the rock and filling material on the shear plane to dissipate under full normal stress before shearing.

The consolidation stage may be considered complete when the rateof change of normal displacement is less than 0,05 mm in 10 minutes. The shear load may then be applied.

For each test specimen a consolidation graph and graphs of shearstress - normal displacement, shear stress shear displacement are determined.(ISRM 1974)

DIRECT SHEAR STRENGTH TEST

DIRECT SHEAR STRENGTH TEST

Consolidation curvesof direct shear test

(ISRM 1974)

Shear stress shear and normal displacement

curves(ISRM 1974)

DIRECT SHEAR STRENGTH TEST

Result of the direct shear strength test(ISRM 1974)

Graphs of peak and residual shear strength normal stress are plotted from the combined results for all test specimens.

r: residual friction anglea: apparent friction angle bellow

stress a (point A is a break in the peak shear strength curve resulting from the shearing off of major irregularities on the shear surface)

b: apparent friction angle abovestress a (this is usually equal or slightly greater than r )

c: cohesion intercept of peak shearstrength curve, it may be zero.

c: apparent cohesion at a stresslevel corresponding to b

Roughness of the surface(ISRM 1974)