In a conventional shearing test the normal force or the normal stiffness is kept constant during the experiment. 	

Sliding under constant normal load occurs in slopes if the environment is not changing during the process. The goal of this paper is 	

to investigate the influence of the continuously changing (i.e. increasing) normal load for the increasing shearing load. Regular 	

triangular cement mortar specimens were used to carry out this research. Both the geometry of the specimens and the mechanical 	

constants were well-known. The "Continuous Failure State" (CFS) shear tests were carried out like the ISRM standardized CFS- 	

triaxial tests, with different starting normal stresses.  The differences between the analogous CFS triaxial results are discussed and 	

analyzed. Linear and nonlinear theoretical models are proposed

Ván, Péter

Vásárhelyi, Balázs

English

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 4431. INRODUCTION For triaxial tests to determine the peak and the residual strength of rock materials the ISRM standardized the “Continuous Failure State” triaxial test (CFS-triaxial test) [1]. According to this method confining pressure and axial stress are applied so as to cause the test specimen to be permanently in a state of failure. In this way it is possible to obtain at least parts of the failure envelope for both the peak and the residual strength with the aid of a single specimen. Kovári et al. [2] explained this method and realized that to keep the material in a pre-failure state the best is to chose the rate of the increasing confining pressure so that the slope of the axial stress–axial displacement curve is equal to the  Young’s modulus of the sample. Because the slope of the stress-strain curve of a damaged material is decreasing with the axial stress, one can avoid an early failure and the measured strength will have some reserves. Tisa and Kovári [3] showed that CFS-triaxial test might be directly adapted to the direct shear test, because on comparing the results of conventional triaxial tests with those of direct shear tests on joints or planes of weakness a considerable similarity may be observed. The curves representing the relationship between axial stress and axial strain in the triaxial test exhibit basically the same form as those for shear deformation and shear force in the direct shear test, including the characteristics for peak and residual strength (Fig. 1). After several investigations they realized that using the CFS direct shear test the determination of the residual shear strength is exact. However, for determining the peak strength envelope of rough surfaces (or with teeth) only with decreasing normal load is correct [3]. This material investigation for determining the shearing constants of jointed rocks is also used in the practice. According to the results of Tisa and Kovári [3] using continuously increasing normal load as CFS direct shear test for rough surfaces or those with teeth on cement mortar and brick specimens the slope of shear stress–normal stress curves was always under the curve of the exact failure envelope (measured with single specimens under constant normal load). (see Fig. 1). Fig. 1. Characteristic results of direct tests on rock joints indicating similarity to triaxial test results [3] Shearing tests with regular triangular teeth were carried out with increasing normal load from the maximal shearing stress point according to the research of Tisa and Kovári [3] with nine different starting normal loads and the relationship between the shear and the normal stress was described. NARMS-TAC 2002, Hammah et al. (eds) © 2002 University of Toronto, ISBN 0 7727 6708 4 INFLUENCE OF THE CONTINUOUSLY INCREASING NORMAL STRESS TO THE FAILURE IN CASE OF SHEARING TEST Balázs Vásárhelyi Dept. of Geotechnic, FŐMTERV Engineering Consultancy Ltd., Budapest, Hungary Péter Ván Dept. of Chemical Physics, Budapest University of Technology and Economy, Budapest, Hungary ABSTRACT: In a conventional shearing test the normal force or the normal stiffness is kept constant during the experiment. Sliding under constant normal load occurs in slopes if the environment is not changing during the process. The goal of this paper is to investigate the influence of the continuously changing (i.e. increasing) normal load for the increasing shearing load. Regular triangular cement mortar specimens were used to carry out this research. Both the geometry of the specimens and the mechanical constants were well-known. The "Continuous Failure State" (CFS) shear tests were carried out like the ISRM standardized CFS-triaxial tests, with different starting normal stresses.  The differences between the analogous CFS triaxial results are discussed and analyzed. Linear and nonlinear theoretical models are proposed.  4442. RELATIONSHIPS BETWEEN THE CRITICAL SHEAR STRESS AND NORMAL STRESS Patton [4] was the first who performed a series of constant load stress direct shear tests on rock with regular teeth inclination (i), at varying normal stresses. From these tests he established a bilinear failure envelope – failure from an asperity sliding and asperity shearing mode. The equation for the first part of the two portions of the failure envelope is: τ σ φ µ= +n itan( ),                                              (1) if the σn normal stress is less than the σT transition stress, the boundary between the different modes of failure. Here τ is the shear stress and φµ denotes the sliding friction angle. If the normal stress equal or exceeds the transition stress (σn ≥ σT), the shear stress is: τ σ φ= +c n rtan ,                                                (2) where c is the cohesion and φr is the angle of the internal friction. Generally it can be assumed that  φµ ≈ φr. The theoretical background of the Patton failure envelope supposes rigid asperities in the sliding region and failure according to the Coulomb-Mohr criteria in the shearing region above the transition stress. Later Ladanyi and Archambault [5] extended the Patton Eq. (1), considering natural rock joints with irregular (but rigid) asperities. They proposed the following equation for the sliding part of the failure envelope if the shear area is one : τ σ φ νµ= +n tan( ),                                             (3) where tanν = v&  is the rate of dilation at failure. If the asperities are supposed to be rigid and regular then ν = i therefore Eq. (3) reduces to Eq. (1). For the shear part they proposed a fitting to the Coulomb-Mohr failure criteria as well as to the Fairhurst criteria, extending Eq. (3) with additional terms. Seidel and Haberfield [6] argued in favor of the original Patton equation (1) for the sliding part. They claimed to consider elastic teeth and their theoretical model was supported by constant normal stiffness (CNS) experiments. Vásárhelyi [7] investigated the dependence of the constant normal load on the rate of dilation at failure with constant normal load (CNL) experiments, too. According to his results the Ladanyi and Archambault’s equation (3) can be extended the whole curve (including the shearing part) and it is better then Patton’s (1), then correct until the teeth (or irregularities) are not shorn off. Therefore Eq. (3) is valid far beyond the transition stress and gives a unified approach to the two seemingly independent failure modes. The practical disadvantage of the approach that in this case the rate of dilation ( v& ) is a variable to be measured. The real measurements are better approximated by a smooth curve instead of the bilinear one of Patton. One of the simplest generalizations was suggested by Jaeger [8] on purely phenomenological reasoning: [ ]τ σ φσ µ= − +−c e b nn1 tan                                  (4) where b is an empirical constant. This equation is asymptotically equal with the bilinear one of Patton when the normal load σn goes to infinity. 3. MATERIAL DESCRIPTION AND EXPERIMENT Cement mortar was selected as test material because has rock-like properties. Basic material and shearing constants were determined in the previous researches [3, 7]. All specimens were 150 mm wide and 140 mm long with four regular teeth where the distance between the teeth was kept constant at 20 mm. The teeth were 5 mm high, 15 mm thick in the bottom and the inclination angle (i) of the teeth was 26.6°. The transition stress (σT) and the cohesion (c) of the cement mortar specimen was 2.1 and 2.13 N/mm2, respectively, and the basic friction angle (φµ) and the asperity sliding angle (α) was 33.6° and 59.0°, respectively. The CNL equipment was designed and built in the Rock Mechanics Laboratory of the Swiss Federal Institute of Technology, Zurich [3]. Using this machine the normal load could be changed manually during the research. The test monitoring arrangement is shown schematically in Fig. 2. It is necessary that the shear stress, normal stress and shear displacements were monitored continuously. The two x – y recorders allow to the separate recording of the shear stress – shear displacement development and that of the corresponding stress path. Every research was carried out at constant 0.003 mm/sec shear displacement rate.  445Fig. 2. Schematic diagram of the test monitoring arrangement [3]. S Shear force, ST Shear load transducer, N Normal force, NT Normal load transducer, DT Shear displacement transducer, XY Recorder Till the maximal shearing stress (which was determined by single tests and using the previous results, as well) the normal load was constant. Measurements have been carried out starting with the following constant normal load: 0.3; 0.6; 1.0; 1.5; 2.0; 2.5; 3.0; 3.5 and 4.0 N/mm2. At the maximal shearing stress the normal load was increased manually keeping the slope of the shear stress – shear displacement curve constant which were equal to the slope of this curve at constant normal load, according to the shearing model of [3]. In this case the specimen was maintained in a state of permanent sliding. 4. EXPERIMENTAL RESULTS AND THEORETICAL MODEL The measured shear stress – normal stress curves are shown in Fig. 3. Fig. 3. Measured shear-stresses in the function of the continuously increasing normal stress. Analyzing the curves it was chosen that the shear stress – normal stress curves are linear (or quasi linear) after the maximal shear stress and tend to the residual line. With low normal stress the changing of the direction of the curve is longer (i.e. big curvature of the curve before the second linear part) but beyond 1.5 N/mm2 normal stress the curves have very small curvature. Remarkable that the slope of measured curves is similar to the Ostwald curves for shear stress and shear rate [9]. The linear part of the graphs is quasi parallel with each other both before and after the transition stress, thus they are not influenced by the starting normal stress. Both linear and non-linear model was written for the curves. 4.1. Linear Model The slopes of the shear stress – normal stress lines (Fig. 4) are independent on the starting normal stress and it was approximately 25°. This slope can depend on the mechanical behavior, shear displacement rate and the roughness of the rock. Therefore a linear equation of this curve is: τ = τs + (σnx - σs)tan γ.                                        (5) where τs is the maximal shearing stress at the starting normal load (σs) and σnx is the continuously increasing normal stress and tanγ is the average slope of the normal stress – shear stress line. Fig. 4 compares the measured result with the linear equation in case of 2 N/mm2 starting normal stress. Fig. 4. Comparing the linear equation, the non-linear equation and the measured normal stress-shear stress curve in case of 2 N/mm2 starting normal stress. Accepting the validity of Eq. (3) for both modes of failure (supported by the experiments of [7]) we can get that τs linearly depends on the σs starting normal stress τs = σs tan (φµ + ν)                                              (6) In case of planar surface ν = 0 and the shear stress – normal stress curve is equal to the failure envelope (tan γ = tan φµ) thus τs = σs tan γ. Eq. (5) can be reduced to the easier form with Eqs. (1) & (2). If the starting normal stress is below the   446transition stress (σs < σT) the rate of the dilation is equal (or nearly equal) to the teeth angle (ν = i): τ  = σs (tan (φµ + i) - tan γ ) + σnx tan γ.              (7) If the starting normal stress is equal or above the transition stress τ  = c +σs (tan φµ - tan γ ) + σnx tan γ,                 (8) where the material constants are as it was written to Eq. (2). 4.2. Non-linear Model The previous linear model is not entirely satisfactory because according to Eq. (5) in case of large normal stresses the shear stress can go below the residual strength (see Fig. 4). Therefore a nonlinear modification of the linear equation above should satisfy the following requirements • the curve starts from the same point as the linear one, that is τ(σs)=τs; • the slope of the curve at σnx = σs equals to tanγ; • the asymptote at σnx ∞→  is the residual strength envelope (σnx tanφµ); • the tangent of the curve is positive. In the spirit of Jaeger equation (4) we can suggest the following non-linear equation to get a correct asymptotic behavior ,tanφσ)etanφσ(ττ µnx)σb(σµsssnx +− = −               (9) where µssµtanφστtanφtanγb −−=  and τs is given in Eq. (6). The linear approximation of Eq. (9) gives back Eq. (5) for small normal stresses and goes to the residual strength envelope (σnxtanφµ) if σnx tends to infinity, for large normal stresses. Let us remark that Eq. (9) does not contain any parameters to adjust. Fig. 4 compares the measured curve in case of 2 N/mm2 starting normal stress, the linear and the non-linear equations. Let us remark that the non-linear Eq. (9) does not consider the concave part of the normal stress - shear stress curve, which is typical if the starting normal stress is under the critical value, therefore the initial slope of the non-linear curve on Fig. 4 is under the initial slope of  measured line. 5. CONCLUSION Shearing tests with regular triangular teeth were carried out similarly to the CFS triaxial test with different starting constant normal stress. The shear stress – normal stress curve was analyzed where the normal stress was increased continuously from the maximal shear stress. In this case the specimen is in “Continuous Sliding State” which is not equal to the “Continuous Failure State”, as it was supposed before [3]. The slope of the measured shear stress – normal stress curves are always independent on the starting constant normal stress. Both linear and non-linear equations were suggested to explain the experimental results. The slope of this line depends on the roughness and the mechanical behavior of the rock and the ratio of the shear and normal stress rate. REFERENCES 1. Kovári, K., A. Tisa, H.H. Einstein and J.A. Franklin 1983. Suggested methods for determining the Strength of Rock Materials in Triaxial Compression: Revised Version. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 20: 283-290. 2. Kovári, K., A. Tisa and R.O. Attinger 1983. The concept of “continuous failure state” triaxial tests. Rock Mech. & Rock Engng. 16: 117-131. 3. Tisa, A. and K. Kovári 1984. Continuos failure state direct shear tests. Rock Mech. Rock Engng, 17: 83-95. 4. Patton, F.D. 1966. Multiple modes of shear failure in rock. Proc. 1st Congress of ISRM, Lisbon, I/509-513. 5. Ladanyi, B. and G. Archambault 1970. Simulation of shear behavior of jointed rock mass. Proc. 11th Symp. Rock Mech.: Theory and Practice, AIME, New York, 105-125. 6. Seidel, J.P. and C.M. Haberfield 1995. The application of energy principles to the determination of the sliding resistance of rock joints, Rock Mech. & Rock Engng, 28: 211-226. 7. Vásárhelyi, B. 1998. Influence of normal load on joint dilatation rate, Rock Mech. & Rock Engng. 31: 117-123. 8. Jaeger, J.C. 1971. Friction of rocks and stability of rock slopes. Gèotechnique, 21: 97-134. 9. Verhás, J. 1997. Thermodynamics and Rheology, Kluwer-Academic Press, Budapest. 

Continuos failure state direct shear tests. Rock Mech. Rock Engng,

Friction of rocks and stability of rock slopes.

Influence of normal load on joint dilatation rate, Rock Mech.

Multiple modes of shear failure in rock.

Simulation of shear behavior of jointed rock mass.

Suggested methods for determining the Strength of Rock Materials in Triaxial Compression: Revised Version.

The application of energy principles to the determination of the sliding resistance of rock joints, Rock Mech.

The concept of “continuous failure state” triaxial tests. Rock Mech.

Thermodynamics and Rheology,

Influence of the continuously increasing normal stress to the failure in case of shearing test

Influence of the continuously increasing normal stress to the failure in case of shearing test

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