A Laboratory Shear Cell Used for Simulation of Shear Strength and Asperity Degradation of Rough Rock Fractures

Abstract

Different failure modes during fracture shearing have been introduced including dilation, sliding, asperity cut-off and degradation. Several laboratory studies have reported the complexity of these failure modes during shear tests performed under either constant normal load (CNL) or constant normal stiffness (CNS) conditions. This paper is concerned with the mechanical behaviour of synthetic fractures during direct shear tests using a modified shear cell and related numerical simulation studies. The modifications made to an existing true triaxial stress cell (TTSC) in order to use it for performing shear tests under CNL conditions are presented. The large loading capacity and the use of accurate hydraulic pumps capable of applying a constant shear velocity are the main elements of this cell. Synthetic mortar specimens with different fracture surface geometries are tested to study the failure modes, including fracture sliding, asperity degradation, and to understand failure during shearing. A bonded particle model of the direct shear test with the PFC2D particle flow code is used to mimic the tests performed. The results of a number of tests are presented and compared with PFC2D simulations. The satisfactory results obtained both qualitatively and quantitatively are discussed.

1 Introduction

The shear behaviour of rock fractures, which may also be simulated by numerical methods (e.g. the discrete element method), is studied in the laboratory using a recently developed direct shear apparatus. It is well understood that the amount of energy dissipated during fracture shearing and asperity contact damage is a function of normal load, contact surface roughness, temperature, loading velocity, and hardness (Engelder 1978; Scholz and Engelder 1976). The influence of normal load and surface roughness is studied in this paper.

Different direct shear testing equipments have been developed to study the effects of surface roughness on shear strength and asperity degradation (i.e. damage). These are different in terms of loading capacity and loading conditions, i.e. under constant normal load (CNL) or constant normal stiffness (CNS).

In CNL tests the normal load is kept constant during the shearing process (Barla et al. 2009; Gehle 2002; Hans and Boulon 2003; Huang et al. 2002; Indraratna and Haque 2000; Jafari et al. 2003; Jiang et al. 2004; Konietzky et al. 2012; Yang and Chiang 2000). For example, shear testing under CNL conditions is appropriate for non-reinforced rock slopes. However, in deep tunnels, where the normal stress is high, the shear behaviour is controlled by stiffness (shear and normal) and direct shear tests under CNS conditions are more appropriate.

In this paper, a modified true triaxial stress cell (TTSC) has been used in order to perform shear tests under CNL conditions and to study shear strength and asperity degradation of synthetic fractures with different surface geometries. Numerical simulations with the discrete element method and the PFC2D code have also been carried out to compare with the laboratory results. It is noted that the authors have already reported PFC2D simulations of rough fractures (Asadi and Rasouli 2010, 2011; Asadi et al. 2012) and that the methods previously used have also been adopted in the present simulations.

Many researchers have attempted to examine the shear behaviour of fractures by using laboratory tests (e.g. Barla et al. 2009; Barton and Choubey 1977; Gehle 2002; Grasselli et al. 2002; Hans and Boulon 2003; Huang et al. 2002; Indraratna and Haque 2000; Jafari et al. 2003; Jiang et al. 2004; Konietzky et al. 2012; Yang and Chiang 2000).

Yang and Chiang (2000) studied the progressive shear behaviour of composite rock fractures with two different triangle-shaped asperities (with 15 and 30° asperity angle) under CNL conditions. The effects of the asperity angle and base-length on the shear behaviour of fractures were investigated. The results obtained were confirmed by using finite element and discrete element modelling by Giacomini et al. (2008) and Kazerani et al. (2011).

Similarly, Huang et al. (2002) tested artificial fractures with regular triangle-shaped asperities with different angles under CNL conditions. They observed asperity sliding and cut-off mechanisms and developed a mathematical expression to estimate the shear strength of rough fractures with asperities by using both numerical modelling and experimental studies.

Grasselli et al. (2002) developed expressions to assess the shear strength of rough fractures based on the results of testing under CNL conditions. These authors analysed several rock fracture surfaces based on quantified 3D roughness parameters and investigated damage and sliding during shearing. They stated that damage, which is apparently not present prior to peak, occurs principally during the softening and residual phases. In addition, they concluded that it is the asperity degradation at peak-shear stress that initiates sliding.

Jafari et al. (2003) also developed mathematical models for evaluating the shear strength of rock joints, performed laboratory shear tests under both CNL and CNS conditions, and studied asperity degradation at low, intermediate, and high normal stress. Number of loading cycles, stress amplitude, dilation angle, degradation of asperities and wearing were reported to be the main parameters controlling the shear behaviour of rock joints.

The authors have previously reported a comprehensive bibliographic review on the effect of roughness on shear strength of fracture surfaces (Asadi 2011; Asadi et al. 2012; Rasouli and Harrison 2010). They also described the results of laboratory shear tests and showed a good agreement with identical PFC2D simulation results both qualitatively and quantitatively, i.e. onset of failure, magnitude of asperity degradation, micro-cracking pattern, and peak and residual shear strength of the fracture.

Also highlighted in a recently published paper (Asadi et al. 2012) were the effects of large asperities on fracture shear behaviour. To the authors’ knowledge, the phenomena as described by them (i.e. micro-cracking patterns during fracture shear tests under different normal loads) have not been broadly analysed in the past. This is in particular the case of irregular asperities with complicated geometries. In the present paper an attempt is made to further illustrate this point.

Firstly, the modifications of a TTSC introduced in order to perform direct shear tests under CNL conditions are described. The modified equipment, named fracture shear cell (FSC), allows shear tests to be performed at high normal and shear loads. The TTSC, designed in 2009 in the geomechanics laboratory of Curtin University to simulate hydraulic fracturing and sand production, allows vertical and horizontal loads up to 315 kN to be applied independently in each direction on a cubic specimen with 30 cm side length (Rasouli and Evans 2010).

Then, the results of shear tests carried out on synthetic mortar specimens with fractures with symmetric triangular and wavy asperities and a rock-like fracture at a constant normal load are illustrated. It is shown that the shearing mechanism changes from sliding to asperity degradation as the fracture surface becomes rougher. Finally, the results of PFC2D simulations are presented which indicate a good agreement with the results obtained from the corresponding laboratory tests.

Fracture shear strength directionality is also investigated with laboratory shear tests on specimens sheared along the horizontal plane in two opposite directions which results in significant differences of fracture shear strength. In addition, a rock-like fracture is subjected to shear tests and its directional dependency is studied in two shearing cycles. The results indicate that the shear strength is reduced in the second cycle due to a reduced roughness after the first cycle.

Observation, analysis, and interpretation presented in this study, to a large extent agree with the theory of asperity cut-off introduced by Huang et al. (2002), which was further studied by Rasouli and Harrison (2010), and recently simulated using PFC2D by Asadi et al. (2012). The fact that at high normal stress the fracture failure envelope converges to the intact rock failure envelope is also modelled and differences between numerical and experimental results are highlighted. In doing this, it is remarked that very few studies are available regarding fracture contact asperity degradation by using analytical solutions (Ladanyi and Archambault 1970) and results of testing (Huang et al. 2002).

2 Fracture Shear Cell Configuration

A top view of the TTSC is shown in Fig. 1, where the horizontal stresses are applied independently through the A1–A4 rams. The linear variable differential transducers (LVDTs C1–C4) shown in this figure monitor the displacements of the rams. The normal stress is applied using the vertical ram after the top lid of the cell is in place. An LVDT, placed between the vertical ram and the top lid, measures the normal displacement if it occurs.

Fig. 1

A top view of the TTSC where the horizontal stresses applied independently through two sets of rams; LVDTs are shown in each ram

The horizontal stresses are transferred to the specimen through the internal plates. In order to ensure that the plates do not experience any bending or torsion during loading, the cubic specimen is to be cut accurately and its sides need be polished to be precisely parallel. This reduces the chance for asymmetric load distribution across the plates and therefore the specimen. The maximum displacement of the rams is limited to 2 cm, which is thought to be adequate for performing laboratory direct shear tests.

The pressure can be applied using hydraulic pumps with a maximum pressure capacity of 15,000 psi (≈100 MPa) (Fig. 2a). Fluid is injected under a constant flow rate with a maximum capacity of 650 cc/h using high pressure pumps, as shown in Fig. 2b. Loads and displacements are continuously monitored during each test. The data acquisition system shown in Fig. 3a operates through different channels at the rate of one datum per second (it is also adjustable) and transfers the data collected to a PC as shown in Fig. 3b.

Fig. 2

a Handy pumps for applying normal stress and b automatic high-pressure syringe pumps for applying constant shear rate

Fig. 3

a Data acquisition system and b monitoring PC

All the loads, including horizontal and vertical loads, are recorded with high accuracy by load cells located in the rams. Displacements are also recorded by five LVDTs corresponding to the movement of each ram (four horizontal and one vertical). These are the most significant data collected during each test. In order to use the TTSC for fracture shearing experiments some modifications needed to be introduced as described in the following.

In order to perform a fracture shear test with the TTSC, only one horizontal ram is to come into motion and shear the upper block of the specimen over the lower one. The other three rams are kept fixed during the test. In order to do this, based on the current design of the TTSC, a specimen size of 20 cm × 15 cm × 10 cm was adopted as shown in Fig. 4. The shearing area is 150 cm² which enables a maximum shear stress up to 21 MPa to be applied.

Fig. 4

Shearing specimen confined by rigid shims: a perspective and b front-view

A specimen with triangular asperities is shown in the same Fig. 4. The specimen size can be adjusted further close to the boundaries of the cell if needed, but the chosen size was found to be adequate for the purpose of this study. It is noted that a number of rigid shims are placed around the specimen to confine the lower block inside the cell and prevent it from any lateral, axial, and rotational movements.

As shown in Fig. 4, the “T” shaped Shim I on the left of the specimen transfers the shear load to the upper block so that the load applied is kept centred. Shim II prevents any forward movement of the lower block during shearing. The normal stress is applied to the specimen through Shim III sitting on top of the specimen as a cap. Also, in order to limit the lateral movement of the lower block, two shims are set on both sides of the specimen with their height being less than the height of the lower block.

Two Teflon sheets are also used. One is placed between Shim III and the vertical ram and the other one between the T-shaped Shim I and the shearing side of the specimen. The purpose of using these Teflon sheets is to minimise friction along the sliding components of the device which may affect the shearing response of the fracture. It is noted that the Teflon sheet attached to Shim I is used to allow for dilation (i.e. vertical movement of the upper block over the lower one) during shearing under CNL conditions.

2.1 CNL Shear Tests

In the CNL shear tests, dilation of the upper block over the lower one is expected as a result of the normal load being kept constant by using the hydraulic pumps. For this purpose, a duplex high pressure cylinder (DHPC) was designed as shown in Fig. 5. The cylinder consists of two chambers isolated by a diaphragm. One side is filled with nitrogen gas to a pressure equivalent to the normal stress required and the other side is filled with oil. The pressure gauge shows a 300 psi (≈2 MPa) pressure on the vertical ram which in turn applies a 3.5 MPa constant normal stress on the specimen (Fig. 6).

Fig. 5

Duplex high-pressure cylinders (DHPC) to apply constant normal load

Fig. 6

Schematic view of the specimen showing the system configuration

If dilation (i.e. normal displacement) of the upper block occurs, the gas is compressed but the pressure is kept constant. This causes an equivalent amount of oil to be returned from the vertical ram to the DHPC which in turn results in an upward movement of the vertical ram. By recording the load cell data placed in the vertical ram, the fluctuations of the normal load applied to the specimen can be measured. This in turn is related to the amount of oil displaced.

A constant shear load is applied to the specimen using the high-pressure pumps which can be operated in either a constant pressure or constant flow rate mode. This is believed to be a more appropriate approach in applying the shearing velocity to the specimen during testing compared to the more commonly used methods. To this end, Table 1 compares the present apparatus (A in the table) with two other direct shear testing equipments recently developed by Barla et al. (2009) (B in the table) and Jiang et al. (2004) (C in the table). The table indicates an increased capacity of normal and shear loads and a larger specimen size.

Table 1 Comparison between three different shear test apparatus recently developed

Figure 6 gives a schematic front view of the FSC showing all the components and connections used. The connection of the DHPC to and from the normal ram is also shown. One of the unique features of the FSC is that when the top lid is in position, the inner part of the cell becomes completely isolated from the outside. Sealing is obtained with metal-to-metal contact and by O-rings placed between the top lid and the upper part of the cell. The cell can be pressurised by any fluid or gas to a certain pressure (21 MPa) and the specimen inside the cell can be saturated with the fluid in the cell.

Although the modifications introduced to the TTSC allow shear tests to be performed under CNL conditions, there is no practical reason why the test could not be performed under CNS conditions. This can be achieved in the FSC by inserting constant stiffness springs between the vertical ram and the upper block of the specimen to be sheared.

3 Specimen Preparation

To understand the fracture shearing mechanisms in the laboratory, synthetic specimens with simple fracture geometries were tested first. These consisted of mortar fracture specimens with symmetric triangular shape asperities. In order to prepare them for testing in the FSC, a metal mould as shown in Fig. 7 was used.

Fig. 7

A metal mould used to prepare synthetic rough fracture geometries

The artificial plates (galvanised iron of 5 mm thickness) with the desired surface geometry are placed in the middle of the mould. Typically, Fig. 7 shows a fracture with a 45° asperity angle. Filling the mould with mortar produces the desired fracture geometry. It is noted that only one mortar mixture has been used in order to ensure similar mechanical properties for all the specimens tested. As shown in Fig. 7, the shearing block has a width of 15 cm, a height of 20 cm, and a thickness of 10 cm. Rock fracture surfaces from cored samples (usually less than 5 cm in diameter) can also be accommodated in this mould with the remaining space being filled with high-strength mortar.

A number of blocks with different fracture geometries were prepared under the same conditions to perform shear tests under different normal stress and in opposite directions, along the fracture horizontal plane. Hard plates were used to shape symmetric triangular and wavy asperities as well as rock-like fractures, where a variation of surface elevation is only in the x–z plane. This is thought to be the closest approach in order to compare the laboratory results with the 2D simulations with the PFC2D code. A setup for making a synthetic fracture with symmetric triangular asperities is shown in Fig. 7. The plates are removed soon after the mortar is cured and a mate fracture geometry is produced.

The properties of the mortar used for the synthetic specimens are given in Table 2 (cement and sand contact bond strength properties are from Lambert et al. 2010). The specimens are saturated in water for 28 days, as per ASTM guidelines, to reach the desired ultimate strength before testing. To know the mechanical properties of the specimens used is essential as the results obtained are compared to the corresponding results of PFC2D simulations. For this purpose, an approach similar to that proposed by Lambert et al. (2010) was adopted, consisting in the calibration of the results of laboratory uniaxial compression tests with PFC2D simulated tests.

Table 2 Micro-properties of mortar sample and PFC2D rock-like assembly

To obtain similar uniaxial compressive strength (UCS) values for all the blocks tested, the specimens consisted of 20 % cement, 65 % fine-grain sand, and 15 % fresh water in volume, which resulted in a moderately high strength mortar. This combination of components was found to be suitable for studying asperity failures. This is, however, different from that used by Lambert et al. (2010) (i.e. 45 % cement and 55 % sand) which resulted in greater UCS and greater Young’s modulus (E) values.

3.1 Uniaxial and Confined Compression Tests

Figure 8 shows a cylindrical specimen with 52 mm diameter and 104 mm height used for the uniaxial and confined compression tests in the laboratory. Specimens were made from a similar material (Table 2). The tests were performed at a low loading rate to ensure quasi-static loading conditions. Loads and displacements were recorded during each test.

Fig. 8

UCS test on a cylindrical specimen using the TTSC

The average UCS value obtained was 29.2 MPa. Figure 9 shows one of the specimens after testing in the FSC. By simply using the Mohr–Coulomb criterion and the angle of the failure plane $\beta$ = 30 ± 2° with respect to the loading direction, the average cohesion and internal friction angle are estimated to be 7.0 MPa and 32°, respectively.

Fig. 9

A cylindrical specimen before and after the UCS test showing the shear failure plane

Simulations were performed with the PFC2D code. In addition to unconfined compression tests, confined compression tests were also simulated. The micro-properties of the model are given in Table 2. It is noted that the two-dimensional simulation scheme adopted is the same as described by Asadi et al. (2012), with the average particle radius set to be 0.322 mm, which is in the range of the fine-grain sandstones used for mortar preparation. This allows for a comparison of laboratory and simulation results.

Stress–strain curves for numerically simulated tests are shown in Fig. 10a under different confining stress (0, 10 and 20 MPa). Figure 10b compares simulation and laboratory testing results under a confining stress of 10 MPa. It is noted that the two curves compare well and that the peak strength values are similar. It may be observed that the bonded particle model exhibits a typical brittle behaviour with a substantial drop of strength after peak, when an inclined fracture surface is formed in the specimen upon subsequent loading, with the original intact specimen breaking apart.

Fig. 10

Stress–strain curves for numerical compression tests (a); comparison between numerical and experimental compression test (b); Mohr–Coulomb representation and failure envelope of mortar specimens modelled in PFC2D (c)

Based on the PFC2D simulations, the Mohr–Coulomb failure envelope is obtained as shown in Fig. 10c. The cohesion and internal friction angle are estimated to be 7.5 MPa and 29°, respectively. Table 3 shows the average UCS and E values for mortar obtained from laboratory testing and from simulations with five different randomly packed particles and a particle friction coefficient of 0.05. A satisfactory agreement is found between the values obtained from laboratory tests and PFC2D simulations.

Table 3 Rock strength properties correlated with lab tests and PFC2D simulations

4 Fracture Shear Tests Using FSC

Shear tests of fractures with symmetric triangular and wavy asperities as well as rock-like fractures were performed with the FSC. Three different fractures with symmetric triangular asperities of 15, 30, and 45° base-angle were tested first as shown in Fig. 11.

Fig. 11

Cross sections of symmetric triangular fractures with 15, 30, and 45° asperity angles used for shear tests

4.1 Fractures with Symmetric Triangular Asperities

Shear tests were performed at low and high normal stress and in two opposite directions (LR, shearing the upper block from left to right and RL, shearing the upper block from right to left) along the fracture horizontal plane. As depicted in Fig. 11, a constant asperity wave length of 4 cm was used for the three geometries.

Figure 12 shows the specimens before testing. The tests were conducted a few times to ensure consistency of the results. Constant normal stresses of 1.5, 2.0, and 2.5 MPa were applied during different shear tests using the DHPC. The shear load was applied at a constant rate of 0.5 kN/min.

Fig. 12

Synthetic specimens with triangular shaped fracture surfaces

Each test took approximately 2 h to be completed and this period of time was estimated to be adequate to reach the residual state. Therefore, the post-peak behaviour of the sheared fractures was also recorded after the upper block was displaced horizontally up to 1.0 cm.

The shear load and displacements were recorded using a high-precision data recorder and the pressure versus time curve plotted continuously during the test so as to check the shearing response. Figure 13 shows the specimens after testing under 2.5 MPa normal stress. This is the largest normal stress applied, which was found to cut-off the high amplitude asperities (45°). The asperities in the rough specimen tended to shear-off, which resulted in a greater peak shear strength; the specimen with a small asperity angle (15°) exhibited sliding of the upper block over the lower one, with a sliding dominated mechanism.

Fig. 13

View of specimens after shearing tests under 2.5 MPa normal stress

Plots of the shear stress versus shear displacement curves at 1.5 MPa normal stress are shown in Fig. 14. A 4.3 MPa peak shear stress is obtained for the rougher specimen with 45° asperity angle followed by a drop to a residual stress value of 3.2 MPa. On the contrary, the specimen with a lower asperity angle shows a gradual increase in shear stress with a levelling-off shear stress at approximately 1.39 MPa.

Fig. 14

Plot of shear stress–shear displacement for symmetric triangular fractures based on laboratory shear tests conducted at normal stress of 1.5 MPa

The shear test results for a fracture with asperity angle 15° and normal stress 1.5, 2.0, and 2.5 MPa are plotted in Fig. 15. It is seen, as expected, that as the normal stress increases, both the peak and residual shear strength increase. At larger normal stress, the shear stress fluctuates as the asperities are being degraded and tensile cracks are developing through the intact sample.

Fig. 15

Fracture with asperity angle of 15° sheared in the laboratory at different normal stresses

Once all the asperities are sheared-off completely, the residual shear strength is reached, as observed at a normal stress of 2.5 MPa. The observation of the specimen once the test is completed indicates a major tensile crack to be present which is thought to be linked to the sudden drop of stress in the shear stress–shear displacement curves (Figs. 14, 15).

PFC2D simulations with specimen size, material properties, and fracture geometries defined according to the results of the laboratory tests were performed as illustrated in Fig. 16 for the normal stress equal to 2.5 MPa. A good agreement was observed between the results of testing and PFC2D simulations.

Fig. 16

PFC2D simulations of fracture shearing with the geometries shown in Fig. 11, after 1.0 cm shear displacement at 2.5 MPa normal stress

It is noted that by increasing the asperity angle, the fracture mode changes from asperity sliding to cut-off and tensile cracking, which is consistent with the laboratory results shown in Fig. 13. Since the stiffness of this model is sufficiently high, development of micro-cracks is limited and more pronounced at larger asperity angles (45°), as shown in Fig. 16.

A peak shear stress–normal stress plot for the fracture with asperity angle 30° is shown in Fig. 17, where both the results of laboratory testing and PFC2D simulations are illustrated. A similar trend is observed in the two cases, although the PFC2D simulation appears to overestimate the peak value. This is believed to be due to the cohesive effects of the fracture particles lying on opposite sides of the fracture (Asadi and Rasouli 2011).

Fig. 17

Failure envelopes estimated from laboratory tests and PFC2D simulations

The plot given in Fig. 17 allows one also to estimate the fracture surface mechanical properties. With the cohesion along the fracture ($C_{\text{f}}$) given as difference between the peak and residual shear strength, the peak shear strength of the fracture ($\tau_{\text{p}}$) can be written versus the fracture friction angle ($\varphi_{\text{f}}$) through the Mohr–Coulomb criterion as:

$$ \tau_{\text{p}} = \sigma_{\text{n}} { \tan }\left( {\varphi_{\text{f}} + \theta } \right) + C_{\text{f}} . $$

(1)

where ${{\uptheta}}$ is the fracture asperity angle.

From the fracture failure envelopes shown in the same Fig. 17, friction angles of 29° and 27.3° are obtained from laboratory testing and PFC2D simulations, respectively. The peak shear strength given by the PFC2D model is clearly overestimated due to the already mentioned cohesive effects of the particles lying on opposite sides of the fracture.

Even if fracture shear tests were not performed for normal stresses greater than 2.5 MPa, the fracture shear behaviour for the normal stress greater than this value can be described on the basis of the PFC2D results. As illustrated in Fig. 17, the slope of the curve corresponding to the fracture with the asperity angle equal to 30° is $\left( {\varphi_{\text{f}} + {{\uptheta}}} \right)$ = 59°.

However, when the normal stress exceeds a threshold value, the asperities are expected to be completely sheared-off with failure developing into the interior of the block. The normal stress corresponding to this critical behaviour could be analytically estimated for a symmetric triangular asperity fracture (Asadi 2011; Rasouli and Harrison 2010) as:

$$ \sigma_{\text{n}}^{\text{T}} = c ( {\text{cot}}\theta - { \tan }\varphi ) {\text{cos}}^{ 2} \varphi , $$

(2)

where $\sigma_{\text{n}}^{\text{T}}$ is the critical normal stress, c is the intact rock cohesion, and $\varphi$ is the intact rock internal friction angle.

If the failure envelope of the intact specimen is plotted in the same Fig. 17, the critical normal stress $\sigma_{\text{n}}^{\text{T}}$ value can be identified. For the asperity angle equal 30° the fracture envelope intersects the intact failure envelope at 5.5 MPa normal stress. It is shown that by reducing the fracture surface roughness, the transitional normal stress will be shifted to larger values.

This is because larger asperities with sharper teeth are more likely to be sheared-off earlier than smaller asperities with rounded teeth. Figure 17 shows that the shearing mechanism for a specimen with $\theta$ = 30° is expected to be mainly sliding along the asperities for the normal stress less than 3.0 MPa with asperity shearing more likely to occur at greater normal stress values.

Figure 17 also shows that by increasing the normal stress, the difference between the laboratory and PFC2D results decreases. This is because both methods are expected to give closer results for greater normal stress values. It is noted that the geometry of the fracture surface in PFC2D is made by particles with no bonds (no cement between two walls of fracture).

When shearing is initiated, particles lying on opposite sides of the fracture surface may create a shear stress concentration across the larger particles located along the fracture plane, which is likely to lead to an overestimate of the shear strength. This effect is reduced when using smaller particles (Asadi et al. 2012).

It is to be reminded that particles in PFC2D are rigid bodies which never fail mechanically during simulation. In a blocky system modelled with PFC2D the block boundaries are not planar, and the bumpiness affects the fracture response (Ivars et al. 2008). To overcome such a shortcoming, the contact bond was used and the particle size was reduced so as to minimise the non-planarity effects.

4.2 Fractures with Wavy Asperities

Blocks containing fractures with wavy asperities were built artificially using mortar and according to the procedure previously described. As already noted, the block has an identical geometry along its thickness which allows one to compare the laboratory and the PFC2D simulation results. Figures 18 and 19 show specimens A and B which were subjected to shear tests in two opposite directions in order to investigate the directional dependency of shear strength.

Fig. 18

Shearing block with A and B fracture geometries prepared for testing

Fig. 19

Geometry of wavy fracture profiles A and B extracted from prepared testing block

The micro- and macro-properties of specimens A and B are given in Tables 2 and 3, respectively. Visual observation of the two fracture profiles as depicted in Fig. 19 shows that profile A includes one major asperity which appears to be steeper on one side, whereas profile B includes three asperities with different heights. These two fracture profiles were chosen from several geometries to show the importance of rough asperities in shear strength estimation.

4.2.1 Fracture Profile A

Figure 20 shows block A after shearing in opposite directions (i.e. LR and RL). These tests were performed for the normal stress equal to 1.5 and 2.5 MPa and allowing a shear displacement up to 1.0 cm. The results obtained indicate clearly a shear behaviour which depends on the shearing direction.

Fig. 20

Profile A block view after shear tests at 1.5 MPa normal stress in opposite directions (top) and at 2.5 MPa normal stress (bottom)

Fracture shearing in the LR direction causes sliding of the upper block against the lower one and minor asperity contact damage. This is due to the smaller angle of the left side of the single large-scale asperity compared to that of the right side. Fracture shearing is accompanied by the development of a large tensile crack. This means that in this case failure occurs within the intact specimen and the post-peak behaviour depends on the material mechanical properties (i.e. tensile strength) rather than the fracture surface parameters.

This type of behaviour has been observed by other authors (Huang et al. 2002; Hutson and Dowding 1990; Karami and Stead 2008) when studying asperity cut-off and degradation (i.e. micro-cracking under high normal stress). It is more likely to occur when large asperities with high amplitude exist in the fracture plane (due to stress concentration effects on the asperity doglegs, a new crack will form and develop outside the shear surface). Moreover, failure outside the shear surface occurs as a result of increasing shear displacement in fractures with extremely large asperities.

Numerical simulations also show this to occur during the identical shear tests (Fig. 21). In addition, normal stress must be higher than a critical value to see failure to develop outside the shear plane. For normal stresses below this critical value sliding will take place. Authors agree that this is not an option for planner fractures or for fractures having a small roughness (most of the rock fractures have average asperity angles less than 30°). Therefore, the interest is to model synthetic fractures with large asperities.

Fig. 21

PFC2D simulation of profile A shearing in opposite directions, LR (top) and RL (bottom) at 2.5 MPa normal stress

The failure pattern for the normal stress equal to 2.5 MPa indicates several micro-cracks extending from the tensile crack, which is a result of the shear stresses being concentrated along the fracture surface. To investigate the directional dependency of shear strength using PFC2D simulations, the A specimen was subjected to shearing in both directions (RL and LR). Figure 21 shows the fracture after shearing at 2.5 MPa normal stress, which compares satisfactorily with the laboratory results given in Fig. 20. Again, the dominant mechanism in the LR direction is sliding, whereas tensile and shear failures develop through the large asperity and the intact material when shearing takes place in the RL direction.

Figure 22 shows the shear stress versus shear displacement plot obtained from laboratory tests and PFC2D simulations. Results are shown for shearing in both directions, LR and RL. A significant difference is observed in the shear behaviour due to changing of the direction of shearing. As expected, the pre-peak and peak shear stress are larger when shearing takes place from right to left rather than in the opposite direction.

Fig. 22

Shear stress versus shear displacement curves of Profile A shearing at 2.5 MPa normal stress a results of lab shear tests and b results of PFC2D simulations

The post-peak (or residual) shear strength is also higher when the fracture is sheared in the RL direction. In this case, however, a smaller dilation is observed. The relatively sharp reduction in strength just following the peak value is due to the asperity height and roughness chosen for demonstration purposes. However, for real fractures, in general, a smoother reduction of stress after peak is expected to occur.

The above analyses show why the shearing direction as well as the state of shear stress, i.e. pre- or post-peak, needs to be taken into account when characterising the ultimate shear strength of a fracture. This is caused by the surface roughness, which demonstrates the importance of the method to be used to quantify roughness and integrate it with the fracture shear strength.

4.2.2 Fracture Profile B

Figure 23 shows block B after shearing in the LR direction at 2.5 MPa normal stress and 1.0 cm maximum shear displacement. These tests were performed for the normal stress equal to 1.5 and 2.5 MPa and in both directions of shearing.

Fig. 23

Profile B block view after shear tests under 2.5 MPa normal stress and 1.0 cm shear displacement from left to right

Three wavy asperities with different amplitudes and wavelengths along the horizontal plane were considered. It is of interest to see the contribution of each asperity to the shearing resistance when tested in the LR or RL directions. In the first test, performed under 1.5 MPa normal stress, sliding of the upper block over the lower one was observed with a small dilation taking place. Also, as for block A, under this low normal stress, minor asperity contact damage was observed.

However, as illustrated in Fig. 23, when the normal stress increased to 2.5 MPa, the shearing mechanism was completely changed and all the asperities underwent failure but according to different modes. In LR shearing the first two asperities (from the left) of the lower block were sheared off and detached. However, the right asperity with a larger amplitude and wavelength experienced a tensile failure which extended to the intact material.

Figure 24 gives a close view of the asperities after the completion of the test. It is noted that the first two asperities (a and b) are completely detached from the lower block with no further direct contribution to the shearing process. However, they fill the fracture aperture space as gouge.

Fig. 24

Profile B block view after shear tests at 2.5 MPa normal stress

This, obviously depending on the mechanical properties of the material, is to significantly affect the fracture post-peak shear strength. It is noted that the PFC simulation takes this process into account, which is ignored completely when simple analytical models are used to estimate the shear strength.

As for block A, a large tensile crack developed from this asperity and propagated through the intact specimen. The large asperity amplitude is responsible for this to happen as shown in Fig. 24. It is implied that, in a fracture with a number of asperities, the asperity with the largest amplitude dominates the failure mechanism.

Figure 25 shows the PFC2D results with the specimen sheared under the 2.5 MPa normal stress in two different directions (RL and LR). It is seen that when the fracture is sheared in the RL direction, under 2.5 MPa normal stress, a tensile crack develops in the asperity located to the most right, while the other two asperities experience very limited failure. In LR shearing, however, (Fig. 25, bottom), all the asperities are sheared-off and a small dilation occurs.

Fig. 25

PFC2D simulation of profile B shearing in opposite directions, RL (top) and LR (bottom) at 2.5 MPa normal stress

Figure 25, when compared with Figs. 23 and 24, shows a good agreement between the results of the laboratory tests and the PFC2D simulations. However, in the PFC2D model, where shearing takes place in the LR direction, it is the largest asperity to experience a tensile crack, as observed in the laboratory tests, but also asperity cut-off takes place.

Figure 26 shows the plot of the shear stress versus shear displacement obtained from both laboratory shear tests and PFC2D simulations. The results illustrated are for shearing in the LR direction and normal stress equal to 1.5 and 2.5 MPa.

Fig. 26

Shear stress versus shear displacement curves for profile B sheared at 1.5 and 2.5 MPa normal stresses: results of a laboratory shear tests and b PFC2D simulations

The laboratory results, as shown in Fig. 26a, exhibit a large difference between the peak shear strength of the two fractures. By increasing the normal stress the peak shear strength increases. Interestingly, the residual shear strength of both the curves approaches to an almost similar level (≈3.0 MPa) after the peak shear strength is reached.

A similar trend is observed with the PFC2D simulations as shown in Fig. 26b. The values of the peak shear strength as obtained from numerical modelling are slightly greater than the corresponding laboratory values at low normal stress. However, at high normal stress, this variation reduces and closer values are observed from both approaches. Comparing the peak shear strengths in Fig. 26a, b for normal stress of 2.5 MPa, a shear strength of ≈8.0 MPa is obtained.

The results presented demonstrate the capabilities of the PFC2D to simulate the shear behaviour of fractures and the laboratory results obtained with the FSC experiments confirm this to a large extent. In the next section, the laboratory shear tests performed on a specimen containing a rock-like fracture will be presented and some conclusions will be drawn based on the observed results.

4.3 Rock-Like Fracture

To generate a replica of a rock fracture (i.e. a rock-like fracture), a specimen containing such a fracture was placed inside the mould (Fig. 7) and the parts opposite to the fracture faces were filled with mortar (Fig. 27). The geometrical features of the fracture mating surfaces are thus reproduced satisfactorily. Indeed, the mechanical properties of the specimen may be somewhat different from those of the real rock. However, it is the geometry of the fracture which is of importance.

Fig. 27

Replica of a rock fracture made of mortar

High-resolution photos were taken from each fracture surface (i.e. lower and upper surfaces) and were analysed with photogrammetric methods using the Siro3D software (CSIRO 2009; Haneberg 2006). 3D images of the upper and lower surfaces of the fracture were obtained as shown in Fig. 28.

Fig. 28

Replica of rock fracture lower (top) and upper (bottom) surfaces

The rock block containing the fracture was tested in the laboratory using the FSC. The specimen was sheared in opposite directions along x–y plane and under 2.5 MPa normal stress. Each specimen was tested twice in order to study the evolution of the surface roughness after one shearing cycle.

The specimen containing the fracture is shown in Fig. 29 after shearing in the LR direction. In the first cycle, when the fracture was allowed to displace up to 1.0 cm, limited asperity contact degradations occurred. Then, the fracture surfaces were brought to the initial position and the second cycle of shearing was performed at the same normal stress (2.5 MPa).

Fig. 29

Replica of rock fracture block sheared in the laboratory at 2.5 MPa normal stress and in two shearing cycles

Figure 29, which also gives a view of the specimen after the second shearing cycle, shows that the amount of degradation has increased. Locations of the damaged area on the fracture surface are marked which clearly show that all the asperity contacts were damaged during this cycle of testing.

The shear stress versus shear displacement plot obtained from the laboratory tests is shown in Fig. 30 for shearing in both LR and RL directions at 2.5 MPa normal stress. Figure 30a in particular gives the results for the fractured sheared in the LR direction. A large difference between the peak shear strength obtained in the first and second cycles is noted. This is due to the predominant effects of the surface geometry (i.e. roughness) on the shear strength.

Fig. 30

Plots of shear stress versus shear displacement at 2.5 MPa normal stress a shearing in LR direction and b shearing in RL direction

From the first to the second cycle, the fracture roughness evolves and a different shearing response is observed in the second cycle. The peak shear strengths were measured to be ≈4.7 and ≈2.7 MPa, respectively, for the first and second cycle. It is seen that peak shear strength reduces in the second cycle, as expected, compared to the first cycle, which demonstrates that asperity damage takes place during the first cycle.

A sharp drop in the value of the shear stress is recorded, which is most probably due to a large asperity cut-off followed by the development of micro-cracks along the fracture surface. A different response is seen in the second cycle as no major sharp asperities exist and the broken asperities fill in the fracture opening. The average asperity angle can be calculated based on the mobilised friction angle of fractures in both cycles of shearing.

Assuming the basic friction angle to be 31°, the average asperity angle (i.e. roughness) estimated using Patton’s bilinear equation after the first and second cycle are 30.9° and 16.2°, respectively. It is seen that the asperity angle is reduced in the second cycle to twice as much as in the first cycle, which indicates the effects of asperity degradation in shear strength.

A comparison of the peak shear strength values given in Fig. 30a, b, for the normal stress equal to 2.5 MPa, shows that the fracture shear strength when shearing takes place in the LR direction is much greater than that obtained when shearing in the RL direction. This is in agreement with the expectations from visual observation.

5 Conclusions

In this paper, the modifications of an existing TTSC for fracture shearing experiments were reported. Large shear and normal load capacities, adjustability of the specimen size, and highly controlled shearing velocity are the main features of the FSC which has been developed.

Unconfined compression tests were performed in the laboratory on cylindrical specimens made of mortar and the results obtained were compared with the corresponding results of simulations with PFC2D models. In general, the results of numerical simulations and laboratory tests agreed satisfactorily. Using this approach, the values of the uniaxial compression strength and of the Young’s modulus were calibrated.

Shear tests were carried out on synthetic fractures with symmetric triangular and wavy asperities and a rock-like fracture (i.e. a replica of a real fracture) at a constant normal load. The shearing mechanism was shown to change from sliding to asperity degradation as the fracture surface becomes rougher. PFC2D models of both fracture profiles confirmed the results of testing.

Fracture shear strength directionality was investigated by performing laboratory shear tests on specimens sheared along the horizontal plane in two opposite directions. Fractures were subjected to shear tests and its directional dependency was studied in two shearing cycles. The results indicated that shear strength is reduced in the second cycle due to a reduced roughness after the first shearing cycle.