ENGINEERING BEHAVIOUR OF MODEL JOINTED ROCK UNDER CYCLIC LOADING

Abstract

Rock is widely used since decades as an engineering material for various construction projects in the field of civil, hydropower, mining and petroleum engineering. Rock in the field is encountered by the anisotropy of the rock due to joints, foliations and faults. The joints are the most common planes of weakness and sliding of blocks may occur easily along joint planes. Consequently, the jointed rock offers relatively little resistance against failure and strength of rock is considerably reduced. The strength and deformation behaviour of jointed rock is governed by the complex interaction of the joints with the intact material. In many situations, rocks in the field are subjected to cyclic loading. Examples of such cases are hydraulic tunnels subjected to cyclic changes in water pressure and repetitive freeze-thaw cycles in cold regions. With each progression of cycle, there is accumulation of fatigue and deterioration of material rock. So, to ensure long term stability of structures, an adequate understanding of behaviour of jointed rocks under the action of cyclic loading is a prerequisite. The present thesis attempts to investigate the effect of cyclic triaxial loading on engineering behaviour of jointed rocks and studies the fatigue damage evolution during cyclic loading. Extensive laboratory tests were performed on intact and jointed specimens of a model rock. The specimens were made of NX size. Specimens with a joint oriented at different orientations θ were prepared where θ is the angle between normal to the joint plane and loading direction. The θ ranged from 0º to 75º at an increment of 15º. Three level of roughness (JRC=2-4,12-14 and 14-16) were used while preparing specimens. Uniaxial and triaxial compression tests were conducted on the intact and jointed specimens under monotonic and incremental complete cyclic loading. The loading was applied under displacement-controlled environment at the rate of 0.002 mm/s. In each cycle, the displacement was increased by 0.1mm. Apart from main experimental programme, some pilot tests were conducted on natural sandstone and jointed model rock at different frequencies. The uniaxial strength of the jointed specimens under monotonic loading, showed anisotropic behaviour. Minimum values of strength were obtained at θ= 60º. Increase in roughness of joints has a positive effect on strength for joint orientations, θ=30º to 60º.Monotonic triaxial strength of jointed specimens also showed anisotropic behaviour. The trend of triaxial strength of the jointed specimens was similar to the uniaxial strength with the joint orientation. The influence of joint orientation and joint roughness was not so significant for θ=0º,15º and 30º but was substantial for θ=45º and 60º. With increase in confining pressure, the strength was found to increase in general. The residual strength of UCS and triaxial tests under monotonic loading was also affected by the orientation of the joint and JRC. The trend of the residual strength with the joint orientation was similar to that of the peak strength with the joint orientation. The deformational behaviour under monotonic loading was investigated by obtaining the tangent modulus and secant modulus for jointed specimens at different confining pressures. The anisotropic behaviour of modulus also had similar trend as was obtained for strength. To understand the deformation and failure of rocks, total stored energy (U₀) was computed by calculating the area under stress-strain curve. The stored energy at peak stress was examined for its variation with joint orientation θ and roughness of the joint. The total energy at peak also behaves in anisotropic manner with minimum value at θ=60⁰. The increase in roughness of joint was found to have positive effect on U₀. For tests performed under cyclic loading, the uniaxial and triaxial compressive strength of jointed specimens under cyclic loading was found to behave anisotropically. The peak strength increased with increase in roughness and confinement. In general, the effect of roughness and confinement was more prominent for θ=45º and 60º.The residual strength for the jointed specimens showed similar behaviour as was the peak strength with the joint orientation. The type of the failure mode for θ=0º-15º was vertical splitting and spalling. For θ=30º and 45º, this failure mode changes to shearing along the joint plane. This transition is influenced by roughness of joints. The deformational behaviour was investigated in terms of tangent modulus and secant modulus for all the jointed specimens under cyclic loading. The secant and tangent modulus values were estimated by drawing enveloping curve to stress-strain plot and for each cycle also. The secant and tangent modulus values were found to be lowest for θ=45º and 60º. The loading modulus and unloading modulus were estimated for each cycle and their trend with number of cycles was observed. The loading modulus and unloading modulus increased with increase in cycles up to last cycle. The trend was non-linear with number of cycles. The unloading modulus was higher than the loading modulus. The secant modulus showed increase in value with cycles and formed a hump near failure. The three stress thresholds namely, σcc (crack closure threshold), σci (crack initiation threshold), σcd (crack damage threshold) were obtained for all the jointed specimens. The values of the stress threshold ratios were found to be quite high as compared to the values reported by Eberhardt, 1999. The higher values of crack closure thresholds result in increase in stiffness values of specimen and increasing values of moduli during cyclic loading. The literature states that fatigue damage evolution curve should involve three phases i.e., initial fatigue, uniform velocity and accelerated phase (Xiao et al., 2009, 2010). The fatigue damage evolution was examined for intact and jointed specimens. Three different descriptors i.e., modulus, irreversible strain and dissipated energy were used as damage variable to simulate the fatigue damage evolution. With increase in cycles, there should be accumulation of fatigue damage. For present study, the modulus values were found to increase with increase in cycles. Despite accumulation of fatigue damage with each successive cycle, the modulus increases. Thus, modulus as a descriptor for damage variable is not found to be good representative of fatigue evolution of damage for present study. When irreversible strain was used as a descriptor, the trend of accumulated irreversible strain with the number of cycles was relatively better than the modulus. The accumulated irreversible strain was lower for the specimens with higher roughness and vice-versa. For the specimens where the failure was governed by both intact material and joint, the accumulated irreversible strain had only two phases of fatigue damage evolution. The different phases of evolution were not well reflected for the case of θ=45° and 60° particularly for low roughness, because of sliding being the dominating mode failure. With increase in confining pressure, the three phases were visible as sliding along joint was restricted due to confinement. For higher JRC and higher confinement, the three phases of fatigue damage were visible clearly. On using the accumulated dissipated energy as a descriptor, it is observed that the damage starts gradually and there is very small damage at the beginning. In the next phase, there is gradual increase in damage and near the failure, damage increases rapidly till failure. For intact rock, the damage variable showed the three phases of fatigue damage evolution. For low roughness the trend of damage evolution was reflected well only for the specimens tested under confining pressure of 3MPa. Strength criteria are used to model the strength of rocks at given confining pressure. Peak triaxial strength of the jointed specimens was modelled through linear M-C criterion. In addition, Single plane of weakness theory (Jaeger,1960), Ramamurthy criterion (Ramamurthy, 1993) and Modified-Mohr Coulomb criterion (Singh and Singh, 2012). The M-C parameters, c and ϕ were obtained from test data. The parameter c was found to systematically and substantially be affected by joint orientation for peak and residual strength for both monotonic and cyclic loading. No such behaviour was found for ϕ. SPWT (Single plane of weakness theory) was used to predict the strength of the jointed specimens. For both monotonic as well as cyclic loading, the SPWT fails to capture the influence of joint into governing the strength of specimens where failure was solely governed by the intact rock material properties. The theory is found applicable only for joint orientations when sliding along joint occurs i.e., θ=45⁰ to 60. In this range of orientation, the theory performs better for monotonic as compared to cyclic loading. When Ramamurthy criterion is applied to model non-linear strength of jointed specimens, it is found to predict the strength reasonably well. The criterion worked better for monotonic loading as compared to cyclic loading. When Modified Mohr-Coulomb was used for predicting the triaxial strength of the jointed specimens, the triaxial strength values predicted are in good agreement with the observed experimental values for both monotonic and cyclic loading. It is concluded that as compared to Ramamurthy (Ramamurthy, 1993) and Modified-Mohr Coulomb (Singh and Singh, 2012), Modified-Mohr Coulomb (Singh and Singh, 2012) criterion predicted more accurately the deviatoric stress at failure of jointed specimens for a particular confinement. For applicability of non-linear strength criteria for jointed rocks, UCS of rockmass is an important input parameter. In literature, many correlations are available to estimate the uniaxial compressive strength of jointed rock (RMR, Q system, RQD, Rock Mass Index, Joint factor concept). Joint Factor concept was developed based on extensive test data for natural and model rock. In present study, Joint Factor concept has been used to predict the uniaxial compressive strength of jointed rock for monotonic case. An expression has also been suggested to compute the UCS of jointed rock under cyclic loading from UCS of jointed rock under monotonic loading.Modelling of fatigue evolution was attempted using three descriptors i.e., modulus, dissipated energy and irreversible strain. The modelling of fatigue damage evolution was done by applying the inverted-S curve damage model. Modulus values were not found to be suitably reflecting systematic evolution of fatigue damage. The irreversible strain and dissipated energy both show gradual accumulation of damage with progression of successive cycles and three phases of fatigue damage evolution. When irreversible strain was used as a descriptor, the systematic fatigue damage evolution was reflected only for some cases. These cases involved joint orientation for smooth joint and lower confining pressure, where failure is predominantly by slip along joint. For other cases, the systematic evolution was not prominent. When dissipated energy was used as a descriptor, it was found in general that the dissipated energy has been able to reflect the fatigue damage behaviour well for the specimens whose failure is governed by rock matrix and joint plane. For θ=45° and 60°, under low confinement, the three phases are prominently visible as compared to other cases and systematic evolution of damage is reflected more precisely. The damage evolution parameters were obtained using computer program through minimisation of errors. It was also found that the parameter α and β both were positively correlated to each other whereas the parameter β behaves inversely proportional to parameter p. Similarly, evolution of fatigue damage was modelled for the natural rock sandstone tested under incremental complete triaxial cyclic loading. Modulus, irreversible strain and dissipated energy were used as descriptor to define the damage variable. For sandstone also, it was concluded that the dissipated energy and irreversible strain were better descriptors as compared to modulus. It was also found that the parameter α and β both were positively correlated to each other whereas the parameter β behaves inversely proportional to parameter p. So, overall, it was concluded that the applicability of the inverted-S curve relies on various factors such as the type of cyclic loading applied, confining pressure, type of discontinuities, levels of stress amplitudes and frequencies, and other attributes of jointed specimens such as JRC, persistency, frequency of joint. This would be beneficial for the safe and reliable design for the long-term planning of underground projects in the field of civil, mining and hydropower engineering.