Experimental Study on Progressive Damage Evolution in Rocks Subjected to Post-peak Cyclic Loading History

Fretting fatigue behavior of a titanium alloy was investigated using a dual actuator test setup which was capable to apply the pad displacement independent of the applied cyclic load on specimen. Fretting fatigue tests were conducted using this setup with a phase difference between cyclic load on the specimen and tangential force on the fretting pad with cylinder-on-flat contact configuration under partial slip condition. Two axial stress ratios were used. The relative slip range and tangential force range were related to each other and this relationship was not influenced by phase difference, axial stress ratio, and contact load under the partial slip condition. Change in the phase difference caused the change in relative slip as well as tangential force for a given applied pad displacement and axial load. However, there was no effect of phase difference on fretting fatigue life at a given relative slip level. Fretting fatigue tests with a fully reversed axial stress showed longer fatigue life than tension-tension counterparts at a given relative slip, tangential force range, and axial stress range. Finite element analysis was conducted by including the complete load history effects, which showed that stress distribution on the contact surface stabilized after the first fatigue cycle. Unlike relative slip and∕or tangential force range, a critical plane-based parameter appears to take into account the stress ratio effects to characterize fretting fatigue behavior.

Micro-textural effects on crack initiation and crack propagation of andesitic rocks

We have investigated the thermal creep of cold-worked Zr-2.5Nb tubes for a range of textures and stress states. The creep tests were performed on internally pressurized thin-wall standard (ratio of axial and transverse stress R≈0.5) and end-loaded (ratio of axial and transverse stress, 0.25<R<0.75) capsules 10 mm in diameter×40 mm long×0.5 mm wall-thickness at a stress of 300 MPa at 350°C where dislocation creep is the dominant operating mechanism. The tests showed an obvious correlation of anisotropic creep with the texture under different stress states. A self-consistent visco-plastic polycrystalline model based solely upon crystallographic texture showed a poor correlation with experimental results for radial basal textures, similar to that found previously for in-reactor creep. Hence texture alone is not sufficient to accurately predict the creep anisotropy. A modified self-consistent model is introduced to take into account different pre-existing anisotropic dislocation distributions (from cold-work) in different crystal orientations. Much better agreement with the experimental creep anisotropy was found, indicating that individual dislocation distributions in grains with different orientations are important in controlling the creep anisotropy. The predicted effect on creep anisotropy of introducing dislocation structures by a radically different strain path is very large.

It is beneficial to the sustainable development of expressway engineering to reuse excavated soil as roadbed filling material. There are a large number of filling projects using loess as a filling material in Northwest China. In this paper, the loess subgrade of an expressway in Lanzhou is taken as the research object, and a series of experimental studies are conducted using a hollow cylindrical torsion shear system to simulate the formation of a “heart-shaped” stress path and the principal stress rotation (PSR) under long-term traffic loads. The effects of the vertical cyclic dynamic stress ratio, torsion shear stress ratio, initial static shear stress, and intermediate principal stress coefficient on the axial plastic deformation and rebound deformation of compacted loess in Lanzhou were studied. The results show that the vertical cyclic stress ratio (VCSR) has a significant effect on the axial deformation of compacted loess in Lanzhou. When the VCSR is less than 0.6, all the axial strain curves develop stably with the number of cycles. With an increasing VCSR, the axial plastic deformation increases obviously, and the axial rebound deformation also increases. The vertical cyclic dynamic stress of the specimen is constant. Moreover, increasing the torsional shear stress ratio (that is, increasing the amplitude of cyclic shear stress) can greatly increase the development of axial deformation, but it has no effect on the rebound deformation curve. When the initial static shear stress exists in the specimen, the larger the initial static stress ratio (SSR) is, the larger the axial plastic deformation. The axial plastic deformation increases by approximately 33% for every 0.1 increase in the SSR. The rebound deformation of different SSRs fluctuates at the initial stage of cyclic loading, but the final stable rebound deformation is basically the same as that at the initial stage of cyclic loading. The intermediate principal stress coefficient has no effect on the development of axial strain, and the effect on axial rebound deformation is negligible. Finally, the calculation model of the axial plastic strain of Lanzhou compacted loess under traffic loads is obtained. The research results can provide a reference for the durability and settlement prediction in loess engineering.

Hydromechanical behaviour of an unsaturated silt with various suctions and different overconsolidated ratios (OCRs) was investigated through a series of undrained triaxial tests (constant water contents, CW). All the samples were prepared from the slurry state. Different OCRs (= 1, 2, 4, and 8 in net stress) were achieved by unloading the samples to 400, 200, 100, and 50 kPa from an initial confining net pressure of 400 kPa. Then the samples were dried to various suctions (0, 100, 200, 300, and 400 kPa). Unsaturated samples with different OCRs were then sheared at CW conditions following the conventional triaxial compression (CTC) paths. Full hydromechanical responses including the changes in deviator stress, stress ratio, volumetric strain, suction, and degree of saturation with axial strain were monitored and are presented in this paper. Some key findings include (i) the critical state for unsaturated soils with different OCRs can be well defined by Bishop’s effective stress; (ii) the peak strength in Bishop’s effective stress increases with increase of OCR, but decreases with increase of suction in the undrained condition; and (iii) the volume change of unsaturated soils in undrained conditions is related to OCRs and the volume of pore air.

Through the uniaxial compression tests of sandstone, the crack closure effect and the relationship between the crack parameters and the height to diameter ratio (H/D) were analyzed. Then, a nonlinear model for characterizing energy dissipation based on the crack closure effect was established. The results show that the peak strength and peak axial strain of sandstone decrease gradually with the increase of H/D, but the elastic modulus has a small change. The maximum crack axial closure strain and crack axial closure stress of sandstone increase with the H/D. While the peak crack axial strain and axial crack initiation stress decrease. The dissipative energy firstly increases with the axial stress, and the increase rate decreases gradually. Then, the dissipative energy nearly remains as a constant. The axial crack closure model was established to describe the crack closure effect of sandstone, and the equivalent elastic modulus of crack closure of sandstone calculated by axial crack closure model decreases nonlinearly with the H/D. A rock energy dissipation model based on crack closure under uniaxial compression was established. The experimental results agree well with the theoretical values, which indicates that the proposed model can describe the energy dissipation of rocks under uniaxial compression. The research conclusion provides a theoretical reference for the stability evaluation of underground rock masses with different sizes.

The objective of this study was to examine the shrinkage and creep of reactive power concrete (RPC) with different steel fibre contents (0%, 1% and 2% by volume). A total of 37 RPC specimens were prepared and tested for compression strength, elastic modulus, shrinkage, and creep. In addition, different axial stress ratios (0.2, 0.3 and 0.4) were used in the creep tests. Furthermore, the accuracy of the ACI 209-82 model, CEB-FIP 90 model, B3 model, and GL 2000 model for predicting the shrinkage and creep of RPC was evaluated and new numerical shrinkage and creep models were developed. The experimental results revealed that the compressive strength and elastic modulus increase with increasing steel fibre content. The shrinkage and creep decreased with increasing addition of steel fibre from 0% to 2%. A good linear relationship was found between the axial stress ratios and creep strain. All four existing models were unable to accurately predict the shrinkage and creep of RPC. A good agreement between the experimental results and proposed shrinkage and creep numerical models was observed. Therefore, it is suggested that the proposed shrinkage and creep models can be used to calculate the shrinkage and creep of RPC.

In the present study, mechanical behaviour of three types of rocks has been investigated under uniaxial compression. The stress–strain responses of the tested rocks are composed of four regions: the compaction stage; elastic stage; strain hardening stage and strain softening stage. The elastic modulus and uniaxial compressive strength increase in order from the result of the coal to the mudstone and then to the sandstone, while the Poisson ratio shows a reverse order. In coal and mudstone, volumetric dilation behaviour vanishes gradually with an increase in damage degree, while it remains stable in the sandstone where the strain hardening behaviour is less obvious. Regarding acoustic emission (AE) characteristics, AE hit and AE energy show a similar evolutionary trend in the loading process. A sudden increase in AE energy is accompanied with drastic drop or local fluctuation in the load-bearing capacity of the rock while AE hit fails in predicting such variation in the load-bearing capacity. A quiet stage of AE signal prior to the peak stress is captured, which can be taken as a precursor for rock failure. Failure pattern of the coal, mudstone and sandstone varies from shear faulting to tension-shear mixed fracturing and then to axial splitting, which is in good accordance with that deduced from AE location analysis.

The surrounding rock between two ultra-closely spaced roadways, under biaxial compression (BC) condition, exhibits high failure propensity and consequently poses serious threats to the coal mining operations. The counter-pulled rockbolt (hereinafter referred as “bolt”) is widely employed to improve the stability of this kind of surrounding rock. However, the strength, deformation, macro- and micro-failure behaviors of bolted surrounding rock under BC condition are insufficiently understood. Therefore, these performances of the bolted samples (BSs) are investigated by using biaxial compressive experiments and acoustic emission (AE) technology. The research results indicate that the bolt diameter has an obvious capacity in improving the peak and residual strength of BSs, the bolt pretension force can significantly enhance the peak strength of BSs, yet has a minimal impact on the residual strength. Three types of axial stress-axial strain curves were categorized: post-peak instantaneous stress drop type, post-peak multi-step stress drop type and post-peak stress delay drop type. A new reinforcement effect, termed as the all-directional reinforcement effect of the bolt was observed. Insights into the influence of bolts on the elastic modulus and lateral displacement of the samples under BC condition were obtained, and two mechanisms for the reinforcement effect of bolt on the lateral displacement of samples were revealed. When the lateral pressure σ2 is 8.89 MPa, the effect of the bolt on the failure pattern of BSs is not obvious. Nevertheless, the fracture angle increases with the increase of bolt diameter and pretension force. The micro-failure crack types were classified based on AE parameters of AF–RA and it was found that the micro-failure of the BSs was dominated by shear cracks. The micro-failure process of the BSs underwent three stages, with most micro-failures occurring in Stage II. A new approach capable of computing the peak strength or the equivalent cohesion (c*) and equivalent internal friction angle (φ*) of sample reinforced by pretension bolt is proposed and used to calculate c* and φ* of the BSs under BC condition.

In this study, the water absorption, mechanical properties, and energy evolution characteristics of sandstone were examined through experimental and theoretical analysis. The P-wave velocity was found to initially decrease, then increased with immersion time and water content. The water absorption rates of three sandstone specimens decreased with immersion time and water content. The post-peak deformation of the sandstone changed from brittle failure to strain softening. With the increase in water content, the peak strength and loading Young’s modulus per cycle decreased. The loading Young’s modulus showed that the unloading stress and increment of unloading stress nonlinearly increased with the number of cycles and decreased before peak strength. With the increase in the number of cycles, residual strains of the sandstone specimens decreased slightly initially and then increased, while the elastic strains increased before peak strength and then decreased at the post-peak stage. With the increase in unloading stress, the energy densities nonlinearly increased. At the same unloading stress, an increase in water content led to an increase in the input energy density and energy ratios of the sandstone specimens.

Aggregates are the principal materials of railway ballast, which for the most part contain huge, angular particles with a normal size of roughly 40 mm. Well-designed ballast is attractive to resist the pressures from the sleeper and after that to pass a satisfactory pressure level at the top surface of the subgrade soil. Though the functions of ballast by and large break down when subjected to Repeated traffic loading and in the end come into non-shakedown, (for the sample, ratcheting or incremental failure) reactions. In this work, a progression of expansive scale cyclic triaxial Experiments on aggregate did distinguish diverse cyclic degradation reactions. The permanent axial and volumetric strains are seen under various cyclic stress ratios. Three distinct cyclic reactions, shakedown, cyclic creep and incremental failure, are found. Shakedown happens at a moderately low cyclic stress ratio, under which the IPC (increase per cycle) of fixed axial strain and the IPC (area of hysteretic loop per cycle) of energy, dissipation will, in general, become negligible in the wake of cycling, and the fixed volumetric strains show compacting. Incremental failure happens at a generally high cyclic stress ratio, under which the IPCs of axial strain and energy dissipation increment after a set number of cycles, and the fixed volumetric strains show dilatancy. For cyclic creep, the IPCs of axial and volumetric strain and energy dissipation become about constant after an extensive number of cycles.

Zirconium-niobium (Zr-Nb) alloys are used as cladding materials to encapsulate radioactive fuel in nuclear reactors. They possess excellent corrosion resistance at high temperatures making it possible to achieve high fuel burnup, directly increasing the thermal efficiency of the reactor. While they are commonly used in recrystallized (Rx) form in boiling water reactors, there is a need to understand the effect of cold work and stress relief (CWSR) on the biaxial creep characteristics of these materials due to their use in pressurized water reactors. In this study, the biaxial creep behaviors of as-received Zr-Nb alloys, HANA and Zirlo®, have been investigated at 500°C and 400°C, respectively, using internally pressurized tubing superimposed with axial load under varied hoop σθ to axial σz stress ratios of 0 to 2 while monitoring both the axial and hoop strains using a linear variable displacement transformer and a laser telemetric extensometer, respectively. The crystallographic textures and creep loci of these as-received Zr-Nb alloys have been evaluated to correlate with the previous studies on recrystallized HANA4 and CWSR Zircaloy-4. The creep locus of HANA4 was found to be unaffected by initial state (CWSR or Rx) and showed close correspondence to planar isotropy while the creep locus of CWSR Zirlo exhibited more resistance to axial deformation than diametrical as per CWSR Zircaloy-4 reported earlier. These differences are shown to arise from grain-shape anisotropy of the CWSR Zirlo and Zircaloy-4. The simulated creep loci using crystallite-orientation distribution functions in conjunction with prism slip models showed excellent agreement with experimental results.

Energy is an internal variable during rock deformation and failure, and its dissipation and conversion law can reflect the rock’s internal damage and deterioration state. Analysis of rock deformation and failure process from the perspective of energy is helpful to deeply understand the mechanism of rock damage, fracture and instability failure, and has important theoretical and practical significance for the stability evaluation and support control of surrounding rock. In this study, through single cyclic loading and unloading (SCLU) experiments, cyclic triaxial loading and unloading (CTLU) experiments and conventional triaxial compression (CTC) experiments, the equivalent elastic modulus method based on elastic strain energy is proposed to analyze the energy conversion of rock. The results show that the error of the elastic strain energy calculated by the strain energy formula method is generally higher than 10% with the secant and tangent modulus of the loading and unloading curve as input parameters. Taking the equivalent elastic modulus proposed in this study as an input parameter, more accurate elastic strain energy can be obtained by the strain energy formula. During the rock failure process, the equivalent elastic modulus shows a three-stage characteristic of increase, steady and decrease. The equivalent elastic modulus can be estimated by the quadratic function between the equivalent elastic modulus and confining pressure and axial strain. Under the same deformation and deviatoric stress, the elastic strain energy stored in rock increases with increasing confining pressure. The local maximum energy dissipation rate corresponds to stress drop, and the peak energy dissipation rate appears near the peak strength. High energy dissipation mainly occurs in a short time after peak strength, and energy release and dissipation are more sudden and severe under high confining pressure.

A mechanical degradation index for rock

The creation of microfractures within rock is commonly observed as rock is strained. The presence of these microfractures constitutes damage to the rock, and this damage can reduce the rock’s strength. This paper explores the evolution of rock strength as microfractures within a rock accumulate. Two approaches involving different laboratory tests are used to study how cohesion and internal friction evolve during progressive damage to rock. The mobilized cohesion and friction angle are measured for intact and damaged rock specimens. Intact rock specimens tested under compression were used to determine the peak values of cohesion and friction angle for two types of rock. Specimens of rock with varying amounts of accumulated microfracture damage were tested under direct shear or multi-stage triaxial compression to measure the Coulomb strength parameters for damaged rock. The laboratory testing shows that cohesion decreases with strain as the rock accumulates internal damage caused by microfracturing before the peak strength. The frictional component of the rock strength starts to be mobilized as strain causes internal microfractures. The mobilized internal friction angle increases up to and slightly beyond the peak strength. A small amount of post-peak strain is required to initiate macroscopic slip surfaces, and until these are created, high frictional resistance is mobilized between the many interacting and interlocked pieces of rock in the test specimen. With further post-peak strain, the friction angle decreases as the macroscopic slip surfaces in the rock become well established.