Influence of volume compression on the unloading deformation behavior of red sandstone under damage-controlled cyclic triaxial loading

A reasonable evaluation of unloading deformation characteristics is of great significance for the effective analysis of deformation and stability of surrounding rocks after underground excavation.In this study,the damage-controlled cyclic triaxial loading tests were conducted to investigate the pore compaction mechanism and its influences on the unloading deformation behavior of red sandstone,including Young’s modulus,Poisson’s ratio,volumetric strain,and irreversible strain.The experimental results show that the increases of volumetric and irreversible strains of rocks can be attributed to the compaction mechanism,which almost dominates the entire pre-peak deformation process.The unloading deformation consists of the reversible linear and nonlinear strains,and the irreversible strain under the influence of the porous grain structure.The pre-peak Young’s modulus tends to increase and then decrease due to the influence of the unloading irreversible strain.However,it hardly changes with the increasing volumetric strain compaction under the influence of reversible nonlinear strain.Instead,the initial unloading tangent modulus is highly related to the volumetric strain,and clearly reflects the compaction state of red sandstone.Furthermore,both the reversible nonlinear and irreversible unloading deformations are independent of confining pressure.This study is beneficial for the theoretical modeling and prediction of cyclic unloading deformation behavior of red sandstone.

Evolution of mechanical parameters of Shuangjiangkou granite under different loading cycles and stress paths

Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.

Dynamic failure process of expanded polystyrene particle lightweight soil under cyclic loading using discrete element method

Expanded polystyrene(EPS)particle-based lightweight soil,which is a type of lightweight filler,is mainly used in road engineering.The stability of subgrades under dynamic loading is attracting increased research attention.The traditional method for studying the dynamic strength characteristics of soils is dynamic triaxial testing,and the discrete element simulation of lightweight soils under cyclic load has rarely been considered.To study the meso-mechanisms of the dynamic failure processes of EPS particle lightweight soils,a discrete element numerical model is established using the particle flow code(PFC)software.The contact force,displacement field,and velocity field of lightweight soil under different cumulative compressive strains are studied.The results show that the hysteresis curves of lightweight soil present characteristics of strain accumulation,which reflect the cyclic effects of the dynamic load.When the confining pressure increases,the contact force of the particles also increases.The confining pressure can restrain the motion of the particle system and increase the dynamic strength of the sample.When the confining pressure is held constant,an increase in compressive strain causes minimal change in the contact force between soil particles.However,the contact force between the EPS particles decreases,and their displacement direction points vertically toward the center of the sample.Under an increase in compressive strain,the velocity direction of the particle system changes from a random distribution and points vertically toward the center of the sample.When the compressive strain is 5%,the number of particles deflected in the particle velocity direction increases significantly,and the cumulative rate of deformation in the lightweight soil accelerates.Therefore,it is feasible to use 5%compressive strain as the dynamic strength standard for lightweight soil.Discrete element methods provide a new approach toward the dynamic performance evaluation of lightweight soil subgrades.

Mechanical properties and failure modes of stratified backfill under triaxial cyclic loading and unloading

Multiple filling of gobs will lead to a layered structure of the backfill.To explore the influence of layering structure on the mechanical properties and failure modes of backfill,different backfill specimens were prepared with a cement/sand ratio of 1:4,a slurry concentration of 75%,and backfilling times of 1,2,3 and 4,separately.Triaxial cyclic loading and unloading experiments were carried out.The results show that with an increase in backfilling time,the peak strength of backfill decreases as a polynomial function and the peak strain increases as an exponential function.The cyclic load enhances the linear characteristic of backfill deformation.The loading and unloading deformation moduli have a linear negative correlation with the backfilling time.The unloading deformation modulus is always slightly higher than the loading deformation modulus.The failure modes of stratified backfill are mainly characterized by conjugate shear failure at the upper layer and tensile failure across the layer plane,and there is usually no damage in the lower layer away from the loading area.

Mechanical Properties of Deep-buried Marble Material Under Loading and Unloading Tests

The mechanical properties are essentially different when rock material is subjected to loading or unloading conditions. In this study, loading and unloading tests with various confining pressures are conducted to investigate the mechanical properties of marble material samples taken from the deep diversion tunnels of Jinping II Hydropower Station. The stress-strain relationship, failure characteristics and strength criterion are compared and analyzed based on the experiment results. The results show： in the loading and unloading test, peak strength, lateral strain, axial strain and plastic deformation increase significantly as the confining pressure increases. Lateral strain increased significantly and obvious lateral dilatancy can be observed to the change of confining pressure; The fracture mode is mainly the single shear fracture for the triaxial compression test and post-peak test, angle between the failure surface and the ends of the rock material becomes smaller as the confining pressure increases. Hock-Brown strength criterion reflects the strength characteristics of marble material under two different unloading conditions, and has some supplementary effects to the rock material of mechanical field.

Ringlike failure experiment of thick-walled limestone cylinder specimens in triaxial unloading tests

In order to study the failure of surrounding rock under high in situ stress in deep underground engineering projects, disturbed by excavation unloading, we carried out triaxial unloading experiments using thickwalled cylinder specimens on a TATW-2000 rock servo-controlled triaxial testing machine in a laboratory. The specimens were made of limestone material, taken from Tongshan county, Xuzhou city, Jiangsu province, China. In our experiments, rock deformation and failure behavior was studied through loading and unloading of inner hole pressure of thick-walled cylinder specimens. At first, the axial stress, confining pressure and inner pressure were increased simultaneously to a specified designed state of stress. Then, keeping the axial stress and confining pressure stable, the pressure on the inner hole was decreased until the specimen was fractured. When the inner pressure was released completely but the specimen did not fracture, the confining pressure was decreased subsequently until complete failure occurred. Our experimental results suggest that traces of major circular ringlike fractures with a number of radial cracks often appear in thick cylinder walls. This type of ringlike failure phenomenon, similar to intermittent zonal fracturing characteristics of deep exploitation, has, so far, not been published. Our experimental results show that rock deformation and failure behavior of thick-walled limestone cylinders vary under different stress paths between loading and unloading. Tensile failure and orderly failure surfaces occur under unloading conditions while irregular damaged rock blocks are produced during loading failure. This type of triaxial unloading experiment provides for new research methodology and approach for thorough investigations on intermittent zonal fracturing in deep underground excavations.

Experimental investigation on damage evolution behaviour of a granitic rock under loading and unloading

In-situ rock failures can result from stress changes due to pure loading and/or unloading. Understanding of the damage evolution behavior in brittle rocks during loading and unloading is imperative for the designs of rock structures. In this paper, we investigate the damage evolution characteristics of a granitic rock during loading and unloading after a series of triaxial experiments performed at different confining pressures. The axial stress-axial strain variations of the tested specimens revealed that the specimens undergoing unloading fail with a lower axial strain compared to the specimens failed purely by loading. Higher confining pressures were observed to exacerbate the difference. Volumetric strain versus axial strain curves indicated that the curves reverse the trend with the beginning of major damage of specimens. We suggest here a new form of equation to describe the secant modulus variation of brittle rocks against the axial stress for the unloading process. Failure mechanisms of tested specimens showed two distinct patterns, namely, specimens under pure loading failed with a single distinct shear fracture while for the unloading case specimens displayed multiple intersecting fractures. In addition, analysis of the evolution of dissipation and elastic energy during deformation of the specimens under loading and unloading conditions showed differentiable characteristics. Moreover, we evaluated the variations of two damage indices defined based on the energy dissipation and secant modulus evolution during deformation and observed that both of them satisfactorily distinguish key stages of damage evolution.

Strength characteristics and energy dissipation evolution of thawing silty clay during cyclic triaxial loading

Cyclic triaxial tests are conducted to analyze the evolution of strength parameters and energy dissipation of thawing silty clay under different stress paths.The effects of freezing temperature,thawing temperature and confining pressures on the stress-strain and strength characteristics of soil samples are studied through monotonic loading and cyclic loading tests by using high-and low-temperature triaxial apparatus.The variation of the total work,elastic deformation energy,dissipated energy,energy dissipation rate,residual strain,and damage variable during loading and unloading are discussed.The experimental results show that the samples have higher strain tolerance under high confining pressure,low freezing temperature,and low thawing temperature,and the same other conditions.The soil sample state and failure pattern can be judged by using the energy parameters measured in the experiment.

Settlement and Stability Analysis on Soft Clay Under Cyclic Loading

The results of undrained cyclic triaxial tests on three types of clays are collected and a relationship among the accumulated strain, the initial stress state, cyclic stress in the soil, as well as the number of cycles is established based on the experimental data. With this relationship, a procedure is proposed for subsidence and stability analysis on soft clay under the action of cyclic loads.

Dynamic properties and liquefaction behaviour of cohesive soil in northeast India under staged cyclic loading

Estimation of strain-dependent dynamic soil properties, e.g. the shear modulus and damping ratio, along with the liquefaction potential parameters, is extremely important for the assessment and analysis of almost all geotechnical problems involving dynamic loading. This paper presents the dynamic properties and liquefaction behaviour of cohesive soil subjected to staged cyclic loading, which may be caused by main shocks of earthquakes preceded or followed by minor foreshocks or aftershocks, respectively. Cyclic triaxial tests were conducted on the specimens prepared at different dry densities （1.5 g/cm3 and 1.75 g/cm3） and different water contents ranging from 8% to 25%. The results indicated that the shear modulus reduction （G/Gmax） and damping ratio of the specimen remain unaffected due to the changes in the initial dry density and water content. Damping ratio is significantly affected by confining pressure, whereas G/Gmax is affected marginally. It was seen that the liquefaction criterion of cohesive soils based on single-amplitude shear strain （3.75% or the strain at which excess pore water pressure ratio becomes equal to 1, whichever is lower） depends on the initial state of soils and applied stresses. The dynamic model of the regional soil, obtained as an outcome of the cyclic triaxial tests, can be successfully used for ground response analysis of the region.

New artificial neural networks for true triaxial stress state analysis and demonstration of intermediate principal stress effects on intact rock strength

Simulations are conducted using five new artificial neural networks developed herein to demonstrate and investigate the behavior of rock material under polyaxial loading. The effects of the intermediate principal stress on the intact rock strength are investigated and compared with laboratory results from the literature. To normalize differences in laboratory testing conditions, the stress state is used as the objective parameter in the artificial neural network model predictions. The variations of major principal stress of rock material with intermediate principal stress, minor principal stress and stress state are investigated. The artificial neural network simulations show that for the rock types examined, none were independent of intermediate principal stress effects. In addition, the results of the artificial neural network models, in general agreement with observations made by others, show （a） a general trend of strength increasing and reaching a peak at some intermediate stress state factor, followed by a decline in strength for most rock types; （b） a post-peak strength behavior dependent on the minor principal stress, with respect to rock type; （c） sensitivity to the stress state, and to the interaction between the stress state and uniaxial compressive strength of the test data by the artificial neural networks models （two-way analysis of variance; 95% confidence interval）. Artificial neural network modeling, a self-learning approach to polyaxial stress simulation, can thus complement the commonly observed difficult task of conducting true triaxial laboratory tests, and/or other methods that attempt to improve two-dimensional （2D） failure criteria by incorporating intermediate principal stress effects.

Characteristic stress and strain precursor information for fine-grained granite during failure process under triaxial loading and unloading conditions

The unloading effect by excavation may cause irreversible and severe damage to the surrounding rock masses in underground engineering.In this paper,both conventional triaxial compression(CTC)tests and triaxial unloading confining pressure(TUCP)tests were conducted on fine-grained granite to study its triaxial compression failure processes due to unloading.Based on the crack volumetric strain(CVS)method,the crack axial strain(CAS)method and crack radial area strain(CRAS)method were proposed to identify the failure precursor information(including stress thresholds and axial strain at the initiation point of crack connectivity stage)during the rock failure processes.The results of the CTC tests show that the stable crack development stressσsd,unstable crack development stressσusd,and crack connectivity stressσct identified by the CAS method are 6%,74%–84%,and 86%–97%of the peak stress,respectively.For the TUCP cases,as the confining pressure increases,the stress thresholds,axial pressure at failure and axial strain at the start of the crack connectivity stage increase,while the time ratio of the crack connectivity stage to the entire unloading stage decreases.This indicates that fine-grained granite is prone to generate more cracks and leads to fail suddenly under high confining pressure.Furthermore,this new method demonstrates that the point at which the derivative of the radial crack area strain transitions from stable to a sudden increase or decrease is defined as the precursor point of rock failure.The results of axial strain at the starting point of the crack connectivity stage are very close to those predicted by the AE method,withβ1 no more than 11%.

Experimental Study on Excavation Characteristics of Rockmass by Triaxial Test

Applying MTS rock stiffness test machine, tests under triaxial condition were carried out for rockmass under loading and unloading. By measuring and analyzing such mechanical properties as stress, strain, elastic modulus, Poisson ratio and elastic wave velocity during the whole test process, the differences of mechanical characteristics under loading and unloading conditions were revealed, to provide some useful references for excavation.

Experimental study of seismic cyclic loading effects on small strain shear modulus of saturated sands

The seismic loading on saturated soil deposits induces a decrease in effective stress and a rearrangement of the soil-particle structure, which may both lead to a degradation in undrained stiffness and strength of soils. Only the effective stress influence on small strain shear modulus Gmax is considered in seismic response analysis nowadays, and the cyclic shearing induced fabric changes of the soil-particle structure are neglected. In this paper, undrained cyclic triaxial tests were conducted on saturated sands with the shear wave velocity measured by bender element, to study the influences of seismic loading on Gmax. And Gmax of samples without cyclic loading effects was also investigated for comparison. The test results indicated that Gmax under cyclic loading effects is lower than that without such effects at the same effective stress, and also well correlated with the effective stress variation. Hence it is necessary to reinvestigate the determination of Gmax in seismic response analysis carefully to predict the ground responses during earthquake more reasonably.

Finite element analyses of Wanjiazhai water transmission tunnel excavation and service

This paper is devoted to the nonlinear stress and strain analysis oftunneling and working conditions of Wanjiazhai Division Project No.7 Tunnel in Shanxi province ofChina. The initial geological stress of loess was simulated by grading fill; the theory of unloadingproposed by Duncan and boundary stress of elasticity were used to calculate the excavation of thetunnel; Goodman joint elements were applied to simulate the joints of the liners; both loading andunloading tests have been performed to determine the parameters of Duncan-Chang's model and thecalculated results were compared; Terzaghi' s theory on loosening earth pressure was applied. Manyworking conditions were analyzed and some reasonable results were obtained. Based on the analyses,reparative measures were proposed and completed. The tunnel has functioned well since October, 2001.

NMR-based damage characterisation of backfill material in host rock under dynamic loading

It is not uncommon that backfill material used in underground mining being exposed to repetitive dynamic stresses induced by blasting operations or rockburst events. Understanding the strength and fracture evolution of backfilled stopes is critical to maintain the long-term stope stability and ensure safe mining activities. This paper aims to study the damage evolution of the backfill material and its host rock behaviour under three-dimensional(3D) dynamic loading. Using a true-triaxial testing machine, multiple samples of backfill material enclosed by country rock were fabricated and tested under various dynamic loadings with different true-triaxial confining stress conditions. In addition, the nuclear magnetic resonance(NMR) measurement was conducted on the samples before and after exerting static and dynamic loading to obtain their porosity distribution changes. The experiment results suggested that with the increase of the dynamic loading, the porosity of the backfill sample goes through a two-stage process,which shows a slightly linear decrease and then followed by an exponential increase. The research findings can help understand the damage mechanism and fracture development of backfilled stopes and its host rock in deep underground mines, which are constantly subject to the combination of 3D static confining stress and dynamic loading.

Experimental study of dynamic resilient modulus of subgrade soils under coupling of freeze–thaw cycles and dynamic load

Although the dynamic properties of subgrade soils in seasonally frozen areas have already been studied, few researchers have considered the influence of shallow groundwater during the freeze–thaw(F–T) cycles. So a multifunctional F–T cycle system was developed to imitate the groundwater recharge in the subgrade during the freezing process and a large number of dynamic triaxial experiments were conducted after the F–T cycles. Some significant factors including the F–T cycle number, compaction degree, confining pressure, cyclic deviator stress, loading frequency, and water content were investigated for the resilient modulus of soils. The experimental results indicated that the dynamic resilient modulus of the subgrade was negatively correlated with the cyclic deviator stress, F–T cycle number, and initial water content, whereas the degree of compaction, confining pressure, and loading frequency could enhance the resilient modulus. Furthermore, a modified model considering the F–T cycle number and stress state was established to predict the dynamic resilient modulus. The calculated results of this modified model were very close to the experimental results. Consequently, calculation of the resilient modulus for F–T cycles considering the dynamic load was appropriate. This study provides reference for research focusing on F–T cycles with groundwater supply and the dynamic resilient moduli of subgrade soils in seasonally frozen areas.

New shakedown criterion and permanent deformation properties of unbound granular materials

Unbound granular material specifications for road pavements in Australia are primarily based on physical material specification rather than mechanical characterisation. This simplified approach does not reflect the actual material performance under repeated dynamic traffic loads. There is a little information available on the influence of the local crushed rock properties and compacted layer properties on permanent deformation (PD). This study aims to characterise the local unbound granular materials in Victoria according to their PD behaviour under repeated loads and to develop a suitable shakedown criterion that could describe the PD of the tested materials to simplify the flexible pavement design. Repeated-load triaxial tests were conducted over several samples with a range of moisture contents, gradations, densities, and stress conditions. The laboratory test results showed that PD behaviour was influenced by several factors. In addition, the tested subbase-specified unbound granular materials reflect high PD resistance that is almost equivalent to basequality unbound granular materials. This may indicate that current requirements for the subbase-quality unbound granular materials are over-prescribe. Moreover, as the existing shakedown criterion was not applicable for the multi-stage repeated-load triaxial test and the local tested materials, a new shakedown criterion and new boundaries are proposed based on the PD behaviour. In the proposed criterion, the shakedown ranges are identified based on the curve angle of the PD vs. logarithm of the number of loading cycles, and this new criterion was validated using several materials from existing literature. The local tested base and subbase materials can be assigned as Range A when PD\1%, Range B when 1%\PD\3%, and Range C when PD[3%. The proposed criterion could provide a useful and quick approach to assess the PD of the unbound granular materials with both single and multistages of stresses.

Dilatancy and liquefaction behaviour of clean sand at wide range of confining stresses

The state of clean sand was mainly dependent on its void ratio(density)and confining stress that greatly influenced the mechanical behavior(compression,dilatancy and liquefaction)of clean sand.Confirming whether the confining stress was a state variable of sand required precise element tests at different confining stress,especially the tests under very low confining stress whose test data were very limited.In this study,static-dynamic characteristics of clean sand was comprehensively investigated by a unified test program under low and normal confining stress ranging from 5 to 98 kPa,under monotonic/cyclic and drained/undrained conditions,together with the literature available data under confining stress of 1.0 to 3.0 MPa.For monotonic loading tests,the contraction/dilation phase transition was observed for loose sand at low confining stress,and dilatancy angles were stress-dependent.In addition,the liquefaction resistance was observed to increase with reducing of confining stress,and the axial strain varied from compressive to dilative when confining stress increased.Special attention was also paid to the enhancement effect of membrane,and it was observed that its influence on the test results was limited.In addition,the experimental results were proved reliable by reproducibility.

Effect of vertical stress rest period on deformation behaviour of unbound granular materials:Experimental and numerical investigations

Repeated load triaxial test is used to assess the deformation behaviour of unbound granular materials(UGMs) in flexible road pavements. Repeated load pulse characteristics(i.e. shape, loading period and rest period) are the stress configurations used in the experimental set-up to simulate the passing axle loads. Some researchers and standard testing protocols suggest a rest period of varying durations after a loading phase. A thorough review of existing literature and practises has revealed that there is no agreement about the effect of the rest period of vertical stress pulse on the deformation behaviour of the UGMs. Therefore,the main objective of this study is to investigate the effect of repeated stress rest period on the deformation behaviour of UGMs experimentally. Experiments are conducted, both with and without rest period, using basalt and granite crushed rocks from Victoria, Australia. Furthermore, in order to gain insight into the effect of the rest period, finite element modelling is also developed. Both the experimental and modelling results show that the rest period has a noticeable effect on both resilient and permanent deformation behaviours of UGMs. It is, therefore, recommended to take extra precautions while adopting a particular standard testing protocol and to supplement the results by additional tests with different loading configurations.