Unloading Stress Research Articles

Calculation method and evolution rule of the strain energy density of sandstone under true triaxial compression

Deep rock masses are typically in complex stress states, and research on the evolution of their strain energy density is of highly important for understanding their failure characteristics. In this work, a true triaxial stress‒balanced unloading test is designed to analyze the ud and ue evolution of sandstone under true triaxial compression conditions. The study results indicate that as σ1 increases, the elastic strain decreases in the σ2 and σ3 directions, whereas the residual strain progressively increases, and the magnitude of decrease in elastic strain exceeds the magnitude of increase in residual strain. Throughout the loading process of σ1, ue progressively decreases in the σ2 and σ3 directions, whereas ud gradually increases, and the magnitude of decrease in ue surpasses the magnitude of increase in ud. The ud and ue of sandstone under different stress levels were calculated via true triaxial stress‒balanced unloading tests, and the evolution of ud and ue in the three principal stress directions and the overall strain energy density of sandstone followed a linear energy storage law. On the basis of this law and the true triaxial stress‒balanced unloading test, a new method for calculating the true triaxial ud and ue was proposed. A study on the σ1 unloading stress path revealed that the σ1 unloading stress path significantly affects the storage and dissipation of the strain energy density in the three principal stress directions of sandstone. On the basis of the research results, the criteria for determining rockbursts were discussed.

Artificial intelligence-based investigation of fault slip induced by stress unloading during geo-energy extraction

Artificial intelligence-based investigation of fault slip induced by stress unloading during geo-energy extraction

Experimental study on shear mechanical properties of concrete joints under different unloading stress paths

In order to study the shear mechanical properties of rock joint under different unloading stress paths, the RDS-200 rock joint shear test system was used to carry out direct shear tests on concrete joint specimens with five different morphologies under the CNL path and different unloading stress paths. The unloading stress paths include unloading normal load and maintaining constant shear load (UNLCSL), unloading normal load and unloading shear load (UNLUSL), unloading normal load and increasing shear load (UNLISL). The results show that the peak shear strength, cohesion, internal friction angle, pre-peak shear stiffness and residual shear strength of concrete joints under CNL path increases with the increasing JRC and normal stress. Under the UNLCSL path, under the same initial shear stress τ1, instability normal stress σi decreases with the increasing JRC, and normal stress unloading amount Δσn increases with the increasing JRC. Under the same JRC, σi increases with the increase of τ1, and Δσn decreases with the increasing τ1. Under the same JRC and σi, τi is significantly smaller under the UNLCSL path than the CNL path. Under the same JRC, the cohesion under the UNLCSL path is less than the CNL path, and the internal friction angle is higher than that the CNL path. Under the same JRC and σi, τi is the largest under the path of CNL and UNLISL, followed by the UNLCSL path, and τi under the UNLUSL path is the smallest. Compared with the CNL path, the variation range of the specimen internal friction angle is within 3% while the average decrease percentage of the specimen cohesion reaches 37.6% under the UNLCSL path, UNLISL, and UNLUSL. Therefore, it can be inferred that the decrease in cohesion caused by normal unloading is the main reason for the decrease in joint instability shear strength. After introducing the correction coefficient k of cohesion to modify the Mohr-Coulomb criterion, the maximum average relative error after correction is only 3.5%, which is significantly improved compared with the maximum average relative error of 56.9% before correction. The research conclusions can provide some reference for the accurate estimation of shear bearing capacity of rock joints under different unloading stress paths, which is of great significance to the stability evaluation and disaster prevention of rock mass engineering.

Mechanical behaviour and macro-micro failure mechanisms of frozen weakly cemented sandstone under different stress paths

Significant unloading failure zones in artificial freezing shaft sinking projects in western China are primarily caused by stress release. To investigate the deformation and failure mechanisms of frozen weakly cemented sandstone (FWCS), three groups of triaxial unloading tests were conducted under different initial principal stresses (σ₃ = 3, 6, and 10 MPa) with an unloading rate of 0.05 MPa/s. Scanning electron microscopy (SEM) was employed to examine the micro-fracture characteristics of the failure surfaces. The results revealed that, compared to traditional triaxial and room-temperature triaxial compression tests, the strength and plastic deformation characteristics of FWCS are significantly weakened under unloading conditions. However, lateral deformation, particularly volumetric strain, increased markedly, exhibiting pronounced dilatancy characteristics, especially along stress path III (i.e., post-peak axial stress loading with confining pressure unloading). Unloading leads to a reduction in cohesion and an increase in the internal friction angle of FWCS, with the most significant changes observed along stress path IV (i.e., pre-peak constant axial displacement loading with confining pressure unloading). Macroscopic and microscopic analyses indicate that the failure mechanism of FWCS under complex unloading stress paths is driven by the rapid accumulation of energy caused by unloading, which results in the development and propagation of axial and circumferential cracks, widespread particle breakage, and the formation of inter-granular and trans-granular fractures, as well as shear scratches at the micro level, ultimately manifesting macroscopically as shear-tensile composite failure.

Mechanical Properties of Latex-Modified Cement Stone under Uniaxial and Triaxial Cyclic Loading.

During the cyclic injection and extraction process in underground storage wellbores, the cement sheath undergoes loading and unloading stress cycles. In this study, we investigated the mechanical properties of latex-modified cement stone (LMCS), widely used in oil and gas wells, through uniaxial and triaxial cyclic loading and unloading tests. The aim of the study was to determine the effect of various loading conditions on the compressive strength and stress-strain behavior of LMCS. The results show that the stress-strain curve of LMCS exhibits a hysteresis loop phenomenon, with the loop intervals decreasing throughout the entire cyclic loading and unloading process. As the number of cycles increases, the cumulative plastic strain of the LMCS increases approximately linearly. Under uniaxial cyclic loading and unloading conditions, the elastic modulus tends to stabilize. However, under triaxial conditions, the elastic modulus increases continuously as the number of cycles increases. This result provides data for engineering predictions. Furthermore, a comparison of the uniaxial and triaxial cyclic loading and unloading of LMCS shows that its cumulative plastic strain develops rapidly under uniaxial conditions, while the elastic modulus is larger under triaxial conditions. These findings provide a valuable reference for constructing underground storage wellbores.

Effect of stress unloading rate on fine-scale deformation mechanism of rock under high osmotic pressure

To explore the influence of the working face excavation rate on the rock deformation mechanism and seepage characteristics, deformation and seepage tests of sandstone under different loading and unloading stress paths, such as constant axial pressure unloading confining pressure and loading axial pressure unloading confining pressure, were carried out. Particle Flow Code in 3 Dimensions (PFC3D) and Python were used to realize fluid-solid coupling, and numerical simulation calculations were performed along the test path to analyze the influence of the unloading rate on the fine-scale deformation mechanism and permeability characteristics of sandstone, and the relationship between crack type and permeability was obtained. A sandstone fracture mechanics model is established to analyze the stress concentration degree at the end of the branch crack of the test path. The results show that the rate of confining pressure unloading is inversely proportional to the strain. Additionally, permeability correlates with the principal stress difference in an exponential manner. Interestingly, the sensitivity of permeability to stress shows an inverse trend with the unloading rate of confining pressure. Furthermore, there exists a linear relationship between permeability and the number of cracks. During the unloading process, tensile cracks predominate, and the propagation of shear cracks lags behind that of tensile cracks. The proportion of tensile cracks decreases with the increase of the unloading rate when the axial pressure is unchanged but increases when axial pressure is added, resulting in axial compression deformation and expansion deformation along the unloading direction. These research outcomes offer theoretical insights for the prudent selection of mining rates, and they hold significant implications for mitigating water inrush disasters in deep mining operations.

Effect of true triaxial principal stress unloading rate on strain energy density of sandstone

Deep rock are often in a true triaxial stress state. Studying the impacts of varying unloading speeds on their strain energy (SE) density is highly significant for predicting rock stability. Through true triaxial unloading principal stress experiments and true triaxial stress equilibrium unloading experiments on sandstone, this paper proposes a method to compute the SE density in a true triaxial compressive unloading principal stress test. This method aims to analyze the SE variation in rocks under the action of true triaxial unloading principal stresses. Acoustic emission is used to verify the correctness of the SE density calculation method in this paper. This study found that: (1) Unloading in one principal stress direction causes the SE density to rise in the other principal stress directions. This rise in SE, depending on its reversibility, can be categorized into elastic and dissipated SE. (2)When unloading principal stresses, the released elastic SE density in the unloading direction is influence by the stress path and rate. (3) The higher the unloading speed will leads to greater increases in the input SE density, elastic SE density, and dissipative SE density in the other principal stress directions. (4) The dissipated SE generated under true triaxial compression by unloading the principal stress is positively correlated with the damage to the rock; with an increase in unloading rate, there is a corresponding increase in the formation of cracks after unloading. (5) Utilizing the stress balance unloading test, we propose a calculation method for SE density in true triaxial unloading principal stress tests.

Energy and deformation field evolution characteristics of layered cemented paste backfill under cyclic loading and unloading

Due to the mining environment, layered cemented paste backfill (LCPB) is usually subjected to the cyclic pressure. Therefore, it is of great significance to investigate the mechanical behavior, failure mode and energy evolution characteristics. LCPB samples were prepared and subjected to constant lower limit cyclic loading and unloading test. The digital image correlation (DIC) technology was applied to monitor deformation field of LCPB. The obtained results indicate that: (1) The area of the hysteresis loops increases sequentially with increasing unloading stress level, while the spacing between the hysteresis loops gradually increases, showing the typical “dense-sparse” two-stage variation law. (2) Energy density and the unloading stress level is in agreement with the power function. The limiting elastic energy density (uemax) shows a linear decrease with the increase of h. The exponential function can well characterize the quantitative relationship between uemax and c/t ratio. (3) The damage mode of LCPB gradually tends to x-shape shear-dominated damage with the increase of h. The damage mode of LCPB is gradually dominated by shear-type damage with the decrease of c/t ratio. Ultimately, the findings of this work can provide a reference for the design of LCPB.

Improved calculation method for corresponding characteristics of foundation pit excavation on the diaphragm wall

The excavation of the pit causes displacement of the surrounding soil, and the excessive deformation causes damage to the existing support structure, which in turn affects the safety of the pit. Reasonable calculation of structural deformation and internal force is crucial for design and construction. Most of the existing theoretical methods simplify the diaphragm wall(DW) as an Euler-Bernoulli beam acting on the Winkler foundation, consider beam-soil interaction, and simplify the soil as isotropic and continuous. However, the shear effects due to the differential deformation of the structure, the unloading stresses acting on the structure due to foundation excavation, and the discontinuous nature of the multilayered soil are neglected. In this paper, an improved analysis method is proposed based on the elastic foundation beam theory. The DW is simplified as a Timoshenko beam and the foundation is simplified as a Vlasov two-parameter model, and a proposed model considering the shear effect of the DW and the interaction of adjacent springs is established, and the proposed method for the deformation and internal force of the DW is obtained by the finite-difference method. The correctness and applicability of the proposed method are verified by numerical simulation and field monitoring data. The effects of equivalent bending stiffness, equivalent shear stiffness, soil elastic modulus, and excavation depth on the deformation and internal force of the DW were further analyzed. The results show that the proposed method can accurately solve the deformation and internal force of the DW, and the maximum errors between the proposed method and the numerical simulation results are only 4.5 % and 1.3 %, respectively. The equivalent bending stiffness of the DW and the elastic modulus of the soil have more significant effects on the horizontal deformation and internal force. The excavation depth is more sensitive to the deformation of the DW, and there is an exponential decay trend between the two. When the equivalent shear and bending stiffnesses reach 6.8×107 kN·m2 and 2.9×107 kN/m, the effect on the horizontal deformation is no longer obvious. The proposed method in this paper can accurately calculate the internal force and deformation of the DW.

A three-dimensional numerical study on the stability of layered rock spillway tunnels in alpine canyon areas

Rock masses in alpine canyon areas exhibit strong heterogeneity, discontinuity, and are subject to strong tectonic effects and stress unloading, leading to extremely complex distribution of in-situ stress. In addition, the occurrence of layered rock masses makes it more complex, with obvious anisotropic mechanical properties. This study proposes a comprehensive method for evaluating the stability of layered rock spillway tunnels in a hydropower station in an alpine canyon. First, the failure criterion and mechanical model of layered rock masses considering the anisotropy induced by the bedding plane and the true triaxial stress regime were established; an inversion theory and calculation procedure for in-situ stress in alpine canyon areas were then introduced. Finally, by using a self-developed numerical tool, i.e. CASRock, the stability of the layered rock spillway tunnel in a hydropower station was numerically analyzed. The results show that, affected by geological structure and stratigraphic lithology, there is significant differentiation in the in-situ stress in alpine canyons, with horizontal tectonic stress as the main factor. The occurrence of layered rock masses in the region has a significant impact on the stability of surrounding rock, and the angle between the bedding strike and the tunnel axis as well as the bedding dip both exert a significant influence on the failure characteristics of the surrounding rock.

Research on the rebound rule of a pit bottom caused by excavation of typical strata

In practical engineering, the magnitude of soil unloading rebound is closely related to the physical and mechanical properties of the soil. Therefore, there are significant differences in geological conditions among the different regions. As such, targeted research on the rebound law and calculation methods of foundation pits is needed. This article reports indoor experiments and numerical simulation methods which are used to study the trends and calculation methods of foundation pit rebound based on typical geological conditions in South China. Our findings are as follows. 1) At maximum consolidation stress ranging from 100 kPa to 400kPa, the maximum rebound rate of plain fill soil in typical soil layers is 0.0539–0.0704, the rebound rate of silty clay is 0.0373–0.0528, the rebound rate of coarse sand is 0.0296–0.0343, the rebound rate of gravelly cohesive soil is 0.0159–0.0305, the rebound rate of fully weathered granite is 0.0175–0.0344, and the rebound rate of strongly weathered granite is 0.0170–0.0379. 2) The rebound indices do not change with changes in the unloading ratio or initial consolidation stress. The rebound indices of the soil layer from top to bottom are 0.0143, 0.0119, 0.0077, 0.0096, 0.0083, and 0.0076, respectively, and a formula for calculating the rebound modulus of typical soil layers in South China was proposed. 3) The pore ratio of the soil after the end of the recompression process is lower than that which occurs after the first compression. The difference between the compression porosity ratio of the soil layer from top to bottom and the compression porosity ratio is 0.1, 0.08, 0.02, 0.06, 0.02, and 0.03, respectively. 4) The calculation of the depth of influence by the self-weight stress offset method is based on the theory of eliminating self-weight stress and unloading stress. The calculation depth is not affected by geological conditions, the formula for calculating the rebound modulus is consistent with the formula obtained from experimental research, and the calculation results are in good agreement with the numerical values.

Mechanical behavior of rock under uniaxial tension: Insights from energy storage and dissipation

Many rock engineering projects show that the growth of tensile cracks is often an important cause of engineering disasters, and the mechanical behavior of rocks is essentially the transmission, storage, dissipation and release of energy. To investigate the tensile behavior of rock from the perspective of energy, uniaxial tension tests (UTTs) and uniaxial compression tests (UCTs) were carried out on three typical rocks (granite, sandstone and marble). Different unloading points were set before the peak stress to separate elastic energy and dissipated energy. The input energy density ut, elastic energy density ue, and dissipated energy density ud at each unloading point were calculated by integrating stress-strain curves. The results show that there is a strong linear relationship between the three energy parameters and the square of the unloading stress in UCT, but this linear relationship is weaker in UTT. The ue and ud increase linearly with the increase in ut in UCT and UTT. Based on the phenomenon that ue and ud increase linearly with ut, the applicability of Wetp index in UTT was proved and the relative energy storage capacity and absolute energy distribution characteristics of three rocks in UCT and UTT were evaluated. The tensile behavior of marble and sandstone in UTT can be divided into two stages vaguely according to the energy distribution, but granite is not the case. In addition, based on dissipated energy, the damage evolution of three types of rocks in UCT and UTT was discussed. This study provides some new insights for understanding the tensile behavior of rock.

Experimental study on the impact of effective stress and cyclic loading on permeability of methane hydrate clayey sediments

Permeability evolution directly determine gas production and its efficiency of gas hydrates in the South China Sea. Due to existence of submarine overlying rocks and change of soil internal mechanics during the hydrate exploitation, permeability evolution is significantly affected. Therefore, in this paper, influence of effective stress on the porosity and permeability of sediment with different hydrate saturation was studied, and functional relationship between them was revealed. Effect of cyclic loading and unloading stress on the permeability recovery and damage degree was also discussed. The results show that when hydrate saturation increases, the relation of permeability and effective stress are power function rules, while porosity and effective stress are exponential function rules in clayey sediments. An empirical prediction equation for gas permeability of clay sediments with effective stress was presented, which takes into account hydrate saturation and porosity. In addition, during cyclic loading experiments, the results showed a linear increase in permeability during unloading. The permeability recovery rate and permeability damage rate are completely opposite with change of hydrate saturation. Permeability damage rate of kaolin is different from that of other two kinds of sediment. With the increase of cycle times, the proportion of plastic deformation of sediment decreases gradually.

Fracture behavior in blasting under different static stresses and high stress unloading

AbstractIn this paper, the effects of static stresses on the blast‐induced crack in polymethyl methacrylate specimens with an empty hole were investigated by caustic system. The propagation behavior and re‐initiation process of blast‐induced crack under initial static stress and high stress unloading were investigated. The results show that when the direction of the empty hole is perpendicular to the static stress, the static stress reduces the length of the main crack. However, when the static stress is very high, the length of main cracks does not decrease. In addition, the static stress reduces the crack velocity and dynamic stress intensity factor (DSIF) and suppresses the increase of DSIFs and crack velocity due to reflected wave. The crack arrested under high stress unloading propagates again in the later stage. Moreover, the duration of high stress unloading lasts approximately 1 ms.

Dilatancy and Multi-Scale failure characteristics of a foliated rock under triaxial confinement unloading conditions

Controlled by the foliation structure, foliated rocks exhibit mechanical anisotropy and cause squeezing deformation and subsequent supporting structure failure during tunnel excavation. Here, the deformation and failure characteristics of a phyllite under unloading stress paths were experimentally investigated. The strength and elasticity parameters of phyllite exhibited moderate ‘shoulder’ shaped anisotropy, and specimens failed in three different modes: cross-plane shear-tensile fracture, in-plane shear sliding, and interlayer buckling, depending on the foliation angle and initial confining pressure. Meanwhile, the evolution of dilatancy angle during volume dilatancy also showed significant anisotropy, either increasing or decreasing with the increasing plastic shear strain during post-peak loading. We further discussed the mechanism of the evolution of dilatancy angle based on the multi-scale observation of the failure characteristics. Generally, interlayer buckling improved the dilatancy angle and roughness loss during shear failure resulted in dilatancy angle degradation. These findings provided evidence for a deeper understanding of the failure mechanisms of tunnel rock mass in foliated strata.

Influence of interphase type and thickness on the interface properties and tensile damage evolution of C/SiC composites

In this paper, the influence of interphase type (i.e. single-phase (PyC) and co-deposited (PyC+SiC)) and thickness (i.e. 300, 600, 1000, and 2000 nm) on the interface properties and damage evolution of mini-C/SiC composites under cyclic loading/unloading tension was investigated. The micromechanical constitutive model was adopted to derive the damage parameter of inverse tangent modulus (ITM) and perform the hysteresis analysis to estimate the interface properties of the mini-C/SiC composites with large debonding energy. Experimental damage evolution of the ITMs with unloading or reloading stress was analyzed for different interphase types and thickness. The interface properties (e.g. the interface debonding stress and interface debonding energy) were obtained through the hysteresis analysis. Relationships between the loading/unloading ITMs, interface properties, and interphase type and thickness were established.

Simplified method for evaluating tunnel response induced by a new tunnel excavation underneath

AbstractTo estimate the tunnel response induced by a new tunnel excavation underneath, theoretical solutions are proposed in this study. The overlying tunnel is idealized as an infinite Timoshenko beam resting on the Kerr foundation model, then the vertical force balance equation is established. The unloading stress can be expressed as Fourier cosine series and a theoretical solution can be derived. The effectiveness of the proposed method is verified by a centrifuge test and an actual field measurement, which are extracted from previous investigations. Calculation results from the proposed method show good accord to centrifuge test results and field‐measured data. Meantime the predictions given by the proposed method are more accurate to estimate tunnel response compared with the previous method. Parametric analysis indicates that the volume loss ratio and the vertical clearance between two tunnels, are both significantly alleviate the tunnel response, but the effect of tunnel shear stiffness is slight. The theoretical solutions can be adopted to predict the overlying tunnel response induced by tunneling underneath in real projects.

Experimental and numerical analysis of the effect of stress change on methane diffusion in coal matrix

ABSTRACT As a clean energy source and disaster gas, coal gas migrates not only under in-situ conditions, but also under stress disturbance due to mining. Although diffusion/desorption is key to gas extraction effects and gas disaster prevention, but the influence study of stress change is insufficient. This study aims to investigate the mechanism of action of stress change to gas diffusion, and a gas transport model considering stress effects is developed. Firstly, the diffusivity of anthracite coal under different stress conditions was measured using an experimental platform of coal-rock diffusivity. When the loaded stress for coal sample reduces 95%, the diffusion coefficient enhances 34%. Subsequently, the determining mechanism and rule of the pore size for gas diffusion in coal matrix were researched theoretically. The results suggest that the relationship between the diffusion flux and the matrix porosity is a power function, with the power exponent between 1 and 1.5, much smaller than the fractures. Experimental and theoretical studies have shown that the methane diffusivity minishes approximately linearly with increased effective stress. Then a methane transport model that involves the impact of stress change is constructed to analyze the effect on gas extraction. Numerical simulations show that the stress relief of a large diameter borehole has a significant effect on the diffusion, generating a larger drop of gas pressure near the borehole compared to the normal borehole. In the presence of regional stress relief, the diffusivity increases due to stress unloading, resulting in larger pressure drop around the borehole and gas drainage amount. The above results provide an important theoretical foundation for calculating gas migration with disturbed stress.

FRACTAL CHARACTERISTICS OF CORE DISKING FRACTURE SURFACES

The morphological characteristics of core disking can reflect the in-situ stress field characteristics to a certain extent, but a quantitative description method for disking-induced fracture surfaces is needed. The fractal geometry was introduced to refine the three-dimensional characteristics of the core disking fracture surfaces, and the disking mechanism was explored through morphological characteristics. The innovative concentric-different scale method was proposed to divide the circular surfaces into square surfaces of different sizes. Furthermore, the applicability of four cubic covering methods for single fractal calculation was studied. Finally, the relative differential cubic covering method and multifractal method were used to calculate the three-dimensional data of core disking fracture surfaces in the Jinping area. The results showed that the concentric-different scale method fits the fractal dimension changing law in the exploration of different surface sizes. Using the differential cubic covering method and the relative differential cubic covering method can obtain good results for smoother surfaces. The disking was caused by tensile stress due to high crustal stress unloading, and the cracks originated from the inside of the core. Fractal theory is conducive to analyzing the morphology of rock fracture surfaces and provides guidance for exploring the failure mechanism and influencing factors.

Study on dynamic characteristics of sandstone-damaged by loading and unloading

To investigate the impact of unloading on the dynamic mechanical properties of surrounding rock in roadway excavation, sandstone specimens were subjected to loading and unloading at six levels ranging from 0% to 80% of the uniaxial compressive strength (UCS). Subsequently, an improved SHPB was employed to perform dynamic compression tests, aiming to analyze the mechanical characteristics of the sandstone at various degrees of loading and unloading damage, investigate fractal attributes, and examine the dynamic failure process. The study uncovered that the stress–strain curve exhibits three distinct stages. Correspondingly, a more suitable set of dynamic elastic modulus denoted as Ed1, Ed2, and Ed3, were defined. Using 45% of the UCS as the threshold for unloading stress (75 MPa), both the dynamic elastic modulus and dynamic strength displayed an initial upward trend, succeeded by a subsequent decline. In contrast, the defined damage peak strain ratio ηεp and damage ultimate strain ratio ηεm demonstrated the opposite trend, amounting to 45.64% and 51.03% at the threshold. In addition, increasing unloading damage stress (UDS) decreases the sandstone strain rate(ε̇max and ε̇ave) gradually. Simultaneously, the fractal dimension of the cracks exhibited a linear increase, ranging from 1.159 to 1.481. Similarly, the rock exhibited the lowest proportion of reflected energy and absorbed energy at the threshold. This holds noteworthy implications for examining the dynamic load response behavior of surrounding rock in roadway unloading, ensuring the dependability of blasting unloading techniques.