Unloading Paths Research Articles

Failure behaviors of fractured granite during loading and unloading under high confining pressure based on acoustic emission multi-parameter analysis

To investigate failure and mechanical behaviors of fractured rocks during loading and unloading under conditions of high ground stress, a series of loading and unloading tests were conducted on granite containing prefabricated fractures under high confining pressure. Results indicate that the evolution of acoustic emission (AE) events of fractured granite during loading and unloading under high confining pressure is strongly correlated with the deformation and failure and the energy evolution process in the rock, the peak values of AE cumulative energy and AE cumulative count rate in the pre-peak deformation stage decrease first and then increase with the dip angle (the minimum value is reached at 60°), when the dip angle is 0° to 60°, the number of AE events increases abruptly due to closure of the prefabricated fracture in the early stage of loading(only about 30 % of the main fracture time). After the fractured granite enters the unstable crack propagation stage, the crack tips are subject to a dynamic cycle of stress concentration, crack propagation, and stress release, accompanied by significant fluctuations in the energy rate before and after the point of peak AE energy rate. Therefore, the cracks propagate in an intermittent or a stepped manner. Under the unloading path, the process of crack development, gathering, and coalescence in the granite happens earlier, and there are more high-energy AE events in the failure process. The value of the brittleness index Bd is larger under the unloading path under high confining pressure, which reflects more significant brittle failure characteristics. The research provides a basis for judging failure precursors of rocks using AE characteristics in the failure process.

An investigation of shock-induced phase transition in soda-lime glass

There exists a large body of evidence from experiments and molecular dynamics simulations to suggest the occurrence of phase transitions in soda-lime glass (SLG) and other silica glasses subject to shock compression to pressures above 3 GPa. In light of these findings, the current work investigated the existence of phase transition in SLG using shock and release experiments. The experiments employed symmetric SLG–SLG impact to achieve complete unloading to zero stress after shock compression to stresses in the range of 3–7 GPa. The stress–strain response and the Lagrangian release wave speed behavior of SLG obtained from these experiments are seen to reveal a mismatch between the loading and unloading paths of the pressure–strain curve for the material, which serves as compelling evidence for the occurrence of a shock-induced phase transition in the material at relatively low pressures. Furthermore, the release wave speed vs strain data obtained from experiments were used to construct a methodology for modeling the shock and release behavior of SLG. This scheme implemented in numerical simulations was able to capture the release behavior of shock compressed SLG, for which a robust and satisfactory model was previously unavailable.

Unloading and reloading stress-strain relationship of recycled aggregate concrete reinforced with steel/polypropylene fibers under uniaxial low-cycle loadings

To solve the key scientific problems such as low toughness and easy cracking of recycled aggregate concrete (RAC), A new sustainable material (fiber-reinforced recycled aggregate concrete - FRAC) was obtained by adding steel fiber (SF) and polypropylene fiber (PPF) into RAC matrix. Few experimental results were reported for the material under uniaxial low-cycle loading, and consequently, there is a gap in constitutive propositions to predict its behavior. Thus, one purpose of this research is to provide experimental results for FRAC characterizing damage growth and residual strain during cyclic compression in low-cycle tests with increasing strain amplitudes. Another purpose is to present a constitutive model to predict this behavior of FRAC accounting for fiber content. It is worth noting that the present results are relevant to displacement-controlled tests. The development law of residual strain (permanent strain) is explored, and the relationships between residual strain and unloading strain/reloading strain are proposed. The unloading stress-strain/reloading stress-strain equations are given. The damage evolution law of FRAC is revealed. Also, a new damage model represented by residual strain is suggested accounting for the fiber content. Furthermore, a stress-strain constitutive model coupling damage for FRAC is proposed. The model predicted with accuracy the unloading path, reloading path, residual strain development, and damage evolution for the composite accounting for fiber content.

Unloading effect of the shear resistance of rock joints

To investigate the stress path dependent of rock joints, a series of tangential loading tests and normal unloading tests were conducted using 32 cement mortar replicas of artificially split rock joints with 4 different joint roughness coefficients (JRC). The critical normal stresses of the unloading tests were recorded, and a comparative study was conducted by referencing the results under different loading paths and joints conditions. The test results indicate that the shear resistance has a distinct unloading effect, which is mainly influenced by the morphologic characteristics, normal stress levels and stress paths. By analyzing the results, it can be concluded that the variation trend of shear/normal stress ratio against the normal stress and JRC of the two test conditions were identical. However, under low normal stress condition, the stress ratio of the joints under normal unloading stress path is the higher one; while under higher normal stress, the relationship becomes converse. Compared to that of the tangential loading condition, shear/normal stress ratio of the unloading stress path reduces rapidly as the increasing of normal stress, and the influence of the morphology is masked under lower normal stress.

Experimental Study on the Mechanical Characteristics of Saturated Granite under Conventional Triaxial Loading and Unloading Tests

It is essential to study the mechanical properties of saturated rock under different loading and unloading paths for strength calculation, safety assessment and disaster prevention; however, current literature rarely mentions conventional triaxial loading and unloading conditions. To analyze the mechanical properties, strain energy evolution characteristics and failure mode, a series of conventional triaxial unloading tests (with axial loading rate va of 0.06–6 mm/min and circumferential unloading rate vu of 0.1–10 MPa/s) and conventional triaxial compression tests were carried out on saturated granite. The test results showed that the damage sources of specimens in the conventional triaxial unloading test were mainly related to circumferential deformation, while in the conventional triaxial compression test, it was related to the axial deformation. Under the same va, the confining pressure and axial stress at the failure point decreased with the increase of vu, and the stress coordinate of the failure point was located outside the conventional triaxial compression envelope of σ1–σ3. As vu increases, except for the variation of circumferential strain energy ΔUc decreasing slowly, the trend of strain energy changes must be determined together with va. As va increases, the relationship between the magnitude of each energy changes from ΔUa > ΔU > ΔUd > ΔUe > ΔUc to ΔUd > ΔUa > ΔU > ΔUe > ΔUc, while the change of dissipated energy is dominated by vu and va together to become dominated by va. In addition, with the increase of vu and va, the damage pattern of the specimen also changes from shear damage in a single shear plane to mixed damage with tensile strain failure and shear plane during which the dilation angle of the specimen increases in total except for vu = 10 MPa/s, va = 0.6 mm/min and 6 mm/min.

Research on rock permeability and failure characteristics under different loading and unloading paths

Research on rock permeability and failure characteristics under different loading and unloading paths

The Effect of Unloading Path on the Time-Dependent Behavior of Beishan Granite

Abstract Understanding the time-dependent characteristics of Beishan granite after excavation is critically important for the long-term stability and disaster control of the high-level radioactive waste repository. In this context, a series of creep tests under different unloading paths are designed to simulate the time-dependent behavior of rock mass after excavation. Results show that the instantaneous volume deformation under each loading step is greatly influenced by the unloading path. Moreover, the unloading path has minor effects on the creep strain. The axial and lateral creep strain is dominated by creep fracture potential, which can be characterized by a unified time-dependent fracture potential index (ξTFPI) for different stress states. It is observed that the creep strain generally increases with increasing ξTFPI. In order to describe the fracture mechanism during the creep process, a damage mechanical model based on time-dependent subcritical crack growth theory is adopted. It reveals that the strain hardening behavior dominates the granite creep process, and the strain softening effect is gradually strengthened with increasing ξTFPI.

A Study of Dynamic Loading and Unloading Damage of Fiber-Reinforced Concrete under Confining Pressure

Considering the influence of confining pressure in the actual service environment of concrete in underground projects, the damage characteristics of fiber-reinforced concrete under the action of confining pressure are evaluated according to the variation of measured permeability values by means of a triaxial ultralow permeability damage test system. The tests were carried out according to the stress loading and unloading paths of 1⟶5⟶10⟶15⟶20⟶10⟶5⟶1 MPa for an axial pressure when the confining pressure value was 1 MPa and kept constant. Firstly, the damage permeability of the fiber-reinforced concrete specimens was verified to be significantly lower than that of the ordinary concrete under the same confining pressure. Secondly, by conducting single loading and unloading tests at different loading rates (0.5, 1.0, 1.5, and 3.0 MPa/s), it was confirmed that the loading rate had a significant effect on the damage cracking of the specimens, with the faster the loading rate, the more pronounced the damage characteristics. Finally, a triaxial cyclic dynamic load test with a confining pressure value of 1 MPa and an axial loading speed of 1.5 MPa/s was carried out, revealing that the damage characteristics of the test blocks changed from elastic deformation to obvious plastic deformation damage as the number of loading times increased.

An Experimental Study on the Effects of True Triaxial Loading and Unloading Stress Paths on the Mechanical Properties of Red Sandstone

Loading and unloading stress paths play critical roles in investigating the deformation and failure of roadway excavation. In this study, tests under four different loading and unloading stress paths were conducted on red sandstone samples, with the aid of a self-developed true triaxial test system. Meanwhile, the deformation and failure characteristics of the samples were monitored during the tests. The following research conclusions were obtained: The octahedral shear stress is linearly correlated with the average effective stress, and the correlation coefficient R2 is 0.9825. The Mogi–Coulomb strength criterion is superior to the Drucker–Prager strength criterion in reflecting strength failure characteristics of red sandstone during loading and unloading. Shear failure tends to occur under uniaxial compression, whereas shear–tensile composite failure occurs under loading and unloading conditions. Compared with the true triaxial loading test, loading and unloading tests produce a larger strain in the unloading direction. Under loading and unloading stress paths, with the increase in intermediate principal stress (IPS), the strain in the direction of IPS gradually changes from expansion to compression, and the peak strength gradually increases. The state of IPS affects the failure strength of the sample and reflects the strengthening effect of IPS. This paper boasts a certain value and significance for research on the deformation and failure characteristics of sandstone in the actual in situ stress environment with triaxial dynamic changes.

Experimental investigation on the stress-strain behavior of unsaturated polyester polymer concrete subjected to monotonic and cyclic loadings

The use of polymer concrete (PC) in construction requires the development of an accurate stress-strain relationship that can accurately predict the mechanical properties of PC. Given that no constitutive equation for cyclic loading of unsaturated polyester PC (UPPC) is available in the literature, the goal of the current research has been to propose a rational analytical model for estimating the mechanical characteristics of UPPC under tensile and compressive loading. Compressive and tensile cyclic and monotonic tests were performed on specimens which had been cured for 28 days and the average monotonic stress-strain curve was obtained for the monotonic tests. The average maximum stress and strain were determined for both the compressive and tensile tests and the elastic modulus and energy absorption capacity were computed and compared with the values for normal concrete (NC) and high strength concrete (HSC) materials. Analytical models for the monotonic and skeleton curves for both tensile and compressive tests have been provided, and the proposed models were compared to experimental findings and other research results for validation. Stress-strain relationships have been proposed for the unloading and reloading paths and were compared with the cyclic test results. The ultimate stress and strain for the UPPC were three and five times higher, respectively, than for the NC in tension testing. The ultimate strain for UPPC was almost 150% greater than the final strain of HSC in compression. Under compressive loading, the UPPC absorbed to 2.33 and 5.3 times more energy, respectively, than the HSC and NC. The results showed that the skeleton curves agreed well with the monotonic curves for the compressive and tensile tests. All of the proposed models agreed well with the available experimental data and previous study results.

Experimental Study on the Evolution Trend of the Pore Structure and the Permeability of Coal under Cyclic Loading and Unloading.

In the deep mining process of coal seams, the mechanical environment of the coal body is complex and in the state of cyclic loading and unloading. The change in the stress state leads to the change in the pore characteristics and the permeability. To investigate the effects of cyclic loading and unloading on the pore characteristics and the permeability of coal, the seepage experiment was carried out for the coal samples using the self-developed triaxial permeation instrument. By pressure confining and continuous cyclic loading and unloading, the evolution of the porosity and the permeability of the coal samples was investigated. Under the condition of the experiment, the influences of the initial value of the confining pressure and the cyclic load amplitude on the evolution of the permeability and the pore structure characteristics of the coal samples were clarified. The experimental results showed that the porosity and the permeability decreased exponentially with an increase in the number of loading and unloading cycles, and this decreasing trend gradually weakened until the porosity and the permeability became relatively stable. When the cyclic load amplitude was the same and the confining pressure increased, the effective porosity of the coal body and the bound porosity decreased. When the confining pressure was the same and the cyclic load amplitude increased, the effective porosity of the coal body decreased and the bound porosity increased. The loss rate of the permeability of the coal samples increased gradually with an increase in the cyclic load amplitude. The same tendency was observed when the cyclic load amplitude was the same, and the confining pressure was different, while the increasing trend was not so obvious. By analyzing the relationship between the porosity and the permeability of the coal samples under different cyclic loading and unloading paths, it was found that the effective porosity and the permeability of the coal samples conformed to the power–law relationship in the process of cyclic loading and unloading, and the change in the cyclic load amplitude had a significant effect on this relationship. The influences of the cyclic load amplitude and the confining pressure on the stress sensitivity of the coal samples were considered, and the change factor of the stress sensitivity was introduced into the relationship between the porosity and the permeability. This relationship was established considering cyclic loading and unloading.

A topological view on microscopic structural evolution for granular material under loading and unloading path

Granular materials demonstrate complex mechanical behaviors due to the irreversible rearrangements at particle scale. The irreversible behaviors of granular materials can be observed after unloading the granular assembly. In this study, biaxial tests of dense and loose granular assemblies are conducted using discrete element method (2D DEM). We investigate the multiscale behaviors of granular materials under loading–unloading-reloading path. Both dense and loose granular assemblies show hysteresis loops, but their underlying mechanisms and meso-structural evolutions are different. The hysteretic behavior of the dense sample is relevant to the dynamics of contact force network and the evolution of contact loops. The approximate linearity of stress–strain relation during unloading and reloading stages is attributed to the robustness of strong contact network, while the nonlinearity of stress–strain relation is related to the evolution of contact topology. Specifically, loops of 4-sides within the contact network play an important role by transforming into smaller or larger loops by losing and joining particles during the unloading and reloading path. The loose compactness of granular media results in the unapparent evolution of structures at the mesoscale. Besides, the roles of strong and weak subnetworks are not distinguished. The fewer changes in contact loops may cause unconspicuous nonlinear deformation.

Simplified plasticity damage model for large rupture strain (LRS) FRP-confined concrete

Large rupture strain (LRS) fiber-reinforced polymers (FRP) composites with an elongation greater than 5% offer an attractive solution for seismic strengthening of reinforced concrete (RC) columns. For a quick and reliable design of LRS FRP-strengthened RC columns, this paper presents a simplified plasticity damage model for LRS FRP-confined concrete under cyclic axial compression. This model consists of two parts: (a) a recent monotonic LRS FRP-confined concrete model developed by the authors’ group as an envelope curve and (b) a simplified linear plasticity damage cyclic rule for predicting unloading and reloading paths. To solve the cyclic model deviation induced by concrete softening under a large axial strain, a pseudo-plastic strain was proposed, based on which the damage degradation of FRP-confined concrete can be quantified. The model comparisons show that although the proposed model sacrificed some precision when directly applied for the cyclic axial compressive behavior of FRP-confined concrete, it can give similarly accurate predictions as a complex model does for the behavior of conventional or LRS FRP-jacketed RC columns under a combined axial load and cyclic lateral load. Thus, this simplified plasticity damage model serves as a promising basic model for simulation of the seismic performance of FRP-strengthened structures.

Stability prediction and analysis for large underground cavern controlled by weak interlayer zone under high geostress

Due to the special engineering geological characteristics of weak interlayer zone (WIZ) with the initial shear, the pre-consolidation, the water softening and clay generation, that occurs between different rock strata (e.g., tuff and basalt), it tends to represent potential threats to the overall stability of large underground cavern under high geostress, such as the large deformation of upper and lower rock masses, structural stress-induced collapse and the time-dependent plastic squeezing-out failure, which could never be neglected, and requires more widespread concern. Focusing on the prediction and analysis of such stability issues induced by WIZ, a novel constitutive model for WIZ, based on the unearthed macro-meso mechanical response of WIZ under complicated unloading stress paths, has been first established, and well embed into the effective numerical calculation platform, to realize the quantitative descriptions of the mechanical effects of stress path, the particle breakage as well as the mechanical parameter evolution of WIZ. Then the rock failure index for WIZ (RFDwiz) was derivated, to help determine the cracking scale, depth and degree of surrounding rock masses with WIZ. Based on the proposed model, the RFDwiz and the cracking-restraint design method, the prediction of the failure position and degree, as well as the dynamic optimization design of the reasonable supporting parameters of rock masses with WIZ in underground cavern, were ultimately realized. This study will provide theoretical basis for the analysis and prediction of the instability of deep underground projects controlled by rock masses with WIZ.

Effects of high temperatures and unloading confining pressures on granite

The mechanical and permeability properties of rocks under unloading stress path and high temperature are critically important for hot dry rock. A series of unloading confining pressure and gas permeability tests were conducted on granite samples after heating and rapid cooling treatment. Five levels of temperature and three levels of confining pressures were used. The stress–strain curves of unloading confining pressure were obtained. The strength parameters and deformation parameters were further discussed and analysed. When the heat treatment temperature is higher than 600°C, the granite samples experience a significant degree of thermal damage. With the increase in heat treatment temperature and the decrease in confining pressure, the gas permeability increases. Beyond 600°C, the gas permeability of the samples increases significantly. With the increase in temperature, the internal friction angle decreases slightly from 25 to 400°C, while it increases beyond 400°C. The cohesion exhibits an inverse evolution. The initial unloading elastic modulus and deformation modulus decrease gradually during relief of confining pressure. The decrease rate of the deformation modulus increases with the increase in heating temperature. The experimental results could improve knowledge about the effect of thermal shock and stress on the physico-mechanical properties of granite.

Investigations on the Adhesive Contact Behaviors between a Viscoelastic Stamp and a Transferred Element in Microtransfer Printing

Microtransfer printing is a sophisticated technique for the heterogeneous integration of separately fabricated micro/nano-elements into functional systems by virtue of an elastomeric stamp. One important factor influencing the capability of this technique depends on the adhesion between the viscoelastic stamp and the transferred element. To provide theoretical guidance for the control of adhesion in the transfer printing process, a finite element model for the viscoelastic adhesive contact between a polydimethylsiloxane (PDMS) stamp and a spherical transferred element was established, in which the adhesive interaction was modeled by the Lennard-Jones surface force law. Effects of the unloading velocity, preload, and thermodynamic work of adhesion on the adhesion strength, characterized by the pull-off force, were examined for a loading-dwelling-unloading history. Simulation results showed that the unloading path deviated from the loading path due to the viscoelastic property of the PDMS stamp. The pull-off force increased with the unloading velocity, and the increasing ratio was large at first and then became low. Furthermore, the influence of the preload on increasing the pull-off force was more significant under larger unloading velocity than that under smaller unloading velocity. In addition, the pull-off force increased remarkably with the thermodynamic work of adhesion at a fixed maximum approach.

Creep Behavior of Intact Loess Followed Unloading Paths

Several high-fill projects are carried out on the Loess Plateau, China, accompanying the progressive failure of slopes due to excavation. The compelling need requires a deep understanding of variation in the creeping behaviors of intact loess exposed to unloading. A series of creep tests of intact loess were performed under two separated unloading paths: decrease in confining pressure at constant deviator stress and decrease in confining pressure at axial stress. The results demonstrated that axial deformation followed the first unloading path always appears as compression while the three forms of axial deformation followed the second path, depending on the applied axial stress level. At a low unloading stress level, the elongation of axial deformation was observed. At a relatively unloading stress level, the axial deformation of the soil experienced the first elongation and then compression. At a high unloading stress level, the axial deformation appeared as compression, and finally, failure occurred with the increase of the unloading stress level. The failure approach index was introduced to use as the criterion for the loess to transform from stable to accelerated creeping. Finally, a modified Burgers model was proposed to characterize the creeping behavior of intact loess followed unloading paths. There was a good comparison between the calculated and measured data of the soil that establishes the rationality and validity of the proposed model.

Research on the Reasonable Strengthening Time and Stability of Excavation Unloading Surrounding Rock of High-Stress Rock Mass

This study is aimed at better understanding the deformation and failure mechanism of surrounding rock during excavation unloading of a high-stress rock mass and determining the reasonable reinforcement time for the surrounding rock. To fulfill this aim, true triaxial tests were carried out on different loading and unloading paths during the unilateral unloading of a high-stress rock mass. The variational condition for minimization of plastic complementary energy is obtained, the optimal reinforcement time is determined, and the range of the plastic zone in the surrounding rock reinforced by anchor mesh-cable-grouting is compared and analyzed. The results are as follows: (1) Based on the Mohr-Coulomb yield criterion and the deformation reinforcement theory of surrounding rock, the stable state with the minimum reinforcement force is obtained. (2) After the true triaxial tests on the unilateral unloading of the third principal stress were carried out under different confining pressures, loading continued to be performed. Compared with rock failure without confining pressure, in the conventional uniaxial compression test, the failure of samples is dominated by composite splitting-shear failure; the unilateral unloading stress-concentration failure is a progressive failure process of splitting into plates followed by cutting into blocks and then the ejection of blocks and pieces. (3) The relationship between the time steps of the surrounding rock stability and the excavation distance is obtained. The supporting time can be divided into four stages: presupport stage, bolt reinforcement stage, anchor cable reinforcement stage, and grouting reinforcement stage. (4) In the range of within 5 m behind the tunneling face, the plastic zone of the surrounding rock with support is reduced by 7 m as compared with that with no support. In the range of over 5 m behind the tunneling face, the plastic zone of the roadway floor with support is reduced by 2.6 m as compared with that without support, and the deformation is reduced by 90%. These results can serve as a reference for controlling the behavior of surrounding rock during excavation unloading of high-stress rock masses.

Experimental study on rock mechanics characteristics of clastic reservoir with different stress paths

At present, the development of clastic reservoir has become an important way to increase oil and gas productivity in China, and the exploitation of oil and gas will inevitably affect the mechanical properties of rocks. Therefore, it is of great significance to study the rock mechanical properties of clastic reservoir rock. In this paper, the path tests of axial pressure rising-confining pressure rising and axial pressure constant-confining pressure unloading are carried out on the clastic rock samples. The results show that the clastic rock exhibits obvious elastoplastic characteristics under the path of rising confining pressure, but has certain characteristics of elasticity and brittleness under the path of unloading confining pressure; The increase in confining pressure can effectively inhibit the expansion of the rock and increase its bearing capacity; At the same initial confining pressure, the loading failure is less severe than the unloading failure; In the unloading path, the damage of the rock sample during the deformation and failure process is higher; As the confining pressure increases, the degree of rock damage also increases.

Investigating the Macro-Micromechanical Properties and Failure Law of Granite under Loading and Unloading Conditions

The excavation of rock significantly changes the initial stress state of rock slopes, which makes rock in complex loading and unloading conditions. However, the failure mechanisms and macro-micromechanical properties of rock under loading and unloading conditions are not very clear. This study investigates the macro-micromechanical properties and failure law of granite under loading and unloading conditions through traditional laboratory tests and particle flow simulations. Granite specimens are taken from Shuichang iron mine, and stress unloading experiments are designed based on the engineering practices. The stress-strain curves and failure modes under different confining pressures and unloading paths are obtained to analyze the granite properties from the viewpoint of the macroscopic mechanism. Moreover, numerical models are established in PFC software. The microcracks developments, failure characteristics, and energy evolutions under loading and unloading conditions are obtained and discussed. Results show that compared with the loading tests, the brittle failure characteristics of specimens under unloading tests are more obvious. When the confining pressure reduces to about 66% of the initial confining pressure, the specimen loses its load-bearing capacity and destroyed due to the lateral expansion. For loading tests, an inclined plane can be produced as the main failure surface. While for confining pressure unloading tests, there are many damage zones parallel to or intersecting with the main failure surface.