Mechanical response and dilatancy characteristics of deep marble under different stress paths:A sight from energy dissipation

Dilatancy is a fundamental volumetric growth behavior observed during loading and serves as a key index to comprehending the intricate nonlinear behavior and constitutive equation structure of rock.This study focuses on Jinping marble obtained from the Jinping Underground Laboratory in China at a depth of 2400 m.Various uniaxial and triaxial tests at different strain rates,along with constant confining pressure tests and reduced confining pressure tests under different confining pressures were conducted to analyze the mechanical response and dilatancy characteristics of the marble under four stress paths.Subsequently,a new empirical dilatancy coefficient is proposed based on the energy dissipation method.The results show that brittle failure characteristics of marble under uniaxial compression are more obvious with the strain rate increasing,and plastic failure characteristics of marble under triaxial compression are gradually strengthened.Furthermore,compared to the constant confining pressure,the volume expansion is relatively lower under unloading condition.The energy dissipation is closely linked to the process of dilatancy,with a rapid increase of dissipated energy coinciding with the beginning of dilatancy.A new empirical dilatancy coefficient is defined according to the change trend of energy dissipation rate curve,of which change trend is consistent with the actual dilatancy response in marble under different stress paths.The existing empirical and theoretical dilatancy models are analyzed,which shows that the empirical dilatancy coefficient based on the energy background is more universal.

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.

Shear behavior of coarse aggregates for dam construction under varied stress paths

Coarse aggregates are the major infrastructure materials of concrete-faced rock-fill dams and are consolidated to bear upper and lateral loads. With the increase of dam height, high confining pressure and complex stress states complicate the shear behavfor of coarse aggregates, and thus impede the high dam＇s proper construction, operation and maintenance. An experimental program was conducted to study the shear behavior of dam coarse aggregates using a large-scale triaxial shear apparatus. Through triaxial shear tests, the strain-stress behaviors of aggregates were observed under constant confining pressures： 300 kPa, 600 kPa 900 kPa and 1200 kPa. Shear strengths and aggregate breakage characteristics associated with high pressure shear processes are discussed. Stress path tests were conducted to observe and analyze coarse aggregate response under complex stress states. In triaxial shear tests, it was found that peak deviator stresses increase along with confining pressures, whereas the peak principal stress ratios decrease as confining pressures increase With increasing confining pressures, the dilation decreases and the contraction eventually prevails. Initial strength parameters （Poisson＇s ratio and tangent modulus） show a nonlinear relationship with confining pressures when the pressures are relatively low. Shear strength parameters decrease with increasing confining pressures. The failure envelope lines are convex curves, with clear curvature under low confining pressures. Under moderate confining pressures, dilation is offset by particle breakage. Under high confining pressures, dilation disappears.

An improved hypoplastic constitutive model of rockfill considering effect of stress path

An incrementally nonlinear hypoplastic constitutive model was introduced, which was developed without recourse to the concepts in elastoplasticity theory such as yield surface, plastic potential and the decomposition of the deformation into elastic and plastic parts. Triaxial drained tests on rockfill were conducted on a large scale triaxial apparatus under two types of stress paths, which were the stress paths of constant stress ratio and the complex stress paths with transitional features. Motivated by the effect of stress path, the Gudehus-Bauer hypoplastic model was improved by considering the parameter variations with different ratios of stress increment. Fitting parameter a presents a piecewise linear relationship with cosine of the slope angle θ determined by instantaneous stress path. The improved hypoplastic model can present peak stress increasing and volumetric strain changing from dilatancy to contractancy with the increase of transitional confining pressure σ3t and the decrease of slope angle θ of stress path. Compared with the test data, it is shown that the model is capable of fully considering the effect of stress path on rockfill.

Numerical Method for Modeling the Constitutive Relationship of Sand under Different Stress Paths

A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic constitutive relationship of sand was established for three paths： the constant proportion of principle stress path, the conventional triaxial compression （CTC） path, and the p=constant （TC） path. The yield lines of plastic volumetric strain and plastic generalized shear strain were given. Through visualization, the three dimensional surface of the stress-strain relationship in the whole stress field （p, q） obtained under the three paths was plotted. Also, by comparing the stress-strain surfaces and yield locus of the three stress paths, the differences were found to be obvious, which demonstrates that the influence of the stress paths on constitutive law was not neglected. The numerical modeling method overcame the difficulty of finding an analytical expression for plastic potential. The results simulated the experimental data with an accuracy of 90% on average, so the constitutive model established in this paper provides an effective constitutive equation for this kind of engineering, reflecting the effect of practical stress paths that occur in sands.

Influence of hysteretic stress path behavior on seal integrity during gas storage operation in a depleted reservoir

In this study,we numerically investigate the influence of hysteretic stress path behavior on the seal integrity during underground gas storage operations in a depleted reservoir.Our study area is the Honor Rancho Underground Storage Facility in Los Angeles County(California,USA),which was converted into an underground gas storage facility in 1975 after 20 years of oil and gas production.In our simulations,the geomechanical behavior of the sand reservoir is modeled using two models:(1)a linear elastic model(non-hysteretic stress path)that does not take into consideration irreversible deformation,and(2)a plastic cap mechanical model which considers changes in rock elastic properties due to irreversible deformations caused by plastic reservoir compaction(hysteretic stress path).It shows that the irreversible compaction of the geological layer over geologic time and during the reservoir depletion can have important consequences on stress tensor orientation and magnitude.Ignoring depletion-induced irreversible compaction can lead to an over-estimation of the calculation of the maximum working reservoir pressure.Moreover,this irreversible compaction may bring the nearby faults closer to reactivation.However,regardless of the two models applied,the geomechanical analysis shows that for the estimated stress conditions applied in this study,the Honor Rancho Underground Storage Facility is being safely operated at pressures much below what would be required to compromise the seal integrity.

Effect of stress paths on failure mechanism and progressive damage of hard-brittle rock

During deep buried hard-brittle rock tunnel excavation,the surrounding rock experiences a complicated stress path and stress adjustment process.Once the adjusted stress exceeds the ultimate bearing capacity of rockmass,a rock failure mode defined as stress-cracking type will occur.In order to investigate the effect of stress paths on failure mechanism and progressive damage of deep-buried rockmass,the cyclic loading-unloading,loading-unloading,uniaxial,conventional and unloading triaxial compression tests on samples of hard-brittle sandstone were conducted.According to the experimental results,increase in the confining pressure was beneficial to improve the mechanical parameters of rock,but it will reduce the brittle failure features.Compared with conventional triaxial compression,the sandstone under unloading state had more remarkable stress drop and unstable failure characteristics.Meanwhile,it was found that the energy dissipation and energy release in the whole process of rock deformation were the internal power of driven rock progressive damage.With the increase of confining pressure,the energy hardening and energy accumulation features of rock were weakened,while the progressive damage evolution characteristics could be enhanced.In unloading state,more energy could be converted into elastic energy in the energy softening phase(σeb-σP),so that the prepeak damage rate of rock was lower than that of conventional triaxial compression state.Thus,the energy dissipation rate of rock after peak strength decreased linearly with the increase of confining pressure under conventional triaxial compression state,while in unloading state it showed the opposite law.

Macro and micro failure mechanism of surrounding rock of small span tunnel under different stress paths

According to the different stress paths,similar model test and PFC simulation test of tunnel surrounding rock are designed to compare the failure mechanisms at macroscopic and mesoscopic scales.The following conclusions are drawn.1)Excavation unloading will disturb the surrounding rock to form a certain excavation damaged zone.2)Under the loading path,the stress of surrounding rock failure is 1.500 MPa;under the unloading path with initial stress of 60% σ_(Zmax) and 100% σ_(Zmax),the failure stress is 1.583 and 1.833 MPa respectively in the model test.3)In terms of the failure mode of rocks under different stress paths,tensile fractures first appear in two sides of the vertical walls;thereafter,the spandrel and arch foot are loosened due to the stress concentration.The fractures gradually coalesce with those occurring in the vertical walls.4)In the process of excavation unloading,the proportion of shear cracks is 35.3%,and the rock is subject to strong shear effect.The final failure surface is approximately V-shaped.5)The tangential peak stress on the vertical walls at the free face is the lowest;the vertical walls at the free face show the poorest bearing capacity and are easily subjected to tensile failure.

Reservoir stress path and induced seismic anisotropy： results from linking coupled fluid-flow/geomechanical simulation with seismic modelling

We present a workflow linking coupled fluid-flow and geomechanical simulation with seismic modelling to predict seismic anisotropy induced by non-hydrostatic stress changes. We generate seismic models from coupled simulations to examine the relationship between reservoir geometry, stress path and seismic anisotropy. The results indicate that geometry influences the evolution of stress,which leads to stress-induced seismic anisotropy. Although stress anisotropy is high for the small reservoir, the effect of stress arching and the ability of the side-burden to support the excess load limit the overall change in effective stress and hence seismic anisotropy. For the extensive reservoir, stress anisotropy and induced seismic anisotropy are high. The extensive and elongate reservoirs experience significant compaction, where the inefficiency of the developed stress arching in the side-burden cannot support the excess load.The elongate reservoir displays significant stress asymmetry,with seismic anisotropy developing predominantly along the long-edge of the reservoir. We show that the link betweenstress path parameters and seismic anisotropy is complex,where the anisotropic symmetry is controlled not only by model geometry but also the nonlinear rock physics model used. Nevertheless, a workflow has been developed to model seismic anisotropy induced by non-hydrostatic stress changes, allowing field observations of anisotropy to be linked with geomechanical models.

Stress Path Analysis of Deep-Sea Sediments Under the Compression-Shear Coupling Load of Crawler Collectors

The mechanical properties of deep-sea sediments during the driving process of crawler collectors are essential factors in the design of mining systems.In this study,a crawler load is divided into a normal compression load and a horizontal shear load.Then,the internal stress state of sedimentary soil is examined through a theoretical calculation and finite element numerical simulation.Finally,the driving of crawlers is simulated by changing the relative spatial position between the load and stress unit,obtaining the stress path of the soil unit.Based on the calculation results,the effect of the horizontal shear load on the soil stress response is analyzed at different depths,and the spatial variation law of the soil stress path is examined.The results demonstrate that the horizontal shear load has a significant effect on the rotation of the principal stress,and the reverse rotation of the principal stress axis becomes obvious with the increase in the burial depth.The stress path curve of the soil is different at various depths.The spatial variation rule of the stress path of the shallow soil is complex,whereas the stress path curve of the deep soil tends to shrink as the depth increases.The stress path of the corresponding depth should be selected according to the actual research purpose and applied to the laboratory test.

Using true‑triaxial stress path to simulate excavation‑induced rock damage:a case study

This study presents an example illustrating the role of in situ 3D stress path method in simulating the roof damage development observed in the Mine-by tunnel at Underground Research Laboratory(URL)located in Manitoba,Canada.The 3D stress path,at the point 1 cm in the crown of the Mine-by tunnel,was applied to a cubic Lac du Bonnet(LdB)granite sample to further understand the roof damage process and the associated seismicity.After careful calibrations,a numerical model was used to reproduce the experiment,which produced similar seismicity processes and source mechanisms.Acoustic emission(AE)events obtained from laboratory and numerical modeling were converted to locations in relation to the tunnel face and were compared to the feld microseismicity(MS)occurring in the upper notch region of the Mine-by tunnel.The crack development and damage mechanism are carefully illustrated.The diference between tests and feld monitoring was discussed.The intermediate principal stress(σ_(2))unloading process was carried out in numerical simulation to investigate its role in rock damage development.The results clearly showedσ_(2)could play a signifcant role both in damage development and failure mode.It should be considered when predicting the damage region in underground excavations.This study highlights the potential role of laboratory and numerical stress path tests to investigate fracture processes and mechanisms occurring during engineering activities such as tunnel excavation.

Mechanical behavior of iron ore tailings under standard compression and extension triaxial stress paths

The disposal of mining tailings has increasingly focused on the use of dry stacks.These structures offer more security since they use filtered and compacted material.Because of the construction method and the heights achieved,the material that compounds the structure can be subjected to different stress paths along the failure plane.The theoretical framework considered in the design of these structures generally is the critical state soil mechanics(CSSM).However,the data in the literature concerning the uniqueness of critical state line(CSL)is still controversial as the soil is subjected to different stress paths.With respect to tailings,this question is even more restricted.This paper studies two tailings with different gradings due to the beneficial processes over extension and compression paths.A series of drained and undrained triaxial tests was conducted over a range of initial densities and stress levels.In the q-p'plane,different critical stress ratio(M)values were obtained for compression and extension stress paths.However,the critical state friction angle is very similar with a slightly higher critical state friction angle for extension tests.Curved stress path dependent CSLs were obtained in the n-lnp0 plane with the extension tests below the CSL defined in compression.Regarding the fines content,the studied tailings presented very similar M and critical state friction angle values.However,the fines content af-fects the volumetric behavior of the studied tailings and the CSLs on the n-lnp0 plane shift downwards with the increasing fines content for compression and extension tests.In relation to dilatancy analysis,the fines content did not present an evident influence on the dilatancy of the materials.However,different values of mean stress ratio N were obtained between compression and extension tests and can corroborate the existence of non-unique CSLs for these materials.

Influence of stress path change on the resistance to plastic deformation of cold rolled sheets

Flat workpieces have been tested in order to investigate the influence of stress path change （loading mode） while keeping strain path unchanged. These investigations are pertinent to the testing of cold rolled strips and to subsequent forming. The workpieces which first compressed by plane strain compression in thickness direction were then tested in perpendicular direction in order to measure the influence of strain and stress path. The tension workpieces came from flat die compression test at different deformation histories. Two different materials were investigated： 18/8 Ti stainless steel and AW-1050 aluminium. The results show that the plastic flow by tension in lengthwise direction after pre-strain by compression in thickness direction will begin at an appreciably lower stress than that of the workpieces unloaded after pre-compression. Comparing with two materials, it can be seen that both 18/8 Ti stainless steel and AW-1050 aluminium behave similarly. The drop in yield stress is lower for AW-1050 aluminium than that for 18/8 Ti stainless steel. However, reloading in different directions than in the precious step results in significantly higher strain hardening.

A rigid true triaxial apparatus for analyses of deformation and failure features of deep weak rock under excavation stress paths

The squeezing scenario in deep weak rock tunnels can hinder underground construction.However,due to the limitations of test technologies at hand,the real excavation stress path cannot be mimicked in the laboratory.Thus,the large deformation mechanism of deep weak rocks still remains unclear.For this,a true triaxial apparatus(TTA)to investigate the mechanical responses of deep weak rock under excavation stress paths in field and reveal the squeezing mechanism of deep tunnels is assembled and developed at Northeastern University,China.The apparatus can perform instantaneous unloading in s3 direction based on electromagnetism technology.In addition,uniform loading and deformation measurements can be carried out based on the proposed linked interlocking clamp and antifriction device,even if the sample has a strong dilatation deformation performance.Next,a bore trepanning is designed to capture noiseless acoustic emission(AE)signals for deep weak rock at a low threshold.Finally,two tests were are conducted using this instrument to preliminarily understand the failure and deformation features of deep weak rock based on fractured marble.The results show that the complete stressestrain curves of fractured marble have the characteristics of low strengths and large deformations,and the larger deformation and the more serious failure occur when the fractured marble enters the post-peak state after excavation.The results show that the developed apparatus is likely to be applicable for deep weak rock engineering.

Cyclic strength of sand under a nonstandard elliptical rotation stress path induced by wave loading

The principal stress rotation is one of the most important features of the stress state in a seabed subjected to wave loading. Most prior investigations focused their attention on the cyclic behaviour of soil deposits under the circular rotation stress path based on the analytical solutions for a seabed of infinite thickness. In this paper, the nonstandard elliptical, i.e., non-circular, rotation stress path is shown to be a more common state in the soil sediments of a finite seabed with an alternating changeover in stress due to a travelling regular wave. Then an experimental investigation in a hollow cylinder triaxial-torsional apparatus is conducted into the effect of the nonstandard elliptical stress path on the cyclic strength. A special attention is placed on the difference between the circular rotation stress path and the elliptical rotation stress path. The results and observations show that the shear characteristics for the circular rotation stress path in the literature are not applicable for analyzing the cyclic strength of sand in a finite seabed, and also indicate that due to the influence of three parameters about the size and the shape of a nonstandard ellipse, the cyclic strength under a nonstandard elliptical rotation stress path is evidently more complex and diversified as compared with that under a circular rotation stress path. Especially the influence of the initial phase difference on the cyclic strength is significant.

A 3D elastic-plastic-viscous constitutive model for soils considering the stress path dependency

In order to consider the stress path dependency of soils,this paper decomposes any arbitrary stress path into several infinitesimal stress paths.Then the infinitesimal stress path is further transformed into the superposition of two parts,i.e..a constant stress ratio part and a constant mean stress part,which arc sufficiently close to the real stress path.T he plastic strain increments under the transformed paths arc determined separately,and then the plastic strain under any path is obtained.Based on the instantaneous loading line of normally consolidated soil,a reference state line is proposed to determine the overconsolidation ratio and creep time of soil.The overconsolidation ratio is introduced into the viscous How rule to obtain the viscous strain increment.The strcss-strain-timc relationship for triaxial compression condition is extended to 3D stress condition by the transformed stress method.The proposed model adopts only seven material parameters and each of them has a clear physical meaning.Comparisons with test results demonstrate that the model can not only reasonably predict the plastic strain under typical stress paths of excavation,but adequately capture the time-dependent behaviours of soils,including creep,stress relaxation and strain rate effect.

Experimental study of two saturated natural soils and their saturated remoulded soils under three consolidated undrained stress paths

In this paper,an experimental investigation is conducted to study the mechanical behavior of saturated natural loess,saturated natural filling in ground fissure and their corresponding saturated remoulded soils under three consolidated undrained triaxial stress tests,namely,conventional triaxial compression test(CTC),triaxial compression test(TC)and reduced triaxial compression test(RTC).The test results show that stress-strain relation,i.e.strain-softening or strain-hardening,is remarkably influenced by the structure,void ratio,stress path and confining pressure.Natural structure,high void ratio,TC stress path,RTC stress path and low confining pressures are favorable factors leading to strain-softening.Excess pore pressure during shearing is significantly affected by stress path.The tested soils are different from loose sand on character of strain-softening and are different from common clay on excess pore water pressure behavior.The critical states in p′-q space in CTC,TC and RTC tests almost lie on one line,which indicates that the critical state is independent of the above stress paths.As for remoulded loess or remoulded filling,the critical state line(CSL)and isotropic consolidation line(ICL)in e-log p′space are almost straight,while for natural loess or natural filling,in e-log p′space there is a turning point on the CSL,which is similar to the ICL.

DEM simulations of critical state behaviour of granular materials under various drained triaxial stress path tests

The present study investigates the critical state behaviour of granular assemblies composed of clumped particles under four different drained axisymmetric triaxial stress paths,using the discrete element method(DEM).A series of numerical samples were prepared at initial states with different density indexes(1D)and different initial confining pressures(ρ′0).These samples were sheared to large strains,at which constant stresses and volumes were maintained to reach the critical state.The evolution of stress ratio under the same loading mode(for the same intermediate principal stress ratio,b)is shown to yield an almost identical behaviour independent of stress paths,whereas the stress-strain response depends on the stress paths.Four different axisymmetric stress paths all share the same unique friction angle at critical state,indicating the Mohr-Coulomb failure criterion is the appropriate critical state strength criterion,which is at least true for the axisymmetric stress conditions.A unique coordination number(CN)is achieved at the critical state for a given po,which is independent of the stress path.The critical state CN is found to increase with the increase in po,which could be attributed to the decrease in the critical state void ratio(ec)as mean effective stress(ρ′0)increases.Interestingly,a unique linear functional relationship is found between the critical state values of cN and ec,and a unique polynomial functional relationship is found between the critical state values of CN andρ′.These functional relationships indicate no dependency on the stress paths or loading modes,thus characterizing unique features at critical states at both macroscopic and microscopic levels for a given type of granular material.

Effect of stress path on the mechanical properties of calcareous sand

Calcareous sand is widely observed in the foundation of off-shore infrastructure.Although a lot of research has been carried out on the mechanical properties of calcareous sand,study into the influence of the stress–strain path on the mechanical behaviour of calcareous sand is very limited.In this study,a series of triaxial tests were performed on calcareous sand under three different stress paths.The particle morphology of calcareous sand before and after the tests,the stress–strain relationship under different stress paths,and the char-acteristics of shear strength and deformation were investigated.The results show that the consolidation pressure and stress path have significant effects on the volume strain,strength,and particle breakage of calcareous sand.In addition,the underlying mechanisms of the different behaviours of calcareous sand observed in this study were discussed.

Stress path constraints on veined rock deformation

Although rock mechanical behaviour has a long record of study,attempts to understand the role of fractures on rock deformation still have unresolved issues.Due to technical and/or economic challenges,natural rock fractures are often dealt with crudely,without detailed consideration of fracture geometry and heterogeneity in many geoscience applications.Veined rocks that are ubiquitous in the upper Earth crust fall in that category where sustained efforts are needed to offer key information for rock mechanics and geomechanics applications.Following on from a recent study on the rupture of veined rocks(DOI:10.1029/2019JB019052),we further examine stress path constraints on the deformation of veined rocks(i.e.,stress-path-dependent behaviour of veined rocks)under polyaxial conditions.The Discrete Element Method is used to establish a calcite veined model where constant mean stress(σm)and constant least principal stress(σ3)paths that are representative in the subsurface activities are considered.The results reveal the stress-path dependency of brittleness for models under different loading paths.Models tested under constant-σm conditions exhibit no brittleness,compared to cases where constant-σ3 is applied.Sliding along the strike of an inclined vein is evident under constant-σm deformation,irrespective of the level of stress.Shear bands along the dominated(inclined)veins exhibit apparent particle trajectory anisotropy for the constant-σm deformations which is demonstrated by the evident colour contrast of the adjacent rock matrix and the displacement dispersion of the particles forming the shear bands.We envisage that the reactivation of veins is of relevance to Enhanced Geothermal Systems(EGS)development in terms of seismicity mitigation and multiphysics control of fracture and reservoir permeability.