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.

Study of hydro-mechanical behaviours of rough rock fracture with shear dilatancy and asperities using shear-flow model

The geometric properties of fracture surfaces significantly influence shear-seepage in rock fractures,introducing complexities to fracture modelling.The present study focuses on the hydro-mechanical behaviours of rough rock fractures during shear-seepage processes to reveal how dilatancy and fracture asperities affect these phenomena.To achieve this,an improved shear-flow model(SFM)is proposed with the incorporation of dilatancy effect and asperities.In particular,shear dilatancy is accounted for in both the elastic and plastic stages,in contrast to some existing models that only consider it in the elastic stage.Depending on the computation approaches for the peak dilatancy angle,three different versions of the SFM are derived based on Mohr-Coulomb,joint roughness coefficient-joint compressive strength(JRC-JCS),and Grasselli’s theories.Notably,this is a new attempt that utilizes Grasselli’s model in shearseepage analysis.An advanced parameter optimization method is introduced to accurately determine model parameters,addressing the issue of local optima inherent in some conventional methods.Then,model performance is evaluated against existing experimental results.The findings demonstrate that the SFM effectively reproduces the shear-seepage characteristics of rock fracture across a wide range of stress levels.Further sensitivity analysis reveals how dilatancy and asperity affect hydraulic properties.The relation between hydro-mechanical properties(dilatancy displacement and hydraulic conductivity)and asperity parameters is analysed.Several profound understandings of the shear-seepage process are obtained by exploring the phenomenon under various conditions.

A post-peak dilatancy model for soft rock and its application in deep tunnel excavation

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy(PPD)behavior and simulate surrounding rock deformation;however,simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms.This study developed a PPD model for rocks(rock masses)based on the Alejanoe-Alonso(A-A)dilatancy model.The developed model comprehensively reflects the influences of confining pressure(σ_(3))and plastic shear strain(γ^(p)),with the advantages of a simple mathematical form,while requiring fewer parameters and demonstrating a clear physical significance.The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A-A model,particularly for Witwatersrand quartzite and jointed granite.The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated,and the model was found to be more suitable for the soft and large-scale rocks,e.g.deep rock mass.The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass,and the developed semi-analytical solution was compared and verified with existing analytical solutions.The sensitivities of the rock dilatancy to γ^(p) and σ_(3) showed significant spatial variabilities along the radial direction of the surrounding rock,and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elasticeplastic boundary to the tunnel wall,thereby presenting the σ3-or γ^(p)-dominated differential effects of rock dilatancy.Tunnel deformation parabolically or exponentially increased with increasing in situ stress(buried depth).The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling,which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.

Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand.This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand.Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment(i.e.dilatancy rate).Lack of an article that gathers these formulas is clear in the literature.Thus,this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands.Stress-dilatancy relation is usually not the same under compression and extension conditions.Furthermore,it may also be different under loading and unloading conditions.Therefore,the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading.Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship,more weight is allocated to stress-dilatancy relationship in this research.

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson＇s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.

Experimental investigation on dilatancy behavior of water-saturated sandstone

It is important to study the dilatancy property of water-saturated rock for understanding the engineering behavior of loaded rock mass. This study carried out the uniaxial and triaxial compressive experiments on the water-saturated red sandstone, analyzed the influences of confining pressure and pore pressure on dilatancy property of water-saturated rock, and discussed the reasonable basis of the stress of dilatancy onset as a strength design parameter of rock engineering, finally established the prediction model of the stress of dilatancy onset under the impacts of confining pressure and pore pressure. The results show that the strength parameters(the stress of dilatancy onset and peak strength) and deformation parameters(axial strain and circumferential strain) of water-saturated sandstone increase with the confining pressure, and the relations can be fitted with a positive linear function. The cohesion and internal friction angle obtained from the stress of dilatancy onset decrease by 11.57% and 7.33%, respectively, when compared with those obtained from the peak strength. The strength parameters and deformation parameters of water-saturated sandstone decrease basically with the increase of pore pressure, in which the relations between strength parameters or axial strain and pore pressure can be fitted with a negative linear function. However, the relation between the peak circumferential strain and the pore pressure should be characterized by a negative exponential function, and the circumferential strain at dilatancy onset isn't affected by the pore pressure.

Response models of weakly consolidated soft rock roadway under different interior pressures considering dilatancy effect

Surrounding rocks of weakly consolidated soft rock roadway show obvious strain softening and dilatancy effects after excavation. A damage coefficient concerning modulus attenuation was defined. Response models of stress and displacement of surrounding rock of soft rock roadway and analytical expressions to calculate plastic zones under different interior pressures and non-uniform original rock stresses were derived based on damage theories and a triple linear elastic-plastic strain softening model. Influence laws of dilatancy gradient on damage development, distributions of stresses and displacement in plastic region were analyzed. Interior pressure conditions to develop plastic region under different origin rock stresses were established and their influences on plastic region distribution were also discussed. The results show that the order of maximum principle stress is exchanged between ~0 and trr with the increase of interior pressure P0, which causes distributions of plastic zone and stress shift. Dilatancy effect which has great influences on the damage propagation and displacements in plastic region has little effect on the size of plastic region and stress responses. The conclusions provide a theoretical basis for a reasonable evaluation of stability and effective supporting of weakly consolidated soft rock roadway.

Influences of material dilatancy and pore water pressure on stability factor of shallow tunnels

Explicit finite difference code was used to calculate the stability factors of shallow tunnels without internal support in limit state. The proposed method was formulated within the nonassociative plasticity. For the shallow tunnels in soft clay, without considering the influences of pore water pressure and dilatancy, numerical results were compared with the previously published solutions. From the comparisons, it is found that the present solutions agree well with the previous solutions. The accuracy of the strength reduction technique was demonstrated through the comparisons. The influence of the pore water pressure was discussed. For the shallow tunnels in dilatant cohesive-frictional soils, the dilatant analysis was carried out.

Shear Strength and Dilatancy of Calcareous Sand in the South China Sea

The shear strength and dilatancy of typical uncemented calcareous sand from the South China Sea are investigated by soil lab tests.According to drained triaxial tests at various relative densities and confining stresses,it is found that the constant volume friction angle is approximated as 39°and the traditional Bolton’s equations can be modified to estimate the peak friction angle and dilation angle.The reliability of the equation proposed for the peak friction angle is verified in terms of calcareous sands from more onshore and offshore sites worldwide,while the errors of the predicted dilation angles scatter in a relatively large range.Totally,the dilation angles of sands in the South China Sea are estimated by the equation presented with an error of±30%.The peak friction angle measured by the undrained is similar to that by the drained tests as the relative density smaller than 60%,while the former is slightly lower for denser samples.

Numerical simulation of influence of shear dilatancy on deformation characteristics of shear band-elastic body system

The paper was numerically focused on investigation of deformation, failure and instability of shear band-surrounding elastic rock system in plane strain direct shear test considering shear dilatancy according to fast lagrangian analysis of continua (FLAC). The adopted failure criterion was a composite Mohr-Coulomb criterion with tension cut-off and post-peak constitutive relation of rock, i.e. linear strain-softening. Numerical results show that dilation angle affects the responses of elements, the number and the position of yielded elements. Increasing dilation angle results in higher load-carrying capability of elements, higher deformation or strain corresponding to peak stress, less brittle post-peak stress-deformation curve. Strain-hardening behavior can occur if dilation angle is high. Therefore, shear band-elastic rock body system tends to be stable and rock burst does not occur as dilation angle is increased. Moreover, the number of yielded elements is in- creased with dilation angle increase and two parallel plastic zones initially generated in the middle of two loading ends of specimen no longer remain collinear, reflecting increase in deformation resistant of the system. Evolution of volumetric strain rate was investigated based on three-dimensional curved surface diagrams. Approximately, volumetric strain rate concentration regions coincide with plastic zones. Volumetric strain rate in yielded elements is very evident. However, in elastic zones volumetric strain has not been nearly changed throughout the numerical tests.

Time-dependent dilatancy for brittle rocks

This paper presents a theoretical study on time-dependent dilatancy behaviors for brittle rocks. The theory employs a well-accepted postulation that macroscopically observed dilatancy originates from the expansion of microcracks. The mechanism and dynamic process that microcracks initiate from local stress concentration and grow due to localized tensile stress are analyzed. Then, by generalizing the results from the analysis of single cracks, a parameter and associated equations for its evolution are developed to describe the behaviors of the microcracks. In this circumstance, the relationship between microcracking and dilatancy can be established, and the theoretical equations for characterizing the process of rock dilatancy behaviors are derived. Triaxial compression and creep tests are conducted to validate the developed theory. With properly chosen model parameters, the theory yields a satisfactory accuracy in comparison with the experimental results.

Phenomenological behavior of rock salt:On the influence of laboratory conditions on the dilatancy onset

Recently,stress-based dilatancy criteria have become essential tools to design underground facilities in salt formations such as gas storage caverns.However,these criteria can depend critically on the volumetric strain measurements used to deduce the dilatancy onset.Results from conventional triaxial compression tests can show different volumetric behavior depending on the loading conditions,as well as on the measurement techniques.In order to obtain a quantitative understanding of this problem,an experimental program was carried out and the testing procedure was investigated numerically under homogeneous and heterogeneous stress states.The experimental results showed that the deviatoric stress corresponding to the dilatancy onset was significantly dependent on the measurement techniques.With a heterogeneous stress state,the simulation results revealed that the strain measurements at different scales (referred to as local,hybrid or global) can provide different volumetric results with moderate to significant deviations from the idealized behavior,and hence different onsets of dilatancy.They also proved that,under low confinement,tensile stresses can take place within the compressed specimen,leading to a great deviation of the dilatancy onset from the idealized behavior.From both experimental and numerical investigations,the difference in sensitivity to the measurement techniques between the deviatoric and the volumetric behaviors is explained by the relatively small values of the volumetric strain.The non-ideal laboratory conditions have more impact on this strain than on the deviatoric one.These findings can have implications for the interpretation of the dilatancy behavior of rock salt,and hence on the geomechanical design aspects in salt formations.

An elasto-plastic and viscoplastic damage constitutive model for dilatancy and fracturing behavior of soft rock squeezing deformation

Soft rock squeezing deformation mainly consists of pre-peak damage-dilatancy and post-peak fracture-bulking at the excavation unloading instant,and creep-dilatancy caused by time-dependent damage and fracturing.Based on the classic elastoplastic and Perzyna over-stress viscoplastic theories,as well as triaxial unloading confining pressure test and triaxial unloading creep test results,an elastoplastic and viscoplastic damage constitutive model is established for the short-and long-term dilatancy and fracturing behavior of soft rock squeezing deformation.Firstly,the criteria for each deformation and failure stage are expressed as a linear function of confining pressure.Secondly,the total damage evolution equation considering time-dependent damage is proposed,including the initial damage produced at the excavation instant,in which the damage variable increases exponentially with the lateral strain,and creep damage.Thirdly,a transient five-stages elasto-plastic constitutive equation for the short-term deformation after excavation that comprised of elasticity,pre-peak damage-dilatancy,post-peak brittle-drop,linear strain-softening,and residual perfectly-plastic regimes is developed based on incremental elasto-plastic theory and the nonassociated flow rule.Fourthly,regarding the timedependent properties of soft rock,based on the Perzyna viscoplastic over-stress theory,a viscoplastic damage model is set up to capture creep damage and dilatancy behavior.Viscoplastic strain is produced when the stress exceeds the initial static yield surface fs;the distance between the static yield surface fs and the dynamic yield surface fd determines the viscoplastic strain rate.Finally,the established constitutive model is numerically implemented and field applied to the-848 m belt conveyer haulage roadway of Huainan Panyidong Coal Mine.Laboratory test results and in-situ monitoring results validate the rationality of the established constitutive model.The presented model takes both the transient and time-dependent damage and fracturing into consideration.

Strength and dilatancy behaviors of deep sands in Shanghai with a focus on grain size and shape effect

With rapid development of infrastructures like tunnels and open excavations in Shanghai,investigations on deeper soils have become critically important.Most of the existing laboratory works were focused on the clayey strata up to Layer 6 in Shanghai,i.e.at depth of up to 40 m.In this paper,Layers 7,9,and 11,which were mostly formed of sandy soils at depth of up to 150 m,were experimentally investigated with respect to physico-mechanical behaviors.The stressestrain behaviors were analyzed by the consolidated drained/undrained(CD/CU)triaxial tests under monotonic loading.One-dimensional(1D)oedometer tests were performed to investigate the consolidation properties of the sandy soils.Specimens were prepared at three different relative densities for each layer.Also,the micro-images and particle size analyzers were used to analyze the shape and size of the sand grains.The influences of grain size,density,and angularity on the stressestrain behaviors and compressibility were also studied.Compared to the other layers,Layer 11 had the smallest mean grain size(D50),highest compressibility,and lowest shear strength.In contrast,Layer 9 had the largest mean grain size,lowest compressibility,and highest shear strength.Layer 7 was of intermediate mean grain size,exhibiting more compressibility and less shear strength than that of Layer 9.Also,the critical state parameters and maximum dilatancy rate of different layers were discussed.

An elasto-plastic constitutive model incorporating strain softening and dilatancy for interface thin-layer element and its verification

The mechanical behaviors of the interface between coarse-grained soil and concrete were investigated by simple shear tests under condition of mixed soil slurry (bentonite mixed with cement grout).For comparison,the interfaces both without slurry and with bentonite slurry were analyzed.The experimental results show that different slurries exert much influence on the strength and deformation of soil/structure interface.Under mixed soil slurry,strain softening and shear dilatation are observed,while shear dilatation appears under the small normal stress of the interface without slurry,and shear contraction is significant under the condition of the bentonite slurry.The thickness of the interface was determined by analyzing the disturbed height of the sample with both simple shear test and particle flow code (PFC).An elasto-plastic constitutive model incorporating strain softening and dilatancy for thin layer element of interface was formulated in the framework of generalized potential theory.The relation curves of shear stress and shear strain,as well as the relation curves of normal strain and shear strain,were fitted by a piecewise function composed by hyperbolic functions and resembling normal functions.The entire model parameters can be identified by tests.The new model is verified by comparing the measured data of indoor cut-off wall model tests with the predictions from finite element method (FEM).The FEM results indicate that the stress of wall calculated by using Goodman element is too large,and the maximum deviation between the test data and prediction is about 45%.While the prediction from the proposed model is close to the measured data,and the error is generally less than 10%.

Stress dilatancy analysis of shallow tunnels subjected to unsymmetrical pressure

Numerical simulation using finite differential code was conducted for the single line railway and four-lane road shallow tunnels subjected to unsymmetrical pressure. The mechanical behavior of weak rock mass was studied considering the influences of stress dilatancy on the failure mechanisms, and the results of numerical simulation were compared with the analytical solutions in specifications. The results show that the dilatancy angle has great influences on the surrounding rock displacement and the shape of failure face for the shallow tunnels. When the dilatancy angle equals zero, the failure face of the surrounding rock forms and extends to the ground surface. With the dilatancy angle increasing, the loose region decreases gradually, and failure surface discontinues. When the dilatancy angle equals the friction angle, the loose region is only distributed in a small range around the crown and sidewalls. On the side of smaller buried depth, the difference of break angle between numerical simulation and the code is less than 10% for single line railway tunnels with the dilatancy angle of zero. However, for the four-lane road tunnels, the difference reaches 20.8%. On the side of larger buried depth, the break angles are smaller than those by the code, the difference reaches 16.8% for single line railway tunnels, and 13.8% for four-lane road tunnels. With the dilatancy angle increasing, especially the dilatancy angle approximating to internal friction angle, it is on safe side to calculate the break angle using the analytical solution method of specifications. Therefore, the influence of stress dilatancy should be considered while determining the failure mechanisms of shallow tunnels subjected to unsymmetrical pressure in weak rocks.

A generalized dilatancy angle equation of granular soil

This paper presents a generalized dilatancy angle equation of granular soil to cover not only the drained tests but also the undrained tests by introducing a generalized structure of soil:soil skeleton formed by soil particles and the fluid in soil voids,under the assumptions of the incompressibility of soil particles and the compressibility of the fluid in soil voids.For the drained tests,the generalized dilatancy angle equation of granular soil would be degenerated to its current dilatancy angle equation.However,for the undrained tests,the generalized dilatancy angle equation of granular soil was derived with aλparameter that was related to the stress-strain state of soil and the nature of the fluid in soil voids.Theλparameter was determined by the initial dilatancy angles of granular soil at the onset of shearing on the same initial state of the soil in the drained and undrained tests.In addition,the generalized dilatancy angle equation of granular soil was verified for application in calculation of the dilatancy angles of sands in the drained and undrained tests.

Prediction of fracture and dilatancy in granite using acoustic emission signal cloud

The invisibility of fracture network evolution in the rock under triaxial compression seriously restricts the correlation modeling between dilatancy behavior and fracture interconnectivity.The key to solving such a challenge is strongly dependent on the accurate modeling of the spatial correlation in fracture network,which could be indirectly re-constructed by the acoustic emission(AE)signal cloud.Considering the interaction of local fractures,a cube cluster approach is established to describe the spatial correlation.The evolutional cube clusters effectively present the geometric characteristics induced by the increasing dilatancy of fracture.Two descriptors(i.e.three-axis length sum and pore fraction)are introduced to correlate cluster model with dilatancy behavior.Most fitting results support the linear correlation between two descriptors and volumetric strain,which verifies the sensitiveness of the cube cluster model to dilatancy.More importantly,by the statistical analysis of cluster structure,the cluster model shows the potential of calculating fracture angle.Moreover,a comparison between dilatancybased damage and porosity-based damage is made not to prove the best but provide an AE-based prediction of local damage evolution.Finally,four classical models for calculating fracture angle are compared.The deviations prove the huge difficulty of describing the development of the fracture network uniquely dependent on a fracture angle.The proximity of measured angle and cluster-based angle supports the effectiveness of predication by the cube cluster approach.

Surface deformation and gravity changes caused by dilatancy in a layered elastic-vis-coelastic half space

Surface deformation and gravity changes caused by dilatancy with magmatic intrusion (Mogi model) in two elastic layers overlying a Maxwell viscoelastic half space were systematically studied. We focused on the numerical calculation technique and the discussion of the effects of rheological properties of Maxwell half spqce on vertical displacements and gravity changes. The results show that the rheological properties of materials has an apparent effect on the results, when the intrusion was placed under Moho discontinuity, and has smaller effect if the intrusion was placed inside the crust. Therefore the elastic model is valid for considering the gravity changes or deformation caused by dilatancy with magmatic intrusion within the crust. The model and numerical calculation technique in this study can be used to model and interpret the long term deformation and gravity observations in volcanic, seismic and geothermal regions.

Intermittent slipping of landslide regulated by dilatancy evolution and velocity-weakening friction law: an efficient numerical scheme

When a block of dense sandy soil moves downhill, the shear-induced soil dilatancy along the basal shear boundary produces a negative value of excess pore pressure that increases the basal frictional resistance. Dilatancy angle,Ψ, the degree to which the basal soil dilates due to the shear, normally evolves during slope failure. A study by other researchers shows that if Ψ is constant, the block of dense soil will remain stable(or unstable) sliding when the velocity-weakening rate of the basal friction coefficient of the block is small(or large) enough. Moreover, during unstable sliding processes, the block of dense soil exhibits "periodic" patterns of intermittent slipping. Here, we used a more efficient and accurate numerical scheme to revisit that study. We expanded their model by assuming Ψ evolves during slope failure. Consequently, we acquired completely different results. For instance, even though the velocity-weakening rate of the friction coefficient is fixed at the same smaller(or larger) value that those researchers use, the stable(or unstable) steady states of landslide they predict will inversely change to unstable(or stable) when Ψ decreases(or increases) with the increase of slide displacement to a value small(or large) enough. Particularly, in unstable processes, the soil block exhibits "aperiodic" styles of intermittent slipping, instead of "periodic". We found out that the stick states appearing later last longer(or shorter) in the case of decreasing(or increasing) Ψ. Moreover, because the basic states of landslides with impacts of dilatancy evolution are not steady nor periodic, traditional stability-analysis methods cannot be "directly" used to analyze the stability of such landslides. Here, we broke through this technical problem to a degree. We showed that combining a concept called "quasi-steady-state approximation" with a traditional stability-analysis technique can qualitatively predict the instability onset of the landslides. Through this study, we demonstrated that the combination of Chebyshev collocation(CC) and 4^(th)-order Runge-Kutta methods is more accurate and efficient than the numerical scheme those researchers use.