Initial Stress State Research Articles

The effect of particle elongations on incremental behavior of granular materials using discrete element method

This study offers a novel investigation into the incremental behavior of granular materials by focusing on the effects of particle elongation on mechanical properties and microstructural evolution. Through a series of Discrete Element Method (DEM) simulations, samples with varying elongation coefficients (η) are systematically analyzed using two strain decomposition methods: the energy dissipation constraint method and the loading cycle method. The results show that as η increases, the strain envelope size decreases, indicating greater stiffness. A ‘memory effect’ is observed in the elastic strain envelope, suggesting internal rearrangement and partial microstructural recovery in later stages. The plastic strain envelope exhibits distinct patterns that vary with loading conditions, with magnitude decreasing as η increases. Despite identical initial stress states, the orientation of the plastic strain envelope shifts significantly, highlighting the impact of loading history and anisotropy. Notably, the misalignment between the normal direction of the yield surface and the incremental plastic flow direction indicates a non-associated flow rule for the generated granular materials. This misalignment varies with η and loading conditions. The study also reveals a transition from contraction to dilation behavior across different probing states, with increasing η leading to a denser packing of particles with a lower void ratio. As η increases, the anisotropy within the granular assembly becomes more pronounced, leading to a stronger directional dependence of the mechanical response.

Data‐Driven Tools to Evaluate Support Pressure, Radial Displacements, and Face Extrusion for Tunnels Excavated in Elastoplastic Grounds

ABSTRACTTwo‐dimensional analysis of tunnel design based on the convergence–confinement method, although commonly used in tunnel design, may not always be applied. For example, in squeezing grounds, if the support is installed very close to the tunnel face, three‐dimensional numerical modeling is required but is computationally expensive. Therefore, it is usually performed before or after tunnel excavation. A machine learning approach is presented here as an alternative to costly computations. Two surrogate models are developed based on synthetic data. The first model aims to assess the support pressure and the radial displacement at equilibrium in the lining and the radial displacement occurring close to the face at the installation distance of the support. The second model is intended to compute the extrusion of the core considering an unlined gallery. It is assumed a circular tunnel excavated in a Mohr–Coulomb elastoplastic perfectly plastic ground under an initial isotropic stress state. In particular, the bagging method is applied to neural networks to enhance the generalization capability of the models. A good performance is obtained using relatively scarce datasets. The modeling of the surrogate models is explained from the creation of the synthetic datasets to the evaluation of their performance. Their limitations are discussed. In practice, these two machine learning tools should be helpful in the field during the excavation phase.

In-plane dynamic analysis of supershear rupture transition due to poroelastic pressurization

Summary Although pore fluid has received increased attention in the problems of earthquake rupture, its effects on coseismic rupture are not fully understood. In this paper, we numerically simulate dynamic rupture in saturated poroelastic media to study the interplay between poroelastic pressurization and rupture evolution. Particular attention is paid to the physical process of the supershear transition. The spontaneous rupture is assumed to be governed by slip weakening law and the fault is treated as a leaky interface where pore pressure equilibrium is delayed. Results show that the pore pressure induced by coseismic mechanical deformation can strengthen the fault on the extensional side but weaken the fault on the compressional side. As a result, the poroelastic pressurization on the compressional side can promote the occurrence of the transition to supershear rupture while its strengthening effect on the extensional side can suppress this transition even in the state of high initial shear stress. Meanwhile, it is found that the permeability distribution along the fault plane also affects rupture evolution. Faults with nucleation zones located in low permeability regions are more likely to undergo a supershear rupture.

Dynamic Ruptures on Bending Fault: Insights from Numerical Simulations of Transient Stress Field

ABSTRACT We delve into the spontaneous rupture propagation on bending faults by numerical simulations based on the boundary integral equation method with unstructured meshes. To study the effect of fault geometry on dynamic rupture propagation, special attention is paid to the role of the dynamic stress field. The numerical results demonstrate that the bending angle is a key geometrical factor influencing the rupture propagation because it affects both the initial stress distribution and the dynamic stress field on the bending branch. The rupture propagation on the bending branch can be separated into two distinct stages: first, the propagation from the main branch to the bending branch, which largely depends on the dynamic stress field near the bend; and second, a subsequent propagation stage primarily influenced by the initial stress state on the bending branch, with the influence of the dynamic stress field decreasing rapidly with distance from the bend. Geometrical smoothing of the bend can be regarded as a modification of the bending angle, which may significantly alter the behavior of rupture propagation near the bend. In theory, if the bending angle ranges between −120° and 60°, there is a potential for rupture to propagate onto the bending branch through the bend.

Power-Law Modeling for Swift Viscoelastic Assessment in Biological Soft Tissues

In addressing the viscoelastic behavior of biological soft tissues, the precise and expeditious measurement methodologies hold paramount significance, given the intrinsic softness and heightened aqueous content of such substrates. We have introduced an expeditious modality for the characterization of viscoelasticity in biological soft tissues, hinged upon a power-law model. This method has been rigorously validated through ramp–hold tests conducted on mechanically stable hydrogels. Notably, during the Ramp phase, the viscoelastic parameters of the material can be readily extracted. Furthermore, we applied unconfined compression stress-relaxation/creep tests with three different ramp–strain rates, namely [Formula: see text], on both white and gray matter to enable rapid quantification. The results indicate that the predicted curves during the Hold phase exhibit notable consistency with experimental data. Moreover, under quasi-static loading conditions, an increase in strain rate significantly enhances the predictive adaptability. Nonetheless, it is crucial to be mindful of the sensitivity to initial stress conditions. This study offers a promising avenue for the expeditious characterization of soft tissue viscoelasticity. It underscores the feasibility of mechanical characterization metrics from a phenomenological model for the assessment of physiological variations and pathological mechanisms in tissue states.

The hydromechanical coupled numerical method in pseudo-3D axisymmetric domain with cracks extension and coalescence applies to the decompression failure problem

The stress-strain state of the saturated porous media determines the behavior of fracturing, which defines the efficiency of developing tight oil, shale, coalbed, and thermal energy fields. Therefore, reliable hydromechanical coupled simulations with destruction reconstruction are critical.The proposed innovative simulator has a strong interrelation between fluid flow and rock deformation of porous media and realizes a fully coupled pseudo-transient numerical method by high-performance computing (HPC) tools. To increase the detail of the results in the problem, a finite difference numerical algorithm was implemented in the axisymmetric cylindrical domain, which reduces from three to two dimensions without loss of precision. Highly efficient parallelization using CUDA on the GPU computes meshes of up to one billion cells, allowing the simulation of a total core sample to sub-micrometer resolution in an appropriate time. The algorithm has been validated to find the exact solution to the cylinder problem. The proposed model accounts for cracks propagation with their coalescence within a single computational static grid, which keeps timing close to the continuous model.This comprehensive implementation enables solving industrial problems, such as modeling core sample damage during rapid decompression. High-resolution simulations help reconstruct fracture propagation, analyze the initial stress state, and identify critical damage factors. The comparison with the exact solution to the cylinder problem confirmed the reliability of the algorithm. The calculation results show a strong dependence of decompression failure on the coalescence and elongation of cracks, influenced significantly by the rock's cohesion. Microcracks length and distribution play a decisive role in the decompressive destruction behavior of the rock sample. For the first time, the simulations demonstrated the decompressive destruction of a core sample during an uncontrolled, rapid core retrieval operation.

Short-term reoxygenation is not enough for the recovery of soybean plants exposed to saline waterlogging

The ability of plants to recover after stressful events is crucial for resuming growth and development and is a key trait when studying stress tolerance. However, there is a lack of information on the physiological responses and the time required to restore homeostasis after the stress experience. This study aimed to (i) enhance understanding of soybean photosynthesis performance during saline waterlogging and (ii) investigate the effects of this combined stress during the reoxygenation and recovery period. Soybean plants (cultivar PELBR10-6049 RR) were subjected to waterlogging, NaCl, or hypoxia + NaCl for 3 and 6 days. Afterward, plants were drained and allowed to recover for an additional two (short-term) and seven days (long-term). Compared to plants exposed to single stress, the combined hypoxia + NaCl treatment resulted in a lower net CO2 assimilation rate, ФPSII, and levels of photosynthetic pigments during the waterlogging period. Furthermore, hypoxia + NaCl increased foliar electrolyte leakage during waterlogging. In response to short-term reoxygenation, these negative effects were amplified, while prolonged reoxygenation resulted in a slight increase in biomass accumulation. In conclusion, full recovery was not achieved under any condition during the reoxygenation periods tested. Notably, the brief reoxygenation phase imposed greater stress than the initial stress conditions for plants facing combined stress. Although extended recovery increased biomass accumulation, it remained lower in plants previously subjected to saline waterlogging.

The Coefficient of Earth Pressure at Rest K0 of Sands up to Very High Stresses

The mechanical behaviour of soils subjected to any stress path in which deviatoric stresses are present is heavily characterised by non-linearity, irreversibility and is strongly dependent on the initial state of stress. The latter, for the majority of geotechnical applications, is normally determined by the at-rest earth pressure coefficient K0, even though this state is valid, strictly speaking, for axisymmetric conditions and for zero-lateral deformations only. Many expressions are available in the literature for the determination of this coefficient for cohesive and granular materials both for normal consolidated and over-consolidated conditions. These relations are available for low to medium stress levels. Results of an extensive experimental investigation on two sands of different mineralogy up to very high stress (120 MPa) are reported in the paper. For reach very high vertical stresses, a special oedometer has been realised. In the loading phase (normal consolidated sands), the coefficient K0n depends on the stress level. It passes from values of about 0.8 to values of about 0.45 in the range of effective vertical stress σ′v = 0.5–4 MPa. Subsequently, K0n is about constant and varies between 0.45 to 0.55 up to very high vertical effective stresses (120 MPa). For the sands employed in the tests, Jaki’s relation did not lead to reliable results at relatively low pressures, while at high pressures, the same relationship seems to lead to reliable predictions if it refers to the constant volume angle of shear strength. For the over-consolidated sands, K0C strongly depends on the OCR, and for very high values of OCR, K0C could be greater than Rankine’s passive coefficient of earth pressure, Kp. This result is due to the very locked structure of the sands caused by the grain crushing, with intergranular contact of sutured and sigmoidal, concavo-convex and inter-penetrating type, that confer to the sand a sort of apparent cohesion and make it similar to weak sandstone.

An analytical solution to ground stresses induced by tunneling considering ground surface boundary conditions and gravity

Accurately predicting the stress distribution around the tunnel is crucial for designing safe and economical support systems. The stress distribution is closely related to the ground stress release induced by tunneling, as well as the initial gravity stress and boundary conditions. In this study, a two-dimensional analytical model considering the ground surface boundary conditions and gravity is presented to investigate the stress field around the tunnel. Then, a numerical model was developed to validate the proposed analytical model. Finally, parametric analyses were conducted, and the limitations of the load calculation method of the code for design of shield tunnel in China were discussed. The results indicate that: (a) Tunnel excavation induces stress redistribution in the soil, resulting in a soil arching effect around the tunnel. This arching effect causes nonlinear load changes around the tunnel. (b) The soil mass around the tunnel can be divided into undisturbed and disturbed zones. Above the tunnel, the disturbance range is C-2D(C and D represent the burial depth and the tunnel diameter), while below and on both sides of the tunnel, the disturbance ranges are 4D and 1.5D, respectively. (c) Once the stress release rate reaches 0.6, a combined arching effect zone, consisting of both major and minor principal stresses, is formed in the disturbance zone above and below the tunnel. (d) The load distribution pattern calculated by the code for design of shield tunnel in China is gourd-shaped, and this calculation method is insufficient for accurately evaluating the load around the tunnel. The research results can provide a reference for the design of the shield tunnel.

Rock failure mechanisms based on rheological dynamics

This paper investigates the mechanisms of rock failure related to axial splitting and shear failure due to hoop stresses in cylindrical specimens. The hoop stresses are caused by normal viscous stress. The rheological dynamics theory (RDT) is used, with the mechanical parameters being determined by P- and S-wave velocities. The angle of internal friction is determined by the ratio of Young's modulus and the dynamic modulus, while dynamic viscosity defines cohesion and normal viscous stress. The effect of frequency on cohesion is considered. The initial stress state is defined by the minimum cohesion at the elastic limit when axial splitting can occur. However, as radial cracks grow, the stress state becomes oblique and moves towards the shear plane. The maximum and nonlinear cohesions are defined by the rock parameters under compressive strength when the radial crack depth reaches a critical value. The efficacy and precision of RDT are validated through the presentation of ultrasonic measurements on sandstone and rock specimens sourced from the literature. The results presented in dimensionless diagrams can be utilized in microcrack zones in the absence of lateral pressure in rock masses that have undergone disintegration due to excavation.

Effect of Residual Stresses on the Fatigue Stress Range of a Pre-Deformed Stainless Steel AISI 316L Exposed to Combined Loading

AISI 316L austenitic stainless steel is utilized in various processing industries, due to its abrasion resistance, corrosion resistance, and excellent properties over a wide temperature range. The physical and mechanical properties of a material change during the manufacturing process and plastic deformation, e.g., bending. During the combined tensile and bending loading of a structural component, the stress state changes due to the residual stresses and the loading range. To characterize the component’s stress state, the billet was bent to induce residual stress, but a phase transformation to martensite also occurred. The bent billet was subjected to combined tensile–bending and fatigue loading. The experimentally measured the load vs. displacement of the bent billet was compared with the numerical simulations. The results showed that during fatigue loading of the bent billet, both the initial stress state at the critical point and the stress state during the dynamic loading itself must be considered. Analysis was demonstrated only for one single critical point on the surface of the bent billet. The residual stresses due to the phase transformation of austenite to martensite affected the range and ratio of stress. The model for the stress–strain behaviour of the material was established by comparing the experimentally and numerically obtained load vs. displacement curves. Based on the description of the stress–strain behaviour of the pre-deformed material, guidelines have been provided for reducing residual tensile stresses in pre-deformed structural components.

Analytical model and stress behavior of consolidated load bearing geotextile tubes

Accurately predicting stress-strain characteristics is crucial to ensuring the regulated capacity and controlled deformation of the tubes during and after construction. However, research on the shear strength of geotextile tubes under surcharge loading, especially after dewatering, is insufficient. This study proposes an analytical model with a Stress-State Boundary (SSB) and Yield Function to comprehensively describe the stress-strain behavior of Load-Bearing Geotextile Tubes (LGTs). The SSB is designed to predict the initial state of stress in the infill soil prior to load application, while the Yield Function is formulated to express the shear stress path experienced by the LGT before fabric failure. The model considers various factors that affect LGT behavior, including diverse soil mechanical parameters, nonlinear fabric stiffness, initial tension due to self-weight and principal stress axes rotation. Results show that a decrease in Poisson's ratio corresponds to an increase in failure stress. Moreover, it was demonstrated that the axial failure strain can be influenced by the geotextile linear or nonlinear behavior. Notably, the study highlights that tube height and inclination angle significantly affect the geotextile's confining effect. Beyond theoretical contributions, the analytical model serves as a valuable tool for optimizing geotextile tube design and execution, contributing to project success and longevity through enhanced structural stability.

Microwave-assisted TBM cutter for efficient hard rock fracturing in high stress environments

Elucidating the effects and fundamental mechanisms of microwave-assisted mechanical excavation under high initial stress conditions is of paramount importance for enhancing the efficiency of deep resource extraction. In this study, indentation experiments were conducted on microwave-damaged rock under initial stress conditions using a tunnel boring machine (TBM) for the first time. By integrating acoustic emission, digital image correlation, and the discrete element method, we conducted a comprehensive analysis of the multifaceted effects of microwave irradiation and initial stress on rock fracturing. The rock-breaking efficiency was evaluated based on the volume of broken rock and the energy consumption. The indentation failure of the sample can be divided into three stages: microfracture closure, elastic deformation, and unstable crack propagation. The microwave irradiation reduced the peak load during the indentation process and simultaneously reduced the brittleness of the specimen. The experimental and simulation results jointly demonstrated the existence of an initial stress threshold in the rock fracturing process. When the initial stress is below the threshold, it suppresses the extension of rock fractures, which is unfavorable for rock fragmentation. When the initial stress exceeds the threshold, stress-induced rock failure occurs, which promotes rock fragmentation. A notable observation is that microwave irradiation alters the initial stress threshold of the rock, where a higher microwave power correlates with a lower initial stress threshold. This indicates that the optimal parameters for microwave equipment must be reconsidered when the initial stress changes. Methods for optimizing rock breakage at initial stress were suggested and examined.

True triaxial modeling test of high-sidewall underground caverns subjected to dynamic disturbances

Seismicity resulting from the near- or in-field fault activation significantly affects the stability of large-scale underground caverns that are operating under high-stress conditions. A comprehensive scientific assessment of the operational safety of such caverns requires an in-depth understanding of the response characteristics of the rock mass subjected to dynamic disturbances. To address this issue, we conducted true triaxial modeling tests and dynamic numerical simulations on large underground caverns to investigate the impact of static stress levels, dynamic load parameters, and input directions on the response characteristics of the surrounding rock mass. The findings reveal that: (1) When subjected to identical incident stress waves and static loads, the surrounding rock mass exhibits the greatest stress response during horizontal incidence. When the incident direction is fixed, the mechanical response is more pronounced at the cavern wall parallel to the direction of dynamic loading. (2) A high initial static stress level specifically enhances the impact of dynamic loading. (3) The response of the surrounding rock mass is directly linked to the amplitude of the incident stress wave. High amplitude results in tensile damage in regions experiencing tensile stress concentration under static loading and shear damage in regions experiencing compressive stress concentration. These results have significant implications for the evaluation and prevention of dynamic disasters in the surrounding rock of underground caverns experiencing dynamic disturbances.

Application of Wave Methods for Determining Comprehensive Soil Model Parameters

Comprehensive hardening soil models are widely used in geotechnical design. Some of the stiffness parameters of such models, characterizing the behavior under very small and small strains, should be determined by wave (dynamic) methods. These techniques can be implemented both in the laboratory and in the field scale. Each of the methods has its advantages and disadvantages, which directly affect the quality of the initial data obtained for calculations and the results of geotechnical forecasts and the reliability of construction facilities. The article provides an overview of wave methods applicable for stiffness parameters of complex soil models estimation. The scope of application of test methods is given depending on the geotechnical task, the defined parameters and engineering-geological conditions. The comparison of the test results by field and laboratory methods at the experimental site is given. It is shown that the results obtained by field methods require additional reference to the initial stress state in the soil mass before their application as input parameters of comprehensive soil models. Recommendations are given for correcting the initial soil shear modulus based on the integration of laboratory and field wave methods.

Influence of Pore Shape and Initial Stress State on the Electroelastic Properties of Porous Piezoceramics PZT-4

Influence of Pore Shape and Initial Stress State on the Electroelastic Properties of Porous Piezoceramics PZT-4

Large Scale Simulation of 3D Fault Rupture Subjected to Far‐Field Loading With PDS‐FEM: Application to the 2018 Palu Earthquake

AbstractSimulating dynamic rupture of fault systems can be computationally demanding, as it requires reproducing complex fault geometry and accurately capturing waves propagating away from the rupture front. It is in particular challenging to predict an initial stress state consistent with fault geometries, heterogeneous distribution of surrounding materials, and far‐field tectonic loading. While standard techniques such as contact analysis and Lagrangian multipliers can be used to model the fault, it can lead to significant computational overhead in FEM. We extended Particle Discretization Scheme‐FEM, which provides numerically efficient crack treatment, without requiring contact analysis, to simulate dynamic fault rupture as a frictional crack propagating along a pre‐existing shear crack surface. Initial stress, which is consistent with initial frictional forces, material distribution and fault geometry, is derived using Coulomb friction and far‐field boundary conditions. The study first demonstrates the ability of the numerical method to reproduce a 2D ideal supershear scenario, and the underlying Burridge‐Andrew rupture mechanism. The methodology is then applied to the large scale simulation of the 2018 Palu earthquake on the Palu‐Koro fault. The simulation successfully reproduces the early and sustained supershear rupture which was observed for the Palu earthquake. Also, it indicates that the presence of an off‐fault damage zone can contribute to the low rupture velocity measured during the earthquake. Unlike sub‐Rayleigh earthquakes, the shockwave propagation was observed to lead to significant amplitudes of the ground motion even far from the fault.

Analytical solutions considering face advance and time-dependent behavior for back-analysis of convergence measurements in deep circular tunnels under isotropic initial stress state

A methodology is presented for the back-analysis of convergence measurements in deep tunnels to determine the constitutive parameters of the surrounding rock mass. Since increasing deformations and stresses with time are due to both the face advance and the time-dependent behavior of the ground, the two effects must be considered during the excavations. To that end, an analytical solution assuming an unlined circular tunnel excavated in a homogeneous isotropic ground under an initial isotropic stress field and assuming a fractional viscoelastic plastic behavior is developed. A second closed-form solution is also derived assuming an instantaneous excavation. Additionally, combining the developed analytical solution that takes into account the progressive face advance and an empirical approach, convergences are back-analyzed based on a least-squares optimization method to calibrate the constitutive parameters of the ground. The presented methodology aims to characterize the long-term behavior of tunnels and offers the advantage of being directly applicable during the excavation phase as soon as convergence measurements are available. Finally, the method is illustrated by two case studies related to the Fréjus road tunnel and the Saint-Martin-la-Porte access gallery (SMP2).

The role of heterogeneous stress in earthquake cycle models of the Hikurangi-Kermadec subduction zone

Summary Seismic and tsunami hazard modelling and preparedness are challenged by uncertainties in the earthquake source process. Important parameters such as the recurrence interval of earthquakes of a given magnitude at a particular location, the probability of multi-fault rupture, earthquake clustering, rupture directivity and slip distribution are often poorly constrained. Physics-based earthquake simulators, such as RSQSim, offer a means of probing uncertainties in these parameters by generating long-term catalogues of earthquake ruptures on a system of known faults. The fault initial stress state in these simulations is typically prescribed as a single uniform value, which can promote characteristic earthquake behaviours and reduce variability in modelled events. Here, we test the role of spatial heterogeneity in the distribution of the initial stresses and frictional properties on earthquake cycle simulations. We focus on the Hikurangi-Kermadec subduction zone, which may produce Mw > 9.0 earthquakes and likely poses a major hazard and risk to Aotearoa New Zealand. We explore RSQSim simulations of Hikurangi-Kermadec subduction earthquake cycles in which we vary the rate and state coefficients (a and b). The results are compared with the magnitude-frequency distribution (MFD) of the instrumental earthquake catalogue and with empirical slip scaling laws from global earthquakes. Our results suggest stress heterogeneity produces more realistic and less characteristic synthetic catalogues, making them particularly well suited for hazard and risk assessment. We further find that the initial stress effects are dominated by the initial effective normal stresses, since the normal stresses evolve more slowly than the shear stresses. A heterogeneous stress model with a constant pore-fluid pressure ratio and a constant state coefficient (b) of 0.003 produces the best fit to MFDs and empirical scaling laws, while the model with variable frictional properties produces the best fit to earthquake depth distribution and empirical scaling laws. This model is our preferred initial stress state and frictional property settings for earthquake modelling of the Hikurangi-Kermadec subduction interface. Introducing heterogeneity of other parameters within RSQSim (e.g. friction coefficient, reference slip rate, characteristic distance, initial state variable, etc) could further improve the applicability of the synthetic earthquake catalogues to seismic hazard problems and form the focus of future research.

Resilient and rutting response of unbound granular material and subgrade soil influenced by initial state and stress conditions

Unbound pavements with thin seals, where traffic loads are primarily supported by unbound granular layers and subgrade soil, are favoured for their low initial cost. Rutting, the primary distress mechanism, leads to rough, uncomfortable surfaces, diminishing serviceability and safety. It depends on the material's initial dry density, degree of saturation, and applied stress levels. Resilient modulus, indicating layer stiffness, is crucial for determining load transmission to underlying layers, making accurate estimation essential for pavement design. This study conducted constant radial stiffness triaxial (CRST) tests on an unbound granular material and a subgrade soil at various dry densities, saturation degrees, and stress conditions. The CRST test applies dynamic confining pressure under constant radial stiffness boundary. New models for rutting and resilient modulus were developed, relating these parameters to initial dry densities, saturation degrees, and stress states. The study also presents rutting and resilient modulus isograms on the compaction plane, aiding field compaction control and robust pavement design.