Framework Of Critical State Soil Mechanics Research Articles

Path and Slip Dependent Behavior of Shallow Subduction Shear Zones During Fluid Overpressure

AbstractElevated pore fluid pressure is proposed to contribute to slow earthquakes along shallow subduction plate boundaries. However, the processes that create high fluid pressure, disequilibrium compaction and dehydration reactions, lead to different effective stress paths in fault rocks. These paths are predicted by granular mechanics frameworks to lead to different strengths and deformation modes, yet granular mechanics do not predict their effects on fault stability. To evaluate the role of fluid overpressure on shallow megathrust strength and slip behavior, we conducted triaxial shear experiments on chlorite and celadonite rich gouge layers. Experiments were conducted at constant temperature (130 and 100°C), confining pressure (130 and 140 MPa), and pore fluid pressures (between 10 and 120 MPa). Fluid overpressure due to disequilibrium compaction was simulated by increasing confining and pore fluid pressure synchronously without exceeding the target effective pressure, whereas overpressure due to dehydration reactions was simulated by first loading the sample to a target isotropic effective pressure and then increasing pore fluid pressure to reduce the effective pressure. We find that the effects of fluid pressure and stress path on the mechanical behavior of the chlorite and celadonite gouges can generally be described using the critical state soil mechanics (CSSM) framework. However, path effects are more pronounced and persist to greater displacements in chlorite because its microstructure is more influenced by stress path. Due to its effects on microstructure, the stress path also imparts greater control on the rate‐dependence of chlorite strength, which is not predicted by CSSM.

Cyclic liquefaction resistance of MICP- and EICP-treated sand in simple shear conditions: a benchmarking with the critical state of untreated sand

AbstractIn the present study, the undrained cyclic behaviour of biotreated sands using microbial and enzyme-induced carbonate precipitation was investigated for a wide range of initial void ratio after consolidation ($$e_{0}$$ e 0 ), initial effective normal stress ($$\sigma^{\prime }_{{{\text{N}}_{0} }}$$ σ N 0 ′ ) and calcium carbonate content (CC) under direct simple shear (DSS) testing conditions. The critical state soil mechanics framework for untreated sand was first established using a series of drained and undrained (constant volume) tests, which served as a benchmark for evaluating the undrained cyclic liquefaction behaviour of untreated and biotreated sands. The results indicated that the modified initial state parameter ($$\psi_{{{\text{m}}_{{0}} }}$$ ψ m 0 ) in DSS condition showed a good correlation with instability states and phase transformation under monotonic shearing. In undrained cyclic DSS loading condition, samples displayed cyclic mobility indicated by an abrupt accumulation of large strain or $$\sigma^{\prime }_{{N_{0} }}$$ σ N 0 ′ transiently reaching zero or a sudden build-up of excess pore water pressure. The linkage between static and cyclic liquefaction was established for untreated and biotreated sand specimens based on the equivalence of characteristic soil states. The number of cycles before liquefaction (NL) for the biotreated sand specimens was mainly controlled by the cyclic stress ratio, $$e_{0}$$ e 0 , $$\sigma^{\prime }_{{{\text{N}}_{{0}} }}$$ σ N 0 ′ and CC. For a similar initial state prior to undrained cyclic loading, the biotreated specimens required a larger NL compared to the untreated sand. The cyclic resistance ratio at NL = 15 (CRR15) increased with decreasing $$\psi_{{{\text{m}}_{{0}} }}$$ ψ m 0 for the untreated sand, while the CRR15 for biotreated sand increased with increasing CC and decreasing $$\sigma^{\prime }_{{N_{0} }}$$ σ N 0 ′ .

Characteristics of MICP- and EICP-treated sands in simple shear conditions: a benchmarking with the critical state of untreated sand

Microbial- or enzyme-induced calcium carbonate (CaCO3) precipitation (MICP and EICP) are relatively new ground improvement techniques. In this study, the mechanical behaviour of biotreated (MICP/EICP) and untreated sands was investigated in light of the critical state soil mechanics framework using a series of direct simple shear (DSS) tests. A wide range of calcium carbonate content (CC), initial void ratio after consolidation (e0) and effective initial normal stress ([Formula: see text]) was considered. The biotreated specimens showed improved shear strength and dilative tendency compared to untreated specimens with similar initial states. The ultimate state (US) for the biotreated sand shifted towards a smaller void ratio (e) than the value of e at the critical state of untreated sand at the same σ′N in e–log σ′N space. Compared to untreated sand, a significantly larger US stress ratio was achieved for the biotreated sand, particularly at high CC and low [Formula: see text]. The characteristic features of undrained behaviour, such as instability stress ratio, stress ratio at phase transformation and flow potential showed good relationships with modified initial state parameter, void ratio after biotreatment and CC. The bonding ratio, (τ/σ′N)bond, was used to quantify the interparticle bonding. The peak value of (τ/σ′N)bond for the biotreated sand was significantly larger than zero, particularly at high CC and low [Formula: see text], while the peak (τ/σ′N)bond for the untreated sand was negligible. It was also observed that the mobilisation and degradation of calcium carbonate bonds in biotreated sand during DSS shearing are influenced by both CC and [Formula: see text].

Investigation of the critical state behavior of unsaturated silty sand with different fine contents in terms of net and effective stresses

This paper investigates the effect of fine content and matric suction on the behavior of silty sand soil through both net and effective stress variables in the critical state soil mechanics framework. For this purpose, a set of CD triaxial tests in saturated and unsaturated states were performed on the samples of sand with different fine contents. The results showed that in term of net stress variables the position of the critical state line (CSL) in stress space for a given non-plastic fine depend on suction. However, these lines approach each other by choosing a proper effective stress relationship. The CSLs in the coordinates of the void ratio in the term of effective stress changed as a function of the non-plastic fine content and matric suction. However, using the concept of the equivalent intergranular void ratio and considering a special mean effective stress variable depending on suction, the CSLs were converged so that a single line can be defined to describe the behavior of the silty sand at the critical state. Finally, the stress-dilatancy relationship of two constitutive models was examined and it was shown that the use of the equivalent state parameter could facilitate the use of these relationships.

Whole-life modelling of anchor capacity for floating systems: The RSN[sbnd]CSI approach

Successive episodes of cyclic loading cause the strength of soft soils to reduce, through pore pressure build-up, and then recover, through consolidation, as shown by model testing, field studies and theoretical considerations. These ‘whole-life’ changes in soil strength affect the capacity of anchoring systems for offshore infrastructure such as floating turbines or platforms. This paper introduces a new macro-model for assessing the through-life changes in seabed strength and anchor capacity as a result of variable cyclic loading and concurrent consolidation. The model combines SN curves for damage accumulation with a critical state soil mechanics framework for changes in soil strength and anchor capacity. These methods allow the full operational lifetime of an anchoring system to be rapidly analysed, encompassing timescales from individual wave-induced load cycles, through to annual seasons and soil consolidation processes. The approach provides a new basis for whole-life modelling of anchoring systems that is sufficiently fast to allow reliability-based assessments via a Monte Carlo method. In soft soils that exhibit beneficial gains in capacity, this method provides a basis for more efficient design through reductions in anchor size.

A Unified Approach for the Analysis of CPT Partial Drainage Effects within a Critical State Soil Mechanics Framework in Mine Tailings

Results from both laboratory and in-situ cone penetration tests (CPTs) on predominantly sandy silt platinum tailings from an operational mine in South Africa are reported. The CPTs were conducted with four different cone diameters at varied penetration rates. With the results interpreted in terms of the normalized tip resistance and the initial state parameter, in addition to dissipation tests, it was possible to identify the CPTs affected by significant partial drainage effects. A review of the partial drainage concept enabled the formulation of a novel characteristic surface approach, which uses a unified continuous equation to estimate the state parameter from the CPT data from drained to partially drained and undrained regimes and from contractive to dilative states. A review of different methods for the estimation of the coefficient of consolidation, and hence the normalized penetration velocity, enables a comparison of the estimated state parameter with independent values calculated from recovered saturated samples, showing the ability of this technique to infer the state parameter from CPT tests where partial drainage occurs.

Double image stress point bounding surface model for monotonic and cyclic loading on anisotropic clays

In this paper, an anisotropic non-associative constitutive model, based on the well-established critical state soil mechanics framework, is developed for the natural and reconstituted clays subjected to monotonic and cyclic loadings. A robust non-elliptical yield surface is implemented in the model which enables it to capture a wide variety of yield stress points. In addition to a realistic soil stiffness simulation, the employed flexible plastic potential surface equips the proposed model to predict a more accurate coefficient of earth pressure at rest. The model uses a combination of conventional volumetric and comprehensive rotational hardening rules to control the evolution of the yield surface caused by plastic strain increments. The adopted rotational hardening rule uses the concept of governing plastic strain increment which not only ensures the existence of the equilibrium state of anisotropy but also takes the effect of plastic strains at different constant stress ratios into account more sensibly. The proposed model is enhanced with a novel double-image stress point bounding surface plasticity type theory to capture nonlinear behaviour inside the yield surface, and also to simulate the cyclic responses. The detailed model formulation is discussed in both triaxial stress space and the e-mathrm{ln}, p plane, and the important features of the model are elaborately explored. The capabilities of the model are also demonstrated by an extensive sensitivity analysis. In the end, the model is used to carry out simulations of monotonic and cyclic element tests on different clays and the results are compared with the available experimental data.

Modeling submerged granular flow across multiple regimes using the Eulerian–Eulerian approach with shear-induced volumetric behavior

The behavior of submerged granular flow is strongly dependent on the solid volume fraction and the viscosity discontinuity over a wide range of flow regimes. To obtain a general description of this type of flow, this study proposes a new model to compute solid effective stresses of submerged granular materials across multiple flow regimes. Here, based on the critical state soil mechanics framework, a new equation is proposed to describe the evolution of elastic reference of materials caused by elastoplastic deformation. The evolution of elastic reference subsequently informs the development of static pressure, and together with the dynamic pressure computed using a well-established blended model, resulting in a new approach to compute the solid pressure induced by both dynamic and static effects. The proposed model is then implemented in the Eulerian–Eulerian approach using the finite volume method to simulate the collapses of submerged granular columns, covering different flow regimes from quasi-static to viscous depositions. Simulation results agreeing well with experimental and numerical data in the literature are a testament to the performance of a well-developed constitutive law. In addition, the simulation results comprehensibly demonstrate the important role of interstitial fluid flow as well as the initial solid volume fraction in the collapsing process across different flow regimes with different packing densities. Furthermore, the effects of initial volume fraction, fluid pressure, and phase interaction forces on the flow responses are also discussed.

Triaxial compression behavior of 3D printed and natural sands

Different particle properties, such as shape, size, surface roughness, and constituent material stiffness, affect the mechanical behavior of coarse-grained soils. Systematic investigation of the individual effects of these properties requires careful control over other properties, which is a pervasive challenge in investigations with natural soils. The rapid advance of 3D printing technology provides the ability to produce analog particles with independent control over particle size and shape. This study examines the triaxial compression behavior of specimens of 3D printed sand particles and compares it to that of natural sand specimens. Drained and undrained isotropically-consolidated triaxial compression tests were performed on specimens composed of angular and rounded 3D printed and natural sands. The test results indicate that the 3D printed sands exhibit stress-dilatancy behavior that follows well-established flow rules, the angular 3D printed sand mobilizes greater critical state friction angle than that of rounded 3D printed sand, and analogous drained and undrained stress paths can be followed by 3D printed and natural sands with similar initial void ratios if the cell pressure is scaled. The results suggest that some of the fundamental behaviors of soils can be captured with 3D printed soils, and that the interpretation of their mechanical response can be captured with the critical state soil mechanics framework. However, important differences in response arise from the 3D printing process and the smaller stiffness of the printed polymeric material.Graphic abstractArtificial sand analogs were 3D printed from X-ray CT scans of sub-rounded and sub-angular natural sands. Triaxial compression tests were performed to characterize the strength and dilatancy behavior as well as critical staste parameters of the 3D printed sands and to compare it to that exhibited by the natural sands.

Unsaturated structured soils: constitutive modelling and stability analyses

The paper presents a new single-surface elasto-plastic model for unsaturated cemented soils, formulated within the critical state soil mechanics framework, which should be considered as an extension to unsaturated conditions of a recently proposed constitutive law for saturated structured soils. The model has been developed with the main purpose of inspecting the mechanical instabilities induced in natural soils by bond degradation resulting from the accumulation of plastic strains and/or the changes in pore saturation. At this scope, the constitutive equations are used to simulate typical geotechnical testing conditions, whose results are then analysed in light of the controllability theory. The results of triaxial tests on an ideal fully saturated cemented soil and on the corresponding unsaturated uncemented one are first discussed, aiming at detecting the evidence of potentially unstable conditions throughout the numerical simulations. This is followed by similar analyses considering the combined effects of both the above features. For each analysed case, a simple analytical stability criterion is proposed and validated against the numerical results, generalizing the results, and highlighting the crucial role of state variables and model parameters on the possible occurrence of failure conditions.

The critical state behaviour of granular material in triaxial and direct simple shear condition: A DEM approach

The critical state (CS), the anchor concept in the critical state soil mechanics (CSSM) framework, has been comprehensively evaluated in triaxial stress conditions, where all the principal stresses are known but the pure shear stresses in the shear directions are absent. Therefore, the evolution of first and second invariants of the stress tensor (σ′) i.e. the mean effective stress (p′) and deviatoric stress (q) along with volumetric strain (εv) is often used to identify the CS. However, the same does not apply for a direct simple shear (DSS) test, which is more representative of the real ground condition, as in most cases the minor principal stresses are not measured. This leads to the challenge of determining the CS line in the e-log(p') space and thus the concept of state parameter (ψ) cannot be used to characterise soil behaviour. Using DEM, this study evaluates CS for DSS, using evolution σ′ and εv, in the e-σ'N space, compare its location with triaxial CS lines in the e-log(p') space. The CS line for DSS in e-σ'N space was then used to define a modified state parameter, ψ, (ψm). It was found that both ψ and ψm showed good correlations with characteristic behaviour e.g. onset of liquefaction, phase transformation state, fabric anisotropy etc. Therefore, ψm maybe a good alternative of ψ for DSS test where the minor principal effective stresses are not measured to define a CSL in e-log(p') space.

Key geomechanical properties of the historically liquefiable TP-Lisbon sand

The intrinsic properties of sands have a strong influence on the behaviour of these soils. Therefore, particle shape and granular packing can provide relevant insights into the mechanical properties of granular geomaterials. This study presents the characterisation of the key mechanical geomechanical properties controlling the behaviour of an alluvial fine sand, which composes the liquefiable layer of the geological profile at ‘Praça do Comercio’ square, located in the downtown of Lisbon (Portugal). For this purpose, a comprehensive experimental plan was conducted in the laboratory using accurate testing procedures. The experimental plan addressed: (i) the evaluation of the particle shape from a large number of particles using a computational geometry algorithm and statistical procedures; (ii) the estimation of the minimum and maximum void ratio through two standard methods; (iii) the assessment of the stress–strain behaviour by triaxial tests using lubricated end platens and an embedded connection piston, and void ratio measurements using end-of-test soil freezing; and (iv) the stress-dependency assessment of seismic wave velocities using bender elements. Results are interpreted within the critical state soil mechanics framework, highlighting the effects of the particle shape and granular package on the behaviour of this natural sand. In addition, critical state and small-strain parameters are compared and thoroughly discussed against selected data of other sands. Results provide experimental evidence about the influence of the particle shape and granular packing on the key geomechanical properties of TP-Lisbon sand.

A constitutive model for municipal solid waste considering mechanical creep and biodegradation-induced compression

A constitutive model is developed to describe the stress–strain–time behavior for decomposing municipal solid waste (MSW) within a critical state soil mechanics framework. The model is an extension of the Modified Cam-Clay plasticity model. In this model, three sources contribute to the hardening of MSW due to volumetric strain: time-independent plastic volumetric strain, time-dependent volumetric mechanical creep strain, and time-dependent volumetric strain due to the biodegradation (decomposition) of MSW. The MSW model was evaluated through numerical analyses of large-scale one-dimensional compression tests in the laboratory and the field and the reported vertical and horizontal deformations of a MSW landfill. The associated model parameters were obtained by compositional analysis of the waste, from values reported in the literature, and by fitting numerical results to observed behavior. For the laboratory compression test, the best-fit numerical simulation over-predicted the early settlement but converged on the experimental values after 200 days. Initially, the calculated vertical strains in the field-scale test deviated from the measured strains by up to 10% over the 398-day period of the test. However, numerical results after adjusting model parameters to provide the best fit with the measured strains resulted in a maximum deviation of less than 3% over the test duration. The calculated vertical displacements of the MSW landfill were consistent with field measurements. However, the calculated horizontal displacements were significantly lower than the measured values. Sensitivity studies showed that the time-dependent settlement predicted by the model is highly sensitive to the biodegradation rate of MSW. The good agreement between numerical values and observed vertical deformations for the SWEAP section on the MSW landfill suggests that the model has the potential to assess the performance of subsystems in landfills (e.g., the performance of a side slope liner system subject to landfill settlement). However, the discrepancy between predicted and observed horizontal displacements suggests that the numerical model can be improved by incorporating deviatoric creep deformations in the constitutive model.

Triaxial Compression on Semi-solid Alloys

Multi-axial compression of the mushy zone occurs in various pressurized casting processes. Here, we present a drained triaxial compression apparatus for semi-solid alloys that allow liquid to be drawn into or expelled from the sample in response to isotropic or triaxial compression. The rig is used to measure the pressure-dependent flow stress and volumetric response during isothermal triaxial compression of globular semi-solid Al-15 wt pct Cu at 70 to 85 vol pct solid. Analysis of the stress paths and the stress–volume data show that the combination of the solid fraction and mean effective pressure determines whether the material undergoes shear-induced dilation or contraction. The results are compared with the critical state soil mechanics (CSSM) framework and the similarities and differences in behavior between equiaxed semi-solid alloys and soils are discussed.

Application of Critical State Approach to Liquefaction Resistance of Sand–Silt Mixtures under Cyclic Simple Shear Loading

An extensive experimental program of constant-volume (undrained) cyclic simple shear tests was undertaken on Ticino, Italy, sand with different contents of nonplastic fines, ranging from 0% to 40%. The samples were reconstituted by moist tamping and tested with different initial states, including void ratios and effective vertical stresses. Test results confirmed that the concept of equivalent granular void ratio e* is appropriate for the interpretation of the undrained cyclic behavior of sand with different amounts of fines up to the limiting fines content. Because a single trend for critical state (CS) data points was observed in the e*-log(p′) plane (EG-CSL) for different amounts of fines, the cyclic simple shear test results were analyzed within a unified critical state soil mechanics (CSSM) framework in terms of an alternative state parameter, Ψ*. A unique correlation between undrained cyclic strength (CRR) and Ψ* was found, irrespective of the fines content and initial state. Although a correlation between the cyclic resistance ratio and the conventional state parameter Ψ works as well, the procedure based on Ψ* has the advantage that the cyclic behavior of a certain sand with different contents of non plastic fines is described by a single reference curve (EG-CSL). In contrast to previous investigations in the literature, which mainly used triaxial tests, the CRR-Ψ* correlation proposed in the present study is based on cyclic simple shear tests, which better represent the real ground conditions under seismic loading.

Discrete element modelling of strength and critical state characteristics of granular materials under axial compression and axial extension stress path tests

The critical state soil mechanics (CSSM) framework has been widely used across a range of problems in geomechanics involving complex loading conditions. However, the uniqueness of the critical state has been disputed for many years and it remains a controversial issue. Motivated by previous investigations, a series of discrete element method (DEM) simulations were performed under both axial compression (AC) and axial extension (AE) stress paths. All samples were isotropically compressed at varying mean normal effective stresses (confining pressures) and sheared to a large axial strain of approximately 60%. It is found that there exist unique values of critical void ratios and stress ratios under critical state, which are independent of the samples’ initial packings but dependent on stress paths. And the critical strength (stress ratio) for the AC stress path tests is higher than that for the AE stress path. The critical state lines (CSLs) are found to path-dependent but unique for each stress path. A unique linear relationship between the critical coordination numbers and critical void ratios is identified under the AC and AE stress paths respectively, but such a relationship depends on the stress paths. It is also found that there exist unique values of microscopic parameters in terms of deviator fabric under critical state, which are independent of the samples’ initial packings but dependent on stress paths. All these simulation results lead to the conclusion of non-uniqueness of CSLs from both macroscopic and microscopic viewpoints.

Cone penetration testing on silty tailings using a new small calibration chamber

This study presents the results of the first cone penetration testing on predominately silty gold tailings in a calibration chamber, with results interpreted within the critical state soil mechanics framework. Samples were prepared in a wide range of void ratios, prioritising loose contractive states. The results are presented in terms of the state parameter against the normalised tip resistance and are compared with some common state parameter interpretation screening tools. The modified laboratory equipment, sample preparation methods and characterisation of the tested silty tailings are described along with the adapted void ratio tracking method.

Evaluating the particle rolling effect on the characteristic features of granular material under the critical state soil mechanics framework

The discrete element method (DEM) has been extensively used to capture the macroscopic and particulate response of granular materials. Although particle rolling (i.e. controlled by rolling resistance) has been acknowledged as a major contributing factor towards micro-mechanical behaviour of idealized spherical granular material, its influence on characteristic behaviour has not been thoroughly investigated within critical state soil mechanics (CSSM) framework. For instance, the influence of particle rolling on characteristic features of undrained and drained behaviour (e.g. phase transformation, characteristic state, instability, dilatancy, critical state) and the state parameter, (ψ) has not been captured. In this study, a series of constant volume (CV) and drained triaxial compression simulations were undertaken using a rolling resistance linear contact model, deployed within a DEM software. The CSSM framework was centrally used to assess the influence of particle rolling tendencies/resistance on CV and drained behaviours from both a macro- and micro-mechanical standpoint. The study advanced the current understanding of the influence of rolling resistance on CS-related behaviour.

Modeling the behavior of sand-fines mixtures using a critical state model

A review of the current literature on soil behavior modeling reveals the great success of constitutive models proposed within the critical state soil mechanics framework. Imam et al. (2005) proposed a critical state constitutive model for predicting the behavior of sand consolidated to a wide range of void ratios and pressures. The model uses capped yield surfaces and was formulated with special emphasis on its ability to simulate the behavior of loose liquefiable sand. Since sands with fines are abundant in nature, it is often necessary to modify existing models proposed for clean sand to enable them to predict the behavior of sand-fines mixtures. In recent years, the equivalent granular void ratio has been used as an alternative state variable in order to obtain a single trend of variation for some aspects of behavior of sand-fines mixtures such as the critical state condition. In this paper, application of this concept for upgrading the mentioned constitutive model in order to enable it to simulate the behavior of such mixtures is attempted. It is shown that the approach implemented in the current study successfully takes into account effects of non-plastic fines on the sand-fines mixture behavior, and that the modified model simulations are in good agreement with the observed behavior of such mixtures. Performances of two relationships proposed for the determination of the equivalent granular void ratio used in the modified model are also compared.

DEM analysis of monotonic and cyclic behaviors of sand based on critical state soil mechanics framework

A series of monotonic and cyclic triaxial shearing tests on Toyoura sand are simulated by discrete element method (DEM) incorporating rolling resistance. The input parameters are calibrated against laboratory triaxial test data considering different initial states and monotonic loading paths. The calibrated DEM model successfully captures the density and stress dependency of sand behavior under both monotonic and cyclic conditions. It is shown that when approaching liquefaction, contact yielding alters from sliding-dominant to rolling-dominant. The expression of mechanical redundancy index (IR) is derived considering both effects of contact sliding and rolling. The IR = 1.0 condition is shown to be a unified criterion distinguishing between solid state and liquid state upon both monotonic and cyclic liquefactions. A unique micro critical state line (CSL) is obtained in MCN-p′ plane. The cyclic resistance ratio is exponentially correlated with both the macro state parameter (ψe0) derived from the e-p′ CSL and the micro state parameter (ψMCN0) determined from the MCN-p′ CSL. The specimens with the same ψe0 may have distinct cyclic behaviors, while cyclic behaviors of specimens with the same ψMCN0 are close to each other, indicating that ψMCN0 is a more plausible state variable for characterizing the behavior of sand than ψe0.