Critical State Soil Mechanics Research Articles

Small Strain Soil Constitutive Models HS-SMALL & RU+MCC – Calibration and Verification

The paper presents two reasonably advanced constitutive laws for soil. First one is a hybrid of the Modified Cam Clay and a new RU (reload, unload) development, and it is author’s conception. The second one is a HS-small model by Benz. In the RU+MCC model, the Modified Cam Clay model, which is an isotropic elastoplastic hardening, describes normal consolidation behaviour - plastic model originated by Burland in 1967 within the critical state soil mechanics. This model describes realistically mechanical soil behaviour in normal consolidation states. The RU part is designed to ensure more adequate soil responses to reloading paths, particularly in the range of small strains. The HS-small model is an improvement of HS model originated form Schanz and Vermeer. This concept base on cap yield surface with incorporation of two hardening mechanisms, stiffness variation at small strains, densification mechanism, Rowe’s dilatancy and some others. The author in the FEM computer code Z_SOIL.pc has implemented the RU + MCC model. The HS-small model has been implemented into the same software by Truty. To test the influence of the small strain nonlinearity on soil - structure interaction as well as to exhibit the ability of the proposed model to simulate realistically this effect, a comparative study based on the FEM solution has been carried out. As a benchmark, a trial loading test of strip footing was used. The calibration process has based on advanced laboratory and field soil tests like resonant columns, triaxial test, dilatometer test and many others.

A simple anisotropic bounding surface model for saturated clay considering the cyclic degradation

A simple elastoplastic bounding surface plasticity model accounting for anisotropy and cyclic degradation of saturated clay is developed within the framework of critical state soil mechanics and the bounding surface plasticity. The associated flow rule is adopted and merely three constants more than those of the Modified Cam-Clay model are required for simplicity. A preferable rotational hardening rule is generalised into the domain of dynamic model after comparing different kinds of rotational hardening rules to describe the development of anisotropy. The radial mapping rule and the mapping origin moving with stress reversal are incorporated into the bounding surface plasticity concept to capture the behaviours of clay under cyclic loads. A new interpolation function of plastic modulus associated with the length of the accumulated deviatoric plastic strain is introduced into the model to describe the cyclic degradation. The developed model is validated by undrained monotonic and cyclic triaxial tests on isotropically and anisotropically consolidated clay. The proposed model is capable of reproducing the stress–strain behaviours of saturated clay, and capturing the anisotropy and cyclic degradation.

Non-coaxial behavior modeling of sands subjected to principal stress rotation

This paper attempts to clarify the necessary elements for describing the non-coaxial behavior of sand in the plasticity framework based on the critical-state soil mechanics. Such sand response to two representative loading types, the monotonic loading with fixed principal stress direction and rotation of principal stress direction, is the main focus. The present constitutive model can be regarded as an extension of the existing platform model for sand considering the inherent anisotropy. A novel non-coaxial flow direction involved in the plastic flow rule is the crucial feature, which is defined as the part of stress increment perpendicular to a reference direction related to the current stress direction through the Gram–Schmidt orthogonalization process. Such incorporation of the effects of the stress increment on the plastic deformation makes the model capture the non-coaxiality for the monotonic loading with fixed principal stress direction. In order to describe the plastic response induced by the pure rotation of principal stress direction, a set of mapping rules included in the bounding surface plasticity are formulated to develop plastic flow mechanism in the general multi-axial stress space. Besides, the effects of fabric anisotropy on simulating the non-coaxial plastic behavior are discussed. The results show that the above-mentioned modifications on these model ingredients make the theoretical simulation fit well with test data for Toyoura sand under the foregoing two loading conditions.

Feasibility of in-situ evaluation of soil void ratio in clean sands using high resolution measurements of Vp and Vs from DPCH testing

For engineering purposes, the density of soil is often expressed in terms of void ratio. Void ratio is a key parameter in critical state soil mechanics and governs our understanding of soil compressibility, permeability, and shear strength. Typically, in-situ void ratio is evaluated based on laboratory measurements on high-quality, samples of soil. While undisturbed sampling of clayey soils is commonplace in geotechnical practice, high-quality samples of granular soils are difficult and expensive to obtain. Hence, void ratio of granular soils is typically estimated using empirical relationships to in-situ measurements from penetration testing. Even for clean sands there is significant variability in these estimates, and for mixed-grain soils the applicability and performance of the empirical relationships is quite uncertain. Therefore, a more reliable way of measuring in-situ void ratio is needed. This paper examines the feasibility of evaluating in-situ soil void ratio based on the theory of linear poroelasticity and the propagation velocity of compression and shear waves (i.e., vp and vs, respectively) through fluid-saturated porous materials. Specifically, soil void ratio is evaluated via a porosity relationship that is a function of vp, vs, and four additional parameters describing the physical properties of the soil (i.e., the Poisson's ratio of the soil skeleton, the bulk modulus and mass density of water, and the mass density of the solid soil particles). In this study, the effectiveness of using high-resolution vp and vs measurements from direct-push crosshole testing to estimate in-situ void ratios is investigated at ten, predominantly clean-sand case history sites in Christchurch, New Zealand, via a comparison with void ratio estimates developed from penetration testing measurements. The seismic-based void ratio estimates are shown to be particularly sensitive to vp, requiring a measurement error of less than 2%. Given the need to make such precise in-situ measurements of vp, the DPCH method is believed to show particular promise for enabling accurate, seismic-based estimates of void ratio in the future.

Undrained response of Sydney sand under non-reversal cyclic loading

Stress history and loading path can significantly influence the cyclic response of sands. It is well known that cyclic behaviour under non-symmetrical cycling is generally different from that under symmetrical loading around zero deviator stress. Anisotropic consolidation prior to cycling in triaxial apparatus changes the behaviour by exerting an initial static shear stress on critical planes. The present paper reports the results from a number of cyclic triaxial tests on anisotropically consolidated samples of Sydney beach sand. The samples are reconstituted in the laboratory and subjected to non-reversal cycling in compression only loading under undrained conditions. Typical test behaviours are described and the effects of cyclic stress ratio and initial state on the response are discussed. It is shown that the state parameter is capable of predicting the cyclic resistance and the trend of excess pore water pressure generation during one-way compressional cycling and, as has been well established for simple loading paths, critical state soil mechanics is able to provide a reliable framework to characterize the behaviour under different cyclic loading conditions.

Cyclic behavior and liquefaction resistance of silty sands with presence of initial static shear stress

The liquefaction resistance of silty sands and the potential effect of initial static shear stress are major concerns in seismic design of dams and embankments. This paper presents a systematic experimental study on non-plastic silty sands to address these concerns. It is shown that the concept of threshold α (αth) proposed by Yang and Sze (2011) to characterize the impact of α (representing the initial static shear stress level) on cyclic resistance (CRR) of clean sands is applicable to silty sands as well. When α < αth, CRR increases with increasing α, otherwise it decreases with increasing α. The threshold α is affected by the initial packing density, the initial effective confining pressure and the fines content. An improved state dependency of the threshold α, which is regardless of fines content, is proposed in the framework of critical state soil mechanics by using the state parameter (ψ). An analysis platform, known as CRR-ψ platform and developed based on clean sand data, is shown to have the capability of characterizing the state dependence of CRR for sands with varying fines contents. This platform in conjunction with the unified αth-ψ correlation provides a unified and consistent framework for understanding the complicated effects of initial static shear stress on soil liquefaction and for quantifying such effects for engineering practice.

Interpretation of piezocone penetration and dissipation tests in sensitive Leda clay at Gloucester test site

A modified piezocone penetration test (CPTu) analytical solution based on spherical cavity expansion and critical state soil mechanics (SCE–CSSM) is employed for assessing yield stress, undrained shear strength, and flow parameters in sensitive Leda clay at the Gloucester test site. For sensitive and structured clays, the formulation relies on the mobilized effective stress friction angle ([Formula: see text]) defined at two parts of the stress–strain curve: (i) peak stress ([Formula: see text]) and (ii) maximum obliquity ([Formula: see text]). Input parameters for assessing the overconsolidation ratio ([Formula: see text], where [Formula: see text] is preconsolidation stress and [Formula: see text] is current effective vertical stress) from CPTu results include: undrained rigidity index (IR= G/su, where G is shear modulus and suis undrained shear strength), plastic volumetric strain potential (Λ = 1 – (Cs/Cc), where Csis swelling index and Ccis virgin compression index), and effective friction angles ([Formula: see text] and [Formula: see text]). A direct CPTu means of assessing the undrained rigidity index in a reliable manner is also developed that gives the Nktcone factor and matches profiles of undrained shear strength from triaxial compression tests (suTC). The modified solution is also implemented on two additional sites: a sensitive-quick clay in Norway and structured varved clay from New England. Interpretations of the coefficient of consolidation and permeability from pore-water pressure dissipation tests at Gloucester are evaluated using the SCE–CSSM formulation and shown to be comparable with independent laboratory and field tests.

Semi-solid deformation of Al-Cu alloys: A quantitative comparison between real-time imaging and coupled LBM-DEM simulations

Semi-solid alloys are deformed in a wide range of casting processes; an improved understanding and modelling capability is required to minimise defect formation and optimise productivity. Here we combine thin-sample in-situ X-ray radiography of semisolid Al-Cu alloy deformation at 40–70% solid with 2D coupled lattice Boltzmann method - discrete element method (LBM-DEM) simulations. The simulations quantitatively capture the key features of the in-situ experiments, including (i) the local contraction and dilation of the grain assembly during shear deformation; (ii) the heterogeneous strain fields and localisation features; (iii) increases in local liquid pressure in regions where liquid was expelled from the free surface in the experiment; and (iv) decreases in liquid pressure in regions where surface menisci are sucked-in in experiments. The verified DEM simulations provide new insights into the role of initial solid fraction on the stress-deformation response and support the hypothesis that the behaviour of semi-solid alloys can be described using critical state soil mechanics.

Numerical analysis of concrete-faced rockfill dams considering effect of face slab – cushion layer interaction

In this study, the effect of concrete face slab – cushion layer interface behavior on the performance of face slabs in concrete-faced rockfill dams (CFRDs) is investigated using the finite element method. The body of the CFRD is simulated by the cap elastoplasticity model while the interface zone between the concrete face slab and the gravelly cushion layer is simulated explicitly by an advanced interface constitutive model, developed in the framework of critical state soil mechanics and state parameters, and capable of simulating volumetric behavior and stress path dependency. The effect of elastic and elastoplastic material behavior and water level on the stress and displacement responses of the concrete face slab is examined, and the influence of the roughness at the interface area between the concrete face slab at the contact face and the cushion layer on the performance of the concrete face slab is investigated. Comparison of the results with and without the explicit consideration of the interface behavior shows the importance of incorporating advanced constitutive interface modeling in the design and analysis of CFRDs.

Generalized Plasticity Model for Sand with Enhanced State Parameters

AbstractThis paper presents a constitutive model for sand based on the framework of generalized plasticity and the concept of critical state soil mechanics. In order to model the nonlinear relation...

Mechanical state of gravel soil in mobilization of rainfall-induced landslides in the Wenchuan seismic area, Sichuan province, China

Abstract. Gravel soils generated by the Wenchuan earthquake have undergone natural consolidation for the past decade. However, geological hazards, such as slope failures with ensuing landslides, have continued to pose great threats to the region. In this paper, artificial model tests were used to observe the changes of soil moisture content and pore water pressure, as well as macroscopic and microscopic phenomena of gravel soil. In addition, a mathematical formula of the critical state was derived from the triaxial test data. Finally, the mechanical states of gravel soil were determined. The results had five aspects. (1) The time and mode of the occurrence of landslides were closely related to the initial dry density. The process of initiation was accompanied by changes in density and void ratio. (2) The migration of fine particles and the rearrangement of coarse–fine particles contributed to the reorganization of the microscopic structure, which might be the main reason for the variation of dry density and void ratio. (3) If the confining pressure were the same, the void ratios of soils with constant particle composition would approach approximately critical values. (4) Mechanical state of gravel soil can be determined by the relative position between state parameter (e, p′) and ec–p′ planar critical state line, where e is the void ratio, ec is the critical void ratio and p′ is the mean effective stress. (5) In the process of landslide initiation, dilatation and contraction were two types of gravel soil state, but dilatation was dominant. This paper provided insight into interpreting landslide initiation from the perspective of critical state soil mechanics.

Multidirectional cyclic shearing of clays and sands: Evaluation of two bounding surface plasticity models

Seismic site response analysis (SSRA) is typically performed considering only one horizontal component of earthquake excitation. In many cases, however, two or three components are needed for the analysis to properly account for the true multidirectional nature of seismic loading. In this type of analysis, it is essential to use multiaxial constitutive models that can realistically describe the stress-strain response of soils. Development and validation of such constitutive models are essential steps toward this goal. Fortunately, a large quantity of experimental data from multidirectional cyclic shear tests is available and can provide physical basis for validating such models. This paper focuses on evaluation of two members of the SANICLAY and SANISAND families of constitutive models for simulating the response of clay and sand, respectively, when subjected to multidirectional cyclic shearing. The models have anisotropic elasto-plastic formulation, within the framework of critical state soil mechanics, and follow the bounding surface plasticity theory. They are calibrated and evaluated against experimental data on Gulf of Mexico clay and Monterey No. 0/30 sand in undrained multidirectional cyclic shear tests, including linear, circular/oval, and figure-8 loading paths. This study provides a basis for evaluation of the capabilities of these models in multidirectional shearing, thereby paving the way towards future applications in multidirectional SSRA.

Analysis of Soil-Compacting Effect Caused by Shield Tunneling Using Three-Dimensional Elastoplastic Solution of Cylindrical Cavity Expansion

Soil squeezing effect and formation disturbance caused by tunnel excavation can be simulated by cylindrical cavity expansion due to the comparability between tunneling and cavity expansion. Although most of the existing theoretical derivation is based on simple constitutive model of soil foundation, not only the relation between principal stress components was simplified in the solution process, but also the stress history, initial stress anisotropy, and stress-induced anisotropy of structural soil were neglected. The mechanical characteristics of soil are closely related to its stress history, so there is a gap between the above research and the actual engineering conditions. A three-dimensional elastoplastic solution of cylindrical cavity expansion is obtained based on the theory of critical state soil mechanics and engineering characteristics of shield tunneling. In order to fully consider the influence of initial anisotropy and induced anisotropy on the mechanical behavior of soils, the soil elastoplastic constitutive relation of cavity expansion is described in the course ofK0-based modified Cam-clay (K0-MCC) model after soil yielding. An equation with equal number of variables is obtained under the elastic-plastic boundary condition based on the Lagrange multiplier method. By solving the extreme value of the original function, the analytical solution of radial, tangential, and vertical effective stresses distribution around the circular tunnel excavation is obtained. In addition, changes of elastic deformation area and plastic deformation area for soil during the shield excavation have been analyzed. Calculation results are compared with the numerical solutions which usually consider isotropic soil behavior as the basic assumption. In this paper, a constitutive model which is more consistent with the actual mechanical behavior of the soil and the construction process of the shield tunnel is considered. Therefore, the numerical solutions are more realistic and suitable for the shield excavation analysis and can provide theoretical guidance required for design of shield tunneling.

Mechanics of Fold‐and‐Thrust Belts Based on Geomechanical Modeling

AbstractWe use a large strain geomechanical model and critical state soil mechanics to study the evolution of stress and deformation in an evolving fold‐and‐thrust belt and its underlying footwall sediments. Both mean effective stress and deviatoric stress contribute to porosity loss within the wedge with 35% of the porosity loss resulting from increased shear. As a result, porosity increases abruptly across the décollement because both mean‐effective and shear stresses are much higher inside the wedge than in the footwall. As the basal friction coefficient (μb) increases, more shear stress is transmitted across the décollement, resulting in additional compaction of the footwall sediment and decrease in the porosity contrast across the décollement. As the internal friction coefficient (μs) increases, the wedge sediment is more compacted because it can withstand higher mean‐effective and deviatoric stresses. Inside the wedge, the sediment experiences subhorizontal shortening strain and subvertical elongation strain. We predict a 10–30 km wide “transition zone” in which the shear‐stress ratios and compaction curves change rapidly between compressional critical state failure and uniaxial strain (K0) state. Our model results agree with the taper angles and the stress orientations predicted by critical taper theory. This large‐strain drained modeling approach provides first‐order insights into the mechanical processes of loading and compaction in fold‐and‐thrust belts and a foundation for understanding field observations of pressure, stress, and deformation in thrust belt systems.

Mechanical properties of a carbonate sand from a dredged hydraulic fill

This paper focuses on the properties of a crushable, uncemented, carbonate sand, retrieved from an artificial island to be used for petroleum production offshore of the United Arab Emirates. The sand was dredged from an offshore borrow area, placed hydraulically within engineered bunds to create the island and densified by vibroflotation. The results of a comprehensive laboratory testing programme are summarised in this paper, providing a set of mechanical properties for carbonate sand. The laboratory programme included static, cyclic and dynamic tests, the results of which are interpreted in a critical state soil mechanics framework, including stress dilatancy. The results of this testing programme contribute to on-going research on the behaviour of carbonate sands under static and cyclic loading conditions. The results are also compared with selected data for other carbonate and siliceous sands, and highlight the behaviour of crushable, carbonate sands used as hydraulic fills.

Pressure and Stress Prediction in the Nankai Accretionary Prism: A Critical State Soil Mechanics Porosity‐Based Approach

AbstractWe predict pressure and stress from porosity in the Nankai accretionary prism with a critical state soil model that describes porosity as a function of mean stress and maximum shear stress, and assumes Coulomb failure within the wedge and uniaxial burial beneath it. At Ocean Drilling Program Sites 1174 and 808, we find that pore pressure in the prism supports 70% to 90% of the overburden (λu = 0.7 to 0.9), for a range of assumed friction angles (5–30°). The prism pore pressure is equal to or greater than that in the underthrust sediments even though the porosity is lower within the prism. The high pore pressures lead to a mechanically weak wedge that supports low maximum shear stress, and this in turn requires very low basal traction to remain consistent with the observed narrowly tapered wedge geometry. We estimate the décollement friction coefficient (μb) to be ~0.08–0.38 (ϕb′ = 4.6°–21°). Our approach defines a pathway to predict pressure in a wide range of environments from readily observed quantities (e.g., porosity and seismic velocity). Pressure and stress control the form of the Earth's collisional continental margins and play a key role in its greatest earthquakes. However, heretofore, there has been no systematic approach to relate material state (e.g., porosity), pore pressure, and stress in these systems.

Modelling tensile/compressive strength ratio of artificially cemented clean sand

The present work proposes a new theoretical model for predicting both the splitting tensile strength (qt) and the compressive strength (qu) of artificially cemented sand and assesses their ratio for a given material. The proposed model is based on the concept of the superposition of the failure strength contributions of the sand and cement phases. The sand matrix obeys the concept of critical state soil mechanics, while the strength of the cemented phase can be described using the Drucker-Prager failure criterion. The analytical solutions are compared against the results of tests on three different types of cemented clean sand cured for different time periods. While the analytical relation fits the experimental data well, it also provides a theoretical basis for the explanation of some features related to the experimentally derived strength relationships for cemented clean sand. The value of the power relationship between the strength and the porosity/cement ratio index seems to be governed by the soil matrix properties, while the interdependency of the strength and the curing time can also be captured. For a given cemented sand, the model equally confirms the existence of a unique tensile/compressive strength ratio (qt/qu), independent of the curing time and primarily governed by the compressive to tensile strength ratio (or the friction properties) of the cement. It is also confirmed that the qt/qu ratio changes within a narrow range for different frictional properties of the cementing phase.

Modelling tensile/compressive strength ratio of fibre reinforced cemented soils

The present work proposes a theoretical model for predicting the splitting tensile strength (qt) - unconfined compressive strength (qu) ratio of artificially cemented fibre reinforced soils. The proposed developments are based on the concept of superposition of failure strength contributions of the soil, cement and fibres phases. The soil matrix obeys the critical state soil mechanics concept, while the strength of the cemented phase can be described using the Drucker-Prager failure criterion and fibres contribution to strength is related to the composite deformation. The proposed developments are challenged to simulate the experimental results for fibre reinforced cemented Botucatu residual soil, for 7 days of cure. While the proposed analytical relation fits well the experimental data for this material, it also provides a theoretical explanation for some features of the experimentally derived strength relationships for artificially fibre reinforced cemented clean sands. A parametric study to analyse the effect of adding different fibre contents and fibre properties is provided. The proposed modelling developments also confirm the existence of a rather constant qt/qu ratio with moulding density, cement and fibre contents .

Characterizing Monotonic Behavior of Pond Ash within Critical State Approach

AbstractThe monotonic behavior of pond ash was studied experimentally and with a particular focus on evaluating the applicability of critical state soil mechanics framework in synthesizing and mode...

Discussion on “A simple critical state interface model and its application in prediction of shaft resistance of non-displacement piles in sand”

In a recent paper (Lashkari, 2017), the author proposed a simple constitutive model for predicting the behaviour of a sand-structure interface under the framework of critical state soil mechanics. However, there are some issues, such as the parameters for the proposed interface model and the algorithm used for the pile segment analysis, that should be discussed in detail.