Limitations of suction‐controlled triaxial tests in the characterization of unsaturated soils

Behavior of unsaturated soils is influenced by many factors, and the influences of these factors are usually coupled together. Suction‐controlled triaxial (SCTX) tests are considered to allow researchers to investigate influences of individual variables on unsaturated soils under specified stress path with controls of stresses, pore water, and air pressures. In the past 50 years, SCTX testing method has been established as a standard approach to characterize constitutive behavior of unsaturated soils. Most important concepts for modern unsaturated soil mechanics were developed upon results from the SCTX tests. Among these, one of the most important contributions in the constitutive modeling of elasto‐plastic behavior for unsaturated soils is the Barcelona basic model (BBM) proposed by Alonso et al. in 1990. The BBM successfully explained many features of unsaturated soils and received extensive acceptance. However, the SCTX tests are designed based upon the divide‐and‐conquer approach in which an implicit assumption is used: soil behavior is stress‐path independent. However, it is well‐established that unsaturated soil behavior is elasto‐plastic and stress‐path dependent. It is found that the SCTX tests in fact cannot control the stress path of an unsaturated soil during loading. This incapability, in combination with complicated loading/collapse behavior of unsaturated soils, makes the SCTX tests for characterizing unsaturated soil questionable. This paper discusses the limitations of the SCTX tests in the characterization of unsaturated soils. A possible solution to the problem was proposed based on a newly developed modified state surface approach. The discussions are limited for isotropic conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Using modified state surface approach to select parameter values in the Barcelona basic model

The Barcelona basic model (BBM) successfully explained many key features of unsaturated soils and received extensive acceptance. It is also one of the few elastoplastic constitutive models for unsaturated soils that have been implemented within finite element codes and applied to the analysis of real boundary value problems. The BBM was proposed in incremental forms according to theories of soil plasticity in which individual aspects of the isotropic virgin behavior are controlled by multiple parameters, whereas at the same time, a single parameter controls more than one aspect of soil behavior. Although a variety of methods have been recently developed for calibrating model parameters for elastoplastic soil models, at present, there are no well‐established, simple, and objective methods for selecting parameter values in the BBM from laboratory tests. This has been one of the major obstacles to the dissemination of this constitutive model beyond the research context. This article presents an optimization approach especially developed for simple and objective identification of material parameters in the BBM. This is achieved by combining a modified state surface approach, recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic stress conditions, with the Newton or quasi‐Newton method to simultaneously determine the five parameters governing isotropic virgin behavior in the BBM. The comparison between results using the proposed method and an existing method for the same laboratory tests was discussed from which the simplicity and objectivity of the proposed method were evaluated. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of different strain rates on hydro-mechanical behaviour of reconstituted unsaturated soil

The hydro-mechanical behaviour of a reconstituted unsaturated soil under different suctions and strain rates was studied through various rate-controlled unsaturated/undrained triaxial tests. The fully saturated reconstituted specimens were desaturated to four different initial suctions (s₀?=?0, 100 kPa, 200 kPa and 300 kPa) and then triaxially sheared (conventional triaxial compression) at three different strain rates in undrained conditions (\(\dot{\varepsilon }_{1} = 0.001\) h^?1, 0.01 h^?1, and 0.1 h^?1). The observed hydro-mechanical behaviour during shearing including the volumetric strain, deviatoric stress, degree of saturation and suction is presented and discussed in this paper. The results indicate that when the strain rate rises at the given initial suctions (or pore water pressures), the maximum deviatoric stress (q_max), critical net stress ratio (M) and critical state suction (s_c) increase but the degree of saturation (S_rc) and volumetric strain at the critical state (ε^c_v ) reduce. The critical effective stress ratio (M′) is not dependent on the strain rate for saturated and unsaturated samples. The critical state lines for unsaturated soils with the constant strain rates are parallel with each other in the e???lnp′ space.

     

Aspects of Mechanical Behavior and Modeling of a Tropical Unsaturated Soil

The research studies the applicability of two elastoplastic models for the collapse prediction of the lateritic soil profile from Southeastern Brazil. These tropical soils have peculiar geotechnical behavior, due to their mineralogical composition and porous structure coming from intense process of formation. Two elastoplastic models were analyzed: the Barcelona Basic Model (BBM) and another one based on BBM, however developed for tropical soils. Oedometric tests with suction control were performed at three distinct depths of the soil profile. The BBM was not suitable for the upper layer of the soil profile, because BBM considers the compressible behavior of the soil in function of the reduction of the elastoplastic compressibility index with the increase of the matric suction. The model developed for tropical soils showed better suited to the compressible behavior of the soil profile, resulting in good prediction of the collapse potential, mainly by accepting increasing values of the elastoplastic compressibility index of the soil profile with the matric suction rise.     

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

A kinematic hardening based model for unsaturated soils considering different hydraulic conditions

At present, several of the existing elastoplastic constitutive models are adapted for describing the stress–strain behavior of unsaturated soils. However, most of them present certain limitations in this field. These limitations can be related to the basic model and/or added unsaturated state variables and formulations. In this regard, inability to model the hydro‐mechanical behavior in constant water (CW) conditions is an example of these limitations. In this paper, an advanced version of CJS model is selected for adaptation to the unsaturated states. Adaptation to unsaturated states is achieved in the framework of effective stress approach. Effective stress equation and unsaturated state variables are selected based on the recent research existing in the literature. The developed model is capable of describing the complex behavior of unsaturated soil in the CW condition in addition to predicting the behavior at failure and post–failure, nonlinear elastoplastic behavior at low levels of stress and strain (by selecting a very small elastic domain), as well as wetting and collapse behaviors. In order to validate the model, results of triaxial tests in CD and CW conditions are used. The validation results indicate the good capability of the proposed model. Behavior of the unsaturated soils during wetting is an important issue. For this reason, the model is also evaluated based on the results of wetting and collapse triaxial tests. A comparison between the tests and simulation results shows that the model is able to predict the soil behavior under the wetting path. Copyright © 2016 John Wiley & Sons, Ltd.     

Explicit stress integration with error control for the Barcelona Basic Model: Part I: Algorithms formulations

The numerical integration of the stress–strain relationship is an important part of many finite element code used in geotechnical engineering. The integration of elasto-plastic models for unsaturated soils poses additional challenges associated to the presence of suction as an extra constitutive variable with respect to traditional saturated soil models. In this contribution, a range of explicit stress integration schemes are derived with specific reference to the Barcelona Basic Model (BBM), which is one of the best known elasto-plastic constitutive models for unsaturated soils. These schemes, however, do not address possible non-convexity of the loading collapse (LC) curve and neglect yielding on the suction increase (SI) line. The paper describes eight Runge–Kutta methods of various orders with adaptive substepping as well as a novel integration scheme based on Richardson extrapolation. The algorithms presented also incorporate two alternative error control methods to ensure accuracy of the numerical integration. Extensive validation and comparison of different schemes are presented in a companion paper. Although the algorithms presented were coded for the Barcelona Basic Model, they can be easily adapted to other unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.     

Collapse behaviour of a lateritic soil

Collapsible soils are problematic by nature. They undergo collapse or sudden settlement or subsidence under a given stress when their water content is increased. Collapse is characterised by collapse potential expressed as ΔH/H x 100, where ΔH is collapse compression. The amount of stress applied and the water content at the time of collapse govern the amount of collapse. In other words, collapse potential depends upon the amount of stress and the water content. Loess and other wind-blown silts are examples of collapsible soils. This paper presents a parametric study on the collapse behaviour of a lateritic soil. Remoulded specimens of a lateritic soil passing through a 425 µm sieve were compacted in 1-D consolidometer or oedometer at a density of 13 kN/m³ for studying collapse under varied initial moisture contents and initial surcharge pressures. Collapse compression of the samples was induced by saturating the specimens with water contents corresponding to 100% degree of saturation. After collapse occurred, the 1-D consolidation tests were continued up to an applied stress of 160 kPa. Collapse behaviour was studied for the applied initial pressures (σ_i) of 10, 20 and 40 kPa and for the initial water contents (w_i) of 5%, 10%, 15% and 20%. Collapse compression and collapse potential decreased with increasing w_i for all σ_i.     

Explicit stress integration with error control for the Barcelona Basic Model.: Part II: Algorithms efficiency and accuracy

The paper compares the accuracy and efficiency of explicit stress integration schemes for elasto-plastic unsaturated soil models with automatic error control. Numerical tests are performed with reference to the Barcelona Basic Model (BBM), one of the most popular elasto-plastic models for unsaturated soils, by using eight explicit Runge–Kutta algorithms of various order as well as a novel application of the extrapolation method described in the companion paper. Initially, the results obtained from the lowest order Runge–Kutta scheme (i.e. Modified Euler) as well as the extrapolation method are checked against accurate solutions of a number of BBM paths involving changes of strains and suction. Subsequently, the efficiency and accuracy of all algorithms are assessed for generic increments of strains and suction, while the difference between two alternative error control methods is also analysed. The results presented, although strictly valid for the Barcelona Basic Model, are expected to be general and relevant to other similar unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.     

Stability of long circular tunnels in sloping ground

Assessment of tunnel stability has become increasingly crucial as more and more tunnels are built in difficult terrains such as sloping ground. The required support pressure on the tunnel walls associates both tunnel stability and liner design considerations. The present analysis attempts to find a uniform internal pressure which can support a circular tunnel built in a sloping ground with a particular level of stability in cohesive-frictional soils. The lower bound finite element limit analysis has been applied to find the required minimum uniform internal support pressure presented as a non-dimensional term p/c; where p is the minimum normal internal pressure on the tunnel boundary to avoid collapse and c is the cohesion of soil. The variation of p/c is presented for a range of normalised embedment depth of tunnel (H/D), stability number (γD/c), internal friction angle of soil (?) and slope angle (β); where H is the crown depth of the tunnel, D is the tunnel diameter and γ is the unit weight of soil. Appropriate comparisons have been carried out with available literature. Failure patterns of the tunnel have also been studied to understand the extent and the type of failure zone which may generate during the collapse.     

Improving a thermal conductivity model of unsaturated soils based on multivariate distribution analysis

Soil thermal conductivity (k) is a key parameter for the design of energy geo-structures, and it depends on many soil properties such as saturation degree, porosity, mineralogical composition, soil type and others. Capturing these diversified influencing factors in a soil thermal conductivity model is a challenging task for engineers due to the nonlinear dependencies. In this study, a multivariate distribution approach was utilized to improve an existing soil thermal conductivity model, Cote and Konrad model, by quantitatively considering the impacts of dry density (ρ_d), porosity (n), saturation degree (S_r), quartz content (m_q), sand content (m_s) and clay content (m_c) on thermal conductivity of unsaturated soils. A large database containing these seven soil parameters was compiled from the literature to support the multivariate analysis. Simplified bivariate and multivariate correlations for improving the Cote and Konrad model were derived analytically and numerically to consider different influencing factors. By incorporating these simplified correlations, the predicted k values were more concentrated around the measured values with the coefficient of determination (R²) increased from 0.83 to 0.95. It is concluded that the developed correlations with the information of different soil properties provide an efficient, rational and simple way to predict soil thermal conductivity more accurately. Moreover, the quartz content is a more important factor than the porosity that shall be considered in the establishment of thermal conductivity models for unsaturated soils with high quartz content.

     

Dynamics of unsaturated poroelastic solids at finite strain

We derive the governing equations for the dynamic response of unsaturated poroelastic solids at finite strain. We obtain simplified governing equations from the complete coupled formulation by neglecting the material time derivative of the relative velocities and the advection terms of the pore fluids relative to the solid skeleton, leading to a so‐called u^s ? p^w ? p^a formulation. We impose the weak forms of the momentum and mass balance equations at the current configuration and implement the framework numerically using a mixed finite element formulation. We verify the proposed method through comparison with analytical solutions and experiments of quasi‐static processes. We use a neo‐Hookean hyperelastic constitutive model for the solid matrix and demonstrate, through numerical examples, the impact of large deformation on the dynamic response of unsaturated poroelastic solids under a variety of loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Site characterization model using least‐square support vector machine and relevance vector machine based on corrected SPT data (Nc)

Statistical learning algorithms provide a viable framework for geotechnical engineering modeling. This paper describes two statistical learning algorithms applied for site characterization modeling based on standard penetration test (SPT) data. More than 2700 field SPT values (N) have been collected from 766 boreholes spread over an area of 220 sqkm area in Bangalore. To get N corrected value (N_c), N values have been corrected (N_c) for different parameters such as overburden stress, size of borehole, type of sampler, length of connecting rod, etc. In three‐dimensional site characterization model, the function N_c=N_c (X, Y, Z), where X, Y and Z are the coordinates of a point corresponding to N_c value, is to be approximated in which N_c value at any half‐space point in Bangalore can be determined. The first algorithm uses least‐square support vector machine (LSSVM), which is related to a ridge regression type of support vector machine. The second algorithm uses relevance vector machine (RVM), which combines the strengths of kernel‐based methods and Bayesian theory to establish the relationships between a set of input vectors and a desired output. The paper also presents the comparative study between the developed LSSVM and RVM model for site characterization. Copyright © 2009 John Wiley & Sons, Ltd.     

A hypoplastic model for mechanical response of unsaturated soils

A new constitutive model is developed for the mechanical behaviour of unsaturated soils based on the theory of hypoplasticity and the effective stress principle. The governing constitutive relations are presented and their application is demonstrated using several experimental data from the literature. Attention is given to the stiffening effect of suction on the mechanical response of unsaturated soils and the phenomenon of wetting‐induced collapse. All model parameters have direct physical interpretation, procedures for their quantification from test data are highlighted. Quantitative predictions of the model are presented for wetting, drying and constant suction tests. Copyright © 2008 John Wiley & Sons, Ltd.     

Predicting effective stress parameter of unsaturated soils using neural networks

In the effective stress equation for unsaturated soils proposed by Bishop, shear strength in these soils depends on the effective stress parameter, χ, a function of soil suction [1]. To estimate the shear strength of unsaturated soils, one must already know this parameter and its variation with soil suction. Though theories on the shear strength of unsaturated soils are consistent with experimental measurements, estimating the effective stress parameter directly from tedious laboratory tests is impractical. Thus, researchers have performed numerous intensive studies to effectively obtain the unsaturated shear strength using simplified empirical methods.This paper shows an adaptive learning neural network method for predicting this parameter, χ. The proposed network is a multilayer perceptron network with six neurons in the input layer representing the air entry value, the volumetric water content at residual and saturated conditions, the slope of soil water characteristic curve, the net confining stress and suction. The available literature uses a database prepared from triaxial shear test results to train and test the network. The results show the suitability of the proposed approach for estimating the effective stress parameter. Network analysis indicates that the χ-parameter depends strongly on the net mean stress.     

Extended Barcelona Basic Model for unsaturated soils under cyclic loadings

The Barcelona Basic Model (BBM) is an extension of the Cam clay model that has become popular in applications involving unsaturated soils and, in particular, in simulations using the finite element method. Partially saturated soils can be loaded in different ways, for instance, mechanically and/or hydraulically. In addition, cycles of loading and unloading can be applied. The present work introduces a modification of the BBM in order to simplify its computer implementation and also to allow the simulation of elastoplastic behaviour during cycles of both mechanical and hydraulic loading. A unique smooth yield surface is introduced and a two-yield surfaces concept is applied in order to represent the cyclic behaviour. The influence of the intermediate principal stress on the strength is also accounted for. Finally, the numerical integration (stress update) of the extended BBM is briefly discussed.     

Central England temperature since AD 1850: the potential of stable carbon isotopes in British oak trees to reconstruct past summer temperatures

In regions with seasonal temperate climatic regimes, tree growth is rarely controlled by any single environmental factor. As a consequence, the development of robust palaeoclimate reconstructions has proved challenging. Tree‐ring stable carbon isotope ratios (δ¹³C), however, are controlled primarily by photosynthetic rate, not by net growth. Therefore, at sites where climatic controls on tree‐ring growth are not strongly expressed, a robust (isotopic) palaeoclimate signal may still potentially be preserved. This hypothesis was tested using a 160‐year record of δ¹³C measured from the pooled latewood cellulose of six Quercus petraea L. (sessile oak) trees from Allt Lan‐las in West Wales, UK. Raw δ¹³C values were corrected for changes in the isotopic ratio of atmospheric carbon dioxide and for changes in the behaviour of trees due to the increasing availability of atmospheric CO₂ since AD 1850. Strong correlations with local summer temperature and sunshine are reported, and also with the Central England Temperature record over the full length of the isotopic chronology (AD 1850–2010) (r = 0.69, P < 0.001). We conclude that tree‐ring stable isotopes can be used to extract strong palaeoclimate signals even from oak trees growing in a temperate maritime climate. This demonstrates the potential for extracting robust palaeoclimatic information from the very long and well‐replicated oak chronologies which have been developed in western and central Europe primarily for dating rather than palaeoclimatic research purposes. Copyright © 2012 John Wiley & Sons, Ltd.     

An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities

This paper presents an advanced constitutive model for unsaturated soils, using Bishop’s effective stress (σ′) and the effective degree of saturation (S_e) as two fundamental constitutive variables in the proposed constitutive model. A sub-loading surface and a unified hardening parameter (H) are introduced into the σ′–S_e modelling framework to interpret the effects of initial density on coupled hydro-mechanical behaviour of compacted soils. Compared with existing models in the literature, the main advantage of the proposed model that it is capable of modelling hydro-mechanical behaviour of unsaturated soils compacted to different initial densities, such as the dependence of loading–collapse volume on initial void ratio and density effect on the shearing-induced saturation change. The proposed model requires 13 material parameters, all of which can be calibrated through conventional laboratory tests. Numerical studies are conducted to assess the performance of the model for a hypothetical soil under two typical hydro-mechanical loading scenarios. The proposed advanced unsaturated soil model is then validated against a number of experimental results for both isotropic and triaxial conditions reported in the literature.     

The Flat Dilatometer Test in an Unsaturated Tropical Soil Site

The site characterization of unsaturated soils is well stablished based on laboratory tests, which are expensive and time-consuming. In-situ testing methods, such as the flat dilatometer test (DMT), are an alternative to the traditional approach of drilling, sampling, and laboratory testing. The literature on DMT interpretation is well established on saturated and well-behaved soils. Only few studies deal with DMT interpretation in unusual soils, and little is known about the influence of soil suction on this test. This paper presents and discusses the influence of soil suction on four DMT campaigns carried out in an unsaturated tropical soil site, also incorporating the soil suction influence on the DMT interpretation. Soil suction was estimated by the soil–water characteristic curve (SWCC) and water content profiles. The water content profiles range from 11.3 to 19.7% which corresponds to a suction range estimated by SWCCs mostly between 6 and 200 kPa. Soil suction significantly influenced DMT data up to 5 m depth at the studied site (the unsaturated active zone) increasing the intermediate DMT parameters. The average horizontal stress index (K_D) was equal to about 1.7 and the average dilatometer modulus (E_D) was about 4.7 MPa in the active zone and practically doubled their values due to in situ soil suction. The estimated peak friction angle (?) was 20–30% higher due to soil suction influence on DMT assuming the soil behaves as a sand like material. Soil suction must be considered to assess the behavior of the investigated soil by the DMT. The suction influence should be incorporated in the effective stress and this approach considerably improved the site characterization of the studied site.

     

Hydro‐mechanical response of collapsible soils under different infiltration events

The behavior of a partially saturated soil during surface‐water infiltration is analyzed by means of an elasto‐plastic constitutive model formulated in terms of effective stress and extended to unsaturated conditions. The model is calibrated considering laboratory‐scale experimental results under suction‐controlled conditions. The wetting process in two collapsing soils, initially loaded at in situ stresses, is simulated by imposing two different boundary conditions: surface ponding and water flow. The stress paths resulting from the imbibition process are analyzed at different points inside the layer. Copyright © 2015 John Wiley & Sons, Ltd.