At-rest Earth Pressure Coefficient Research Articles

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.

Modified method for predicting lateral displacement of PVD-improved ground under combined vacuum and surcharge loading

A modified method is proposed to predict the lateral displacement (δ) of prefabricated vertical drains (PVDs) improved ground under combined vacuum and surcharge loads, which is derived based on a few modified triaxial tests and a series of finite element analyses of PVD unit cells. It is observed that reducing the surcharge load (ps) and loading rate (LR) and increasing the vacuum pressure (pv), pre-vacuum consolidation period (tv), and initial undrained shear strength (su0) could be effective in controlling the outward δ. Variations of the effective stress ratio (Ke) that controlling the δ with ps, pv, LR, tv, and su0 are then presented. A synthetic relationship between the normalized horizontal strain (εh) by a reference one-dimensional vertical strain (εv1) and the normalized Ke by the at-rest earth pressure coefficient (K0) is proposed for cases with and without tv. Further, a modified index parameter (β1) is introduced for quantitatively considering the effect of ps, pv, LR, tv, su0, and consolidation properties of the soil, a relationship between Ke and β1 is then established for evaluating the value of Ke. Combinations of the εh/εv1–Ke/K0 and Ke–β1 relationships enable modified predictions of the δ from basic preloading conditions and soil parameters.

Compressibility of biocemented loose sands under constant rate of strain, loading, and pseudo K0-triaxial conditions

The compressibility behavior of loose sands treated with Microbially Induced Carbonate Precipitation (MICP) is presented in this paper. The paper discusses the strain rate effects and evolution of at-rest earth pressure coefficient and elastic shear modulus during K0-loading. The soil samples were prepared in a triaxial cell in which a biological solution containing the ureolytic bacteria Sporosarcina pasteurii was injected and held under a small back pressure. Cementation treatments were injected following an alternated top and bottom sequence. The constant rate of strain, constant rate of loading, and pseudo K0-triaxial tests were performed at different strain and stress rates. On-specimen internal instrumentation consisting of a submersible load cell, three Hall Effect transducers, and vertical Bender Elements were used to control radial strains during K0-loading and measure small-strain shear modulus changes. Based on shear wave velocity measurements, the MICP-treated sand was lightly cemented and displayed soil-like behavior. The experimental results demonstrated a significant reduction in soil compressibility after MICP treatment. The material response was remarkably similar for every tested strain rate. The very small values of axial strains measured for the biotreated samples in relation to untreated control specimens for vertical effective stress levels below 200 kPa is evidence of the suitability of this treatment and shows its potential for use in field applications at relatively shallow depths.

A unified elasto-plastic constitutive model for sandy and clayey soils accounting for at-rest condition

ABSTRACT Taking advantages of some existing two-surface soil constitutive models in a critical state framework, a unified two-surface constitutive model was developed for rigorous simulation of elasto-plastic deformation of different soils such as loose and dense sands, normally and over-consolidated clayey soils subjected to any type of monotonic loadings. Employing the dilatancy parameter, the strain-softening and stress-dilatancy were described using non-associated flow rule to generalise the application of the model to different soils under various stress states. The applicability of the proposed model was validated comparing the numerical simulations with the existing experimental data for variety of soils subjected to different phases of monotonic loadings. The model was found to be capable of simulating drained and undrained behaviour of clayey and sandy soils under triaxial stress conditions as accurate as the constant stress-ratio loading state. The results also demonstrated the ability of the model to determine the at-rest earth pressure coefficient (K0 ) for variety of soils suitable to be applied to the geotechnical problems affected by this parameter such as piles groups and retaining earth structures. While the formulation of hardening parameter in the integration scheme is based on volumetric and deviatoric plastic strains, the simulation of dilatancy response especially in dense sands showed an excellent agreement with the experimental data.

Cyclic resistance ratio of pleistocene-age sands from the South Carolina coastal plain

Field and laboratory tests were performed on sandy soils from three Pleistocene-age sites in the South Carolina Coastal Plain to investigate the age–related resistance to liquefaction. Reported research indicates that liquefaction resistance of sands increases with the age of the deposit, and that liquefaction may reset the aging clock. The stress-controlled cyclic triaxial test was used to determine the cyclic strength of soil deposits with geologic ages of approximately 200,000, 450,000, and 1,400,000 years and evidence of sand blows that are 467 to 4185 years old. Specimens were obtained using a fixed piston sampler frozen ex situ and include naturally occurring differences in fabric. Cyclic stress ratios ranging from 0.135 to 0.225 were used to determine the peak deviator stress applied during the cyclic triaxial test and were initially estimated from two age-based methods, which were found to over-estimate the laboratory cyclic stress ratio. Estimates of the at-rest earth pressure coefficient were applied to the laboratory cyclic resistance ratio, which resulted in field cyclic resistance ratios that ranged from 0.100 for the oldest deposit (1,400,000 years) to 0.131 for the mid-aged deposit (450,000 years) for initial liquefaction occurring when the generated excess pore pressure was equal to the effective confining stress of 100 kPa (ru = 1.0) at N equal to 15 cycles. The carbon-dated age of the sand blow events correlated with the field cyclic resistance ratios; the geologic ages of the soil deposits did not. A correlation between the clay content, not the fines content, was observed.

Assessment of clay stiffness and strength parameters using index properties

A new approach is developed to determine the shear wave velocity in saturated soft to firm clays using measurements of the liquid limit, plastic limit, and natural water content with depth. The shear wave velocity is assessed using the site-specific variation of the natural water content with the effective mean stress. Subsequently, an iterative process is envisaged to obtain the clay stiffness and strength parameters. The at-rest earth pressure coefficient, as well as bearing capacity factor and rigidity index related to the cone penetration test, is also acquired from the analyses. Comparisons are presented between the measured clay parameters and the results of corresponding analyses in five different case studies. It is demonstrated that the presented approach can provide acceptable estimates of saturated clay stiffness and strength parameters. One of the main privileges of the presented methodology is the site-specific procedure developed based on the relationships between clay strength and stiffness parameters, rather than adopting direct correlations. Despite of the utilized iterative processes, the presented approach can be easily implemented using a simple spreadsheet, benefiting both geotechnical researchers and practitioners.

Measurement, interpretation and recommended use of laboratory strength properties of fibrous peat

Peat deposits are complex natural formations encountered in many geographical areas. Peat itself is considered as a challenging geomaterial, with many aspects of its behaviour seemingly remaining enigmas. This state-of-the-art review paper provides an extensive summary of current knowledge on the strength and shear behaviour of fibrous peats. Critical assessments and interpretations of the undrained strength, effective-stress strength and at-rest earth pressure coefficient parameter values determined for fibrous peat materials using standard and advanced laboratory apparatus are presented, focusing particularly on the consolidated undrained triaxial compression and direct simple shear approaches. Based on documented case histories of embankments, dikes and natural peat slopes, guidance is given for operational shear strength assessments in peat, aimed at bearing capacity and slope stability calculations, considering both the normalised undrained strength ratio and limit equilibrium effective-stress strength approaches. In particular, the botanical origin, structural anisotropy, humification level, likely initial overconsolidated state, tensile resistance associated with the peat fibres and possible scale effect related to the test-specimen size are discussed in the context of the strength mobilised for different testing apparatus. The test methodologies and interpretations of experimental results presented for fibrous peat in this paper should be transferable to other fibrous soil and soil-like materials.

Numerical investigation of earth pressure coefficient along central line of backfilled stopes

The earth pressure coefficient K, defined as the horizontal to vertical normal (effective) stresses ratio (σh/σv), is a key parameter in analytical solutions for estimating the stresses in backfilled stopes. In the case of vertical stopes, the value of K has sometimes been defined using the at-rest earth pressure coefficient K0, while others have applied Rankine’s active earth pressure coefficient Ka. To help clarify this confusing situation, which can lead to significantly different results, the origin and nature of the at-rest and Rankine’s active coefficients are first briefly recalled. The stress state in backfilled stopes is then investigated using numerical simulations. The results indicate that the value of K can be close to Ka for cohesionless backfills along the vertical central line (CL) of vertical stopes, due to sequential placement and partial yielding of the backfill. For inclined stopes, simulations show that the ratio between the minor and major principal stresses (σ3/σ1) along the CL in the backfill, which differs from σh/σv, can also be close to Ka. A simple expression is shown to represent the horizontal to vertical stresses ratio σh/σv (= K) along the CL of such inclined stopes well. A discussion follows on the effects of backfill properties and simulation approach.

Numerical investigation of the at-rest earth pressure coefficient of granular materials

The at-rest earth pressure coefficient, $$\hbox {K}_{0}$$ , is one of the most fundamental values for evaluating in-situ soil stresses and designing foundation. Research has been expanded to investigate the correlation between $$\hbox {K}_{0}$$ and micro-scale characteristic of granular soils, beyond the macroscopic approach empirically correlated with internal friction angle. This study presents the evolution of $$\hbox {K}_{0}$$ values of irregularly shaped natural sand, spherical shaped smooth and rough surfaced glass beads along with the stress history, estimated by the discrete element method. The surface roughness and non-spherical particles were emulated by inter-particle friction coefficient and the clumped particles. Results exhibit that the $$\hbox {K}_{0}$$ during loading stage nonlinearly decreases with increasing values of friction coefficient and the assemblies with clumped particles present the lower values of $$\hbox {K}_{0}$$ than spherical particle assemblies of the same friction coefficient. The varying friction coefficient seems enough to capture the evolution of $$\hbox {K}_{0}$$ during loading, unloading and reloading cycles, while the natural sand inevitably requires the assembly with clumped particles to capture the experimentally observed $$\hbox {K}_{0}$$ evolutions.

The at-rest earth pressure coefficient prediction using simple elasto-plastic constitutive models

The paper deals with the theoretical prediction of the at-rest earth pressure coefficient for normally consolidated soils ( k 0(NC)) using simple elasto-plastic constitutive models. In the first part of the work, the k 0(NC) expressions derived from critical state soil mechanics models are critically discussed. It is shown that, adopting typical values of the models parameters, the experimental k 0(NC) values are usually over-predicted. In the second part, a possible modification of the critical state model formulation, which allows to predict lower k 0(NC) values for a fixed angle of shearing resistance, is considered. Finally, a discussion of the results and some brief conclusions are proposed.

Comment on "Use of the ranking distance as an index for assessing the accuracy and precision of equations for the bearing capacity of piles and at-rest earth pressure coefficient"

Burland and Federico 1719 Orr and Cherubini (2003) compare different predictive equations of (i) the bearing capacity of driven and root piles and (ii) the at-rest earth pressure coefficient K0(NC) of normally consolidated clayey soils. They assess the reliability— or, quoting Orr and Cherubini (2003), “the dependability”— of the considered calculation methods in terms of the ratio Qcalc /Qmeas between calculated and measured values, and of two functions (namely: the ranking index RI and the ranking distance RD) of this ratio. The writers can see the logic of using RD in preference to RI. Orr and Cherubini (2003) introduce a somewhat arbitrary scale of conservatism in Table 1 which, in the writers’ view, is unhelpful and can be misleading. Conservatism (or unconservatism) is measured by the percentage of K values (Qcalc /Qmeas) less than 1. Consider a case in which a method gives values of K that are all less than 1 but are all greater than 0.99. By any standards such a method is both accurate and precise. Yet, according to Table 1, the degree of conservatism would be ranked as 1, and it would be defined as very unconservative (i.e., very unsafe). This is clearly not the case. Moreover the terms “conservative” or “unconservative” will depend on the context of the problem being studied and what is conservative in one problem may well be unconservative in another. We can take the predictive accuracy of the at-rest earth pressure coefficient K0(NC) as a case in point. Orr and Cherubini (2003) consider seven equations. Among these, there is the one proposed by the writers (Burland and Federico 1999) given by eq. [8] and expanded upon in Appendix A. This equation, based on the Modified Cam-Clay model, requires two input constants, i.e., the effective angle of shearing resistance φ′ and the Skempton's pore pressure coefficient at failure Af,i. Both these constants are obtainable from a single isotropically consolidated undrained compression (CIUC) triaxial test with pore pressure measurement. Orr and Cherubini (2003) state: “Equation [8] by Burland and Federico is very unconservative, tending to overpredict K0(NC)” (i.e., it is very unsafe according to Table 1). Taken at face value such a statement could be very prejudicial. Yet there could be situations in which a small overestimate of K0(NC) would lead to a conservative overestimate of loading—as in the case of a retaining wall. In summary, the writers think that the terms “conservative” and “unconservative” are unhelpful and can be positively misleading. In this case of K0(NC) the terms “overpredict” and “underpredict” would be more appropriate. Moreover the writers would not recommend the use of Table 1. Orr and Cherubini (2003) further state: “Burland and Federico (1999) anticipate, however, that this equation will be improved as laboratory testing improves.” Orr and Cherubini (2003) probably mean “...that, as laboratory testing improves, agreement with this equation will improve.” In fact, in their original paper the writers wrote “...as already put in evidence by Roscoe and Burland, this model tends to somewhat overpredicit the observed values of the coefficient of earth pressure at rest K0(NC). However, with better instrumentation and quality of testing, it is likely that higher values of K0(NC) may be obtained, thereby giving improved practical significance to the predictions of the proposed equation.” Finally, many of the columns in Table 6 are incorrectly related to the equations and a corrected version is given below (see Table C1). Note also that in Table 7, K0(NC) should be replaced by K and in the second last row RD should be replaced by K.

Response to the comment by Burland and Federico on: "Use of the ranking distance as an index for assessing the accuracy and precision of equations for the bearing capacity of piles and at-rest earth pressure coefficient"

Orr and Cherubini 1722 The authors are pleased to note that Burland and Federico in their Comment agree with the authors that it is more logical to use the ranking distance, RD in preference to the ranking index, RI for assessing the reliability of the considered calculation methods. The RD and RI values are based on the parameter, K, which is the ratio of the calculated to the measured values. Burland and Federico have questioned the scale of conservatism presented in Table 1, which is based on the percentage of K values less than 1, stating that this scale is arbitrary and can be misleading. The scale of conservatism is indeed arbitrary, but this is the nature of statistical indicators that are based on a range of values, and hence the scale is necessarily subjective. However, the significance of the scale is that it is the first and unique scale of conservatism that, until now, has been proposed. When the method being considered is to calculate a soil resistance, for example the bearing capacity of a pile, then values of K less than 1.0 correspond to underpredictions and hence are conservative. Burland and Federico give the example of the case where a method gives K values which are all less than 1.0 but are all greater than 0.99. Although this is an extremely unrealistic case, by any standards such a method is indeed both accurate and precise. From a statistical point of view, the method is also very conservative. This is confirmed by the scale of conservatism presented in Table 1, since, with 100% of the K values less than 1.0, it is ranked as 5, very conservative, and not 1, very unconservative, as interpreted by Burland and Federico. Improvements to the scale to provide more safety rather than just statistical conservatism are possible by, for example, considering the number of K values less than 0.9 rather than less than 1.0, so as to eliminate K values close to 1.0, as in Burland and Federico’s example. When the method being considered is to calculated a load, for example the earth pressure on a buried structure, then K values less than 1.0, corresponding to underpredicted values, can represent methods that are either conservative or unconservative. They will represent conservative methods when the earth pressure forms part of a soil resistance—for example the shaft resistance on a pile foundation—and unconservative methods when the earth pressure is a load, as in the example of the loading on a retaining wall given by Burland and Federico. Consequently, since methods that provide underpedictions can be either conservative or unconservative, depending on the design situation, the authors agree that the scale of conservatism in Table 1 based on K values less than 1.0 can be misleading and therefore propose Table C1 as a revised and expanded version of Table 1 to take account of the design situation. In this table, instead of just providing a scale of conservatism corresponding to the number of K values that are less than 1.0, as in Table 1, there are two columns: one column (the second column) that relates the scale of conservatism to the number of K values less than 1.0 for design situations where the measured and calculated values are a type of soil resistance or loading that is part of a soil resistance, and another column (the third column) that relates the scale of conservatism

Use of the ranking distance as an index for assessing the accuracy and precision of equations for the bearing capacity of piles and at-rest earth pressure coefficient

In many geotechnical design situations, a number of different calculation models have been developed to predict the value of a particular quantity required for use in design calculations, for example, the bearing capacities of driven and root piles, and K0, the at-rest earth pressure coefficient. In this paper the authors show how the dependability of different calculation methods can be compared and assessed using a synthetic probabilistic approach and the ranking distance (RD) index. Measured values, Qmeas, are compared with calculated values, Qcalc, using the "bias factor," defined as the ratio Qmeas/Qcalc. The bias factor values obtained using a particular calculation method are processed to evaluate the "accuracy" and "precision" by calculating a central tendency and a variability statistical parameter, respectively, from the values. The RD index is a comprehensive statistical parameter for assessing the dependability of a particular calculation method and is based on the central tendency and variability. Using the ratios between calculated and measured bearing capacity and earth pressures values, the RD index is used to assess the accuracy and precision of the most frequently used pile driving formulae, two equations for the bearing capacity of root piles, and seven equations for the at-rest earth pressure coefficient.Key words: accuracy, precision, probabilistic approach, ranking distance.

Anisotropic elastoplastic undrained analysis of soft clays

A new model is presented for soft clays under undrained loading. The model takes into account the dependence of both strength and deformability on stress history during consolidation of the clay. This stress history causes non-homogeneity with depth and anisotropic behaviour. The model includes a new failure condition in terms of total stresses. Parameters defining the proposed rmodel are of two kinds: intrinsic shear strength (based on Hvorslev's parameters), and stress history, namely, consolidation and overconsolidation pressures and at-rest earth pressure coefficient. The validity of the model is checked against different test results previously reported, covering different stress conditions (simple shear and unconfined compression tests with variable orientation). Finally, a finite element model has been developed, based cn a hybrid method in displacements and stresses, which incorporates the proposed stress-strain-strength model for the clay. The case of a footing on a clay stratum over a rigid base is studied and the influence of the parameters of the model is analysed. L'article présente un nouveau modéle se rapportant aux argiles molles en charge non drainée. Ce modéle tient compte du fait que la résistance et la déform-abilité sont dépendantes de l'evolution des contraintes au tours de la consolidation de l'argiles. Ces contraintes entraînent une non-homogénéité qui est fonction de la profondeur et un comportement anisotrope. Le modèle comporte une nouvelle condition de rupture en termes de contraintes totales. Deux sortes de paramètres définissent le modèle proposé: la résistance au cisaillement intrinséque (basée sur les paramètres de Hvorslev), et l'evolution des contraintes, à savoir les pressions de consolidation et de surconsolidation et le coefficient de la pression des terres au repos. La validité du modèle est vérifiée compte tenu des différents résultats d'essais ayant fait l'objet d'un rapport antérieur et qui couvrent différentes conditions de contrainte (essais de cisaillement et de compression simples-avec orientation variable). Enfin, un modble à éléments finis, basé sur une méthode hybride, a été mis au point; il tient compte des déplacements et des contraintes et comprend le modele contrainte-déformation-résistance relatif á l'argile. L'article examine le cas d'une semelle sur une couche d'argile au dessus d'un substratum rigide et analyse les paramétres du modéle.