Variability Of Undrained Shear Strength Research Articles

Probabilistic assessment of bearing capacity of skirted foundation under combined loadings with a rigid base

Skirted foundations are critical components in offshore applications where combined loads are common in deep‐water environments. Their ultimate capacity under VH (vertical‐horizontal) combined loading is traditionally determined using VH failure envelopes, which are primarily constructed using numerical methods. These methodologies, however, frequently ignore the spatial variability inherent in seabed soils due to geological formations. This paper investigates the effect of spatial variability of undrained shear strength and embedment ratio impact on the capacity of skirted foundations subjected to VH combined loading. For this, OptumG2 software is used to perform Monte Carlo simulation combined with random finite element limit analysis. This paper investigates the stochastic analysis of bearing capacity and failure envelopes, with a particular emphasis on understanding the effect of spatial correlation on undrained shear strength. The study focuses on the horizontal scale of fluctuation and the soil strength heterogeneity index, shedding insight on previously undiscovered areas. Novel findings highlight how a rigid base affects VH failure envelopes and offer insights into evaluating the vertical bearing capacity of skirted foundations. [Correction added on 8 July 2024, after first online publication: The above statement has been updated in this version.]

Variability of N-SPT-Correlated Undrained Shear Strength of Alluvial Deposit in Doplang Region, Central Java, Indonesia

The need to better quantify the variability of soil shear strength and its relations with the factor of safety is increasing in Indonesia. However, this aspect has not yet been studied thoroughly. This paper presents an attempt to quantify the variability of undrained shear strength in relation with the factor of safety of an alluvial deposit in the Doplang region, Central Java, Indonesia. A relationship between the undrained shear strength, su, and N-SPT for the deposit was found as su = 3.4 N-SPT. The variability of the undrained shear strength was quantified utilizing the coefficient of variance, s/m (the sample standard deviation, s over the mean, m) of the N-SPT correlated undrained shear strength. The variability of the undrained shear strength was investigated for the soil near ground surface. The deposit had a value of s/m ranging from 0.15 to 0.25 near ground surface. The variation of s/m tended to follow normal and lognormal distributions. Relationships among the coefficient of variance, the probability of failure, and the factor of safety in terms of soil strength for normal and lognormal distributions were developed. For the value of s/m near ground surface, the relationship between the probability of failure and factor of safety was obtained.

Parametric analysis for the large deformation characteristics of unstable slopes with linearly increasing soil strength by the random material point method

Soils often exhibit spatial variability with nonstationarity, which has not yet been studied in the context of postfailure analysis of slopes. In this study, the random material point method is adopted to investigate the influence of nonstationarity on the large deformation characteristics of a slope with spatially variable undrained shear strength (Su). The nonstationarity has significant influences on the mean and standard deviation of the large deformation characteristics, where ignoring the nonstationarity can lead to higher mean and standard deviation values. In addition, when the nonstationarity is insignificant with a small increase in the rate of the soil strength, the model boundary can significantly affect the standard deviation of influence and run-out distances, but the influence is slight on those of the volume of the sliding mass. In addition, the mean and standard deviation of the large deformation characteristics increase with a higher coefficient of variation of Su. This study reveals that the nonstationarity of soil spatial variability can influence the failure mechanism in the failure initiation stage and thus the volume of the sliding mass, which controls the kinetic energy of the sliding mass in the postfailure stage and affects the influence and run-out distances.

Probabilistic Assessment on 3D Stability and Failure Mechanism of Undrained Slopes Based on the Kinematic Approach of Limit Analysis

Most slope collapses have three-dimensional (3D) characteristics due to the uniform soil. The traditional plane-strain analyses neglect the 3D effects and could yield an overestimation or underestimation of the slope stability. The present study analyzes the stability of 3D slopes characterized by spatially variable undrained shear strength. A 3D slope reliability analysis approach that can fully consider the spatial variability of soil properties is proposed based on the plastic limit analysis upper-bound theorem. Within the framework of Monte Carlo simulation, the effects of strength gradient, the coefficient of variation, and the scale of fluctuation of soil undrained shear strength on the slope reliability index are examined. The length of the 3D failure surface is highlighted as an essential characteristic in 3D slope analysis. The slope failure mechanisms are classified, and the occurrence probability of each type is quantified. The obtained results indicate that the degree of nonstationarity and the coefficient of variation of undrained shear strength have significant impacts on the slope failure width, and the variation of failure mechanism highly depends on the combined effect of slope inclination and soil strength. The findings could guide slope reinforcement and facilitate a more efficient and accurate risk evaluation of slopes.

Numerical limit analyses on the uplift capacity of strip plate anchor in anisotropic spatially random cohesive soil

Plate anchors are used to resist uplift forces of both offshore and on-land structures. Numerous studies have been carried out to date to evaluate the ultimate uplift capacity of anchor plates. Most of them assumed the soil as homogeneous and isotropic. Naturally, the soil is heterogeneous and anisotropic. The undrained shear strength of soil may vary significantly within a seemingly homogeneous layer. This paper analyzes the impact of spatial shear strength variability of cohesive soil on the uplift capacity of strip anchors through numerical limit analyses. Repeated Monte Carlo simulations within a selected range of both isotropic and anisotropic spatial correlation length and coefficient of variation of undrained shear strength are conducted using the random field theory to evaluate the effect of probabilistic uplift capacity of shallow and deep strip anchors. The outcomes are then compared to those of a similar study in which the probabilistic uplift capacity was investigated using a displacement-based analysis employing the local averaging subdivision of the random finite element method (LAS-RFEM). The comparison depicts the requirement of a higher safety factor than the published results of RFEM. The findings suggest considering the spatial variation of soil strength for the safe design of plate anchors.

Characterization of Stationary and Nonstationary Random Fields with Different Copulas on Undrained Shear Strength of Soils: Probabilistic Analysis of Embankment Stability on Soft Ground

Soil properties are known to have high spatial variability and often fluctuate with depth. The objective of this study was to investigate the effects of using different models to simulate the spatial variability of undrained shear strength (su) to calculate the failure probability of an embankment on soft ground. Two-dimensional random fields of su were generated based on one Gaussian and two non-Gaussian copulas, with stationary and nonstationary assumptions. Statistical parameters of su variation—mean, coefficient of variance, and scale fluctuation (correlation length)—were estimated from simulated and field data. Monte Carlo probabilistic analyses were performed on embankment stability based on both stationary and nonstationary random fields and all copula approaches; results showed more frequent embankment failures at low water levels in the embankment ditch. In particular, the nonstationary random field (su increases with depth) simulations more closely reflected real observed data, with higher probabilities of slope failure and lower mean factor of safety than the stationary random field simulations. Additionally, the non-Gaussian copulas provided simulated data that more accurately reflected observed field data, highlighting the importance of copula selection when characterizing soil parameter random fields.

Probabilistic bearing capacity of spudcan foundations under combined loading in spatially variable soils

Spudcan foundations are widely used in the offshore gas and oil industry to support mobile jack-up drilling rigs. During the service period, the spudcan foundations need to resist large vertical-horizontal-moment (VHM) loads that are transmitted from the superstructure. The bearing capacity of foundations in complicated stress conditions is usually based on VHM failure envelopes. These are commonly constructed by using numerical methods where the soil properties are assumed to be deterministic, ignoring the inherent spatial variability. This paper investigates the influence of spatially variable undrained shear strength and embedment depth on the capacity of spudcan foundations under VHM combined loads. The linearly increasing undrained shear strength with depth obeying log-normal distribution was taken into account. Probabilistic failure envelops were constructed to analyse the effect of spatial variability on the bearing capacity of spudcan foundations at various embedment depths when subjected to different combinations of VHM loads. The influence of horizontal scale of fluctuation for a specific embedment depth was also investigated. The results indicated that under combined loading the embedment depth significantly influenced the shape and size of failure envelopes. The probability of failure at each embedment depth based on the obtained probabilistic failure envelopes was intuitionally represented by means of a factor of safety, which can provide specific guidance for foundation reliable designs.

Random failure mechanism method for assessment of working platform bearing capacity with a linear trend in undrained shear strength

A bearing capacity evaluation for the surface strip foundation on a working platform modelled on a two-layered substrate is considered in the study. The upper layer is assumed as man-made and well-controlled and thus non-variable. The lower layer modelling natural cohesive soil is subjected to spatial variability of undrained shear strength. The random failure mechanism method (RFMM) is used to evaluate the bearing capacity. This approach employs a kinematic assessment of the critical load and incorporates the averaging of three-dimensional (3D) random field along dissipation surfaces that result from the failure mechanism geometry. A novel version of the approach considering an additional linear trend of undrained shear strength in the spatially variable layer is proposed. The high efficiency of the RFMM algorithm is preserved. The influences of foundation length, trend slope in the spatially variable layer, fluctuation scales, and thickness of the homogenous sand layer on the resulting bearing capacity evaluations are analysed. Moreover, for selected cases, verification of the RFMM based assessment obtained using random finite difference method (RFDM) based on 3D analysis is provided. Two types of analyses are performed using RFDM based on associated and non-associated flow rules. For associated flow rule which corresponds to RFMM, the RFMM is conservative and efficient and thus it seems preferable. However, if RFDM employs non-associated flow rule (much lower dilation angle for sand layer), the efficient RFMM is no longer conservative. For this situation, a combined approach that improves the efficiency of the numerical method is suggested.

Post-Cyclic Mechanical Behaviors of Undisturbed Soft Clay with Different Degrees of Reconsolidation

Soft soil is often subjected to cyclic loading such as that imposed during storms, under traffic, or in an earthquake. Furthermore, the cyclic-loading-induced excess pore water pressure can be partially dissipated after cyclic loading. Thus, different reconsolidation processes should be considered. A series of static and dynamic triaxial tests were conducted on undisturbed soft soil to determine the post-cyclic mechanical behavior thereof, such as the variation of undrained shear strength, the development of excess pore water pressure, and the evolution of effective stress path. The effects of consolidated confining pressure, cyclic stress ratio, and degree of reconsolidation were analyzed. Results show that the trend of all stress–strain curves is similar under different conditions. The effect of the degree of reconsolidation is such that, with increasing the degree of reconsolidation, the shear strength is enhanced. Meanwhile, compared with undrained shear strength without cyclic loading, the shear strength after cyclic loading with full reconsolidation is increased. These factors also have a significant effect on the undrained shear strength: the greater both the confining pressure and cyclic stress ratio are, the higher the undrained shear strength. A positive excess pore water pressure is always observed during post-cyclic shearing process, irrespective of different factors. The S-shaped effective stress paths under different test conditions are observed and cross the critical state line. The microstructures of undisturbed soil and post-cyclic specimens with different degrees of reconsolidation were quantitatively investigated. Besides that, the degree of influence of different factors on the post-cyclic undrained strength was analyzed. Based on the test results, the undrained shear strength with cyclic load-history was well predicted by existing models.

System failure probability analysis of cohesive slope considering the spatial variability of undrained shear strength

System failure probability analysis of cohesive slope considering the spatial variability of undrained shear strength

Random field model of soil parameters and the application in reliability analysis of laterally loaded pile

The bearing capacity of pile under horizontal load is not only related to pile size and pile material, but also closely related to soil parameters. In this paper, based on the probability analysis method of random field theory, a non-stationary random field model is firstly proposed for the undrained shear strength Su of soil. In this model, the uncertainty of the increase trend of Su along the direction of depth is taken into account, and the mean value and standard deviation of random field increase linearly along the depth. Then, by comparing with other random field models, the applicability of the non-stationary random field model for undrained shear strength proposed in this paper is verified. Finally, the random field model is applied to the reliability evaluation of horizontally loaded pile, and the influence of the spatial variability of undrained shear strength on the failure probability of horizontally loaded pile is discussed. The results show that the coefficient of variation and correlation length of undrained shear strength have obvious influence on the failure probability of pile foundation. The uncertainty of increase rate b of undrained shear strength with depth also has influence on the failure probability of pile foundation. If the spatial variability of the soil parameters is not considered in the evaluation and design of pile foundation, the failure probability of pile foundation will be large, which will make the design results of pile biased toward conservative.

Influence of the Spatial Variability of Soil Shear Strength on Deep Excavation: A Case Study of a Bangkok Underground MRT Station

This paper investigates the effects that the spatial variability of a soil's undrained shear strength has on lateral wall movements and ground surface settlements when performing a deep excavation stability analysis. A random finite-element method is employed to statistically assess a deep excavation. A case study based on an actual deep excavation project in Bangkok's subsoils was used to validate the methodology. The two-dimensional spatial variability of the undrained shear strength in the clay layers of Bangkok's subsoil is simulated using the random field theory and Monte Carlo simulation. The Mohr–Coulomb model is used to predict lateral wall movements and ground surface settlements, while the stability analysis of the deep excavation is evaluated by the factor of safety using the strength reduction approach. The results show that spatial variability highly affects the distribution of lateral wall movements and ground surface settlements, as well as the scatter of the factor of safety corresponding to progressing stages of excavation.

Importance of Distribution Type on Bearing Capacity of an Embedded Foundation in Spatially Varying Soils

The objective of this paper is to investigate the effect of soil variability on bearing capacity of an embedded foundation in the presence of nonstationary undrained shear strength. The nonstationary undrained shear strength is simulated by a nonstationary random field generator based on the spectral representation method. An embedded foundation buried into the soil to two times of width is presented to investigate the influence of spatially variable undrained shear strength on bearing capacity. Firstly, Monte Carlo simulations are carried out to discuss the effect of distribution type, nonstationary gradient parameter, and horizontal autocorrelation length on the bearing capacity from the standpoint of mean value and standard deviation. Then, the influence of the distribution type on the failure probability of nonstationary random soil is also investigated, with the failure probability for the Beta distribution being demonstrated to be always larger than that for the Lognormal and Gamma distribution.

Probabilistic analysis of tunnel face stability considering spatially variable undrained shear strength with linearly increasing mean trend

The inherent spatial variability of soil properties has been considered as one of the main sources of uncertainties in geotechnical problems. The need for probabilistic analysis of the tunnel face stability that takes into account the variability of soil properties has been acknowledged. This article employed a probabilistic-based method, called random finite difference method, for evaluating the stability of tunnel face under the influence of the variability of undrained shear strength in clays. The two-dimensional spatial variation in soil undrained shear strength is modeled by random fields, which are discretized by the Covariance Matrix Decomposition method. The procedure for random finite difference method is presented. An illustrative example is employed to investigate the effect of soil variability. Particular attention has been paid to the situation that undrained shear strength increases with depth. The results demonstrate that ignoring the variability of undrained shear strength will result in overestimates of the tunnel face stability if the support pressure of the tunnel face exceeds the deterministic value, especially for higher coefficient of variation of soil undrained shear strength. Minor differences in the failure mechanism are observed in comparison to the deterministic case, considering only the global failure of the tunnel face is observed. In addition, ignoring the increase of undrained shear strength with depth will lead to conservative designs. The random finite difference method can provide a practical tool for evaluating the stability of a tunnel face in variable soils.

On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil

Abstract This paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.

Bearing capacity and reliability analysis of spudcan foundations embedded at various depths based on the non-stationary random finite element method

Spudcan foundations for mobile jack-up units are large diameter conical foundations that can penetrate into the seabed to a maximum depth of three times the diameter of the spudcan. As a deeply penetrated foundation, the bearing capacity of a spudcan is highly dependent on the failure mechanism and the strength distribution of the seabed soil, which exhibits strong spatial variability. While many recent studies have explored the failure mechanism and bearing capacity of spudcan foundations, these studies have commonly deterministically described the soil in which the spudcan is embedded. Therefore, this paper aimed to investigate the probabilistic bearing capacity of spudcan foundations embedded in the seabed at various depths, under the condition of spatially variable undrained shear strength that increased linearly with depth. The random finite element method was used to study this problem, where nonlinear finite element analysis was combined with random field theory within a Monte Carlo framework. The variability in undrained shear strength was modelled as a random field and characterised by a log-normal distribution with anisotropic autocorrelation distances. The influence of autocorrelation distance on the mean bearing capacity and the failure mechanism was discussed for each embedment depth. A correlation between the probability of failure and the factor of safety was established based on the obtained results. These findings can provide guidance for reliability-based design of spudcan foundations embedded in spatially variable soil.

Probabilistic bearing capacity analysis of spudcan foundation in soil with linearly increasing mean undrained shear strength

Spudcan foundations have been widely used in offshore oil and gas engineering for jack-up rigs. During penetration into seabed soil, spudcan foundations may encounter large uncertainties in soil properties, which have a strong impact on its bearing capacity. A large number of studies have been conducted to demonstrate the failure mechanisms and the bearing capacity of spudcan foundations in soils with deterministic properties, but the influence of spatially variable soil properties on spudcan foundations remains unclear and should be accounted for. In this study, we aimed to investigate the failure mechanisms and the bearing capacity of a spudcan foundation embedded in soils where the mean undrained shear strength increased linearly with depth. The spectral representation method (SRM) was used to generate a non-stationary non-Gaussian random field. The random finite element method (RFEM) in conjunction with Monte Carlo simulations was carried out to evaluate the statistical characteristics of the bearing capacity for spudcan foundations, followed by a series of comparisons and discussion. The results indicated that the mean bearing capacity for the spatial variability of undrained shear strength was smaller than that obtained from the corresponding deterministic case. The probability of failure decreased slightly with an increase in the degree of non-stationarity under the constant coefficient of variation (COV) condition. Upon comparing the results obtained from different random field models, we found that the probability of failure under the non-constant condition was smaller than that under the stationary and constant COV conditions.

Effect of spatial variability of block-type cement-treated ground on the bearing capacity of foundation under inclined load

Deep mixing methods are widely used for stabilizing soft clayey soils and improving their bearing capacity. However, spatial variability in the shear strength of the cement-treated ground introduces uncertainties in estimating the bearing capacity for design. This paper evaluates the reliability of, block-type, cement-treated foundation under inclined load conditions using random field numerical limit analyses. The undrained shear strength is modelled as a random field which is characterized by a log-normal distribution and a spatial correlation length. Monte Carlo simulations are then used to interpret the stochastic bearing capacity factor and failure mechanisms for inclined concentric loading conditions at selected ratios of the shear strength ratio of cement-treated ground to original clay, the coefficient of variation in undrained shear strength and correlation length of the cement-treated zone. Variability of the undrained shear strength can reduce the expected bearing capacity of the cement-treated ground by 50–70% compared to homogeneously mixed clay.

Parameter variability of undrained shear strength and strain using a database of reconstituted soil tests

During construction, the mobilization of undrained shear strength must be limited to avoid soil failure. Soil strains must be controlled to avoid compromising structural serviceability. To assess foundation performance by strength mobilization, an understanding of soil strains at various levels of strength mobilization is required. In practice, ground investigation data are often limited, and assessment of the expected variation of stress–strain and undrained shear strength is improved with empirical correlations calibrated with a database. The new database RFG/TXCU-278 contains data of 278 consolidated–undrained triaxial tests on reconstituted fine-grained soil samples compiled from the literature. Analysis of the database to evaluate the variability of undrained strength ratio (cu/[Formula: see text]) and a reference shear strain with shear mode is undertaken in this paper. The new database provides evidence that shear strain (like undrained shear strength) is sensitive to the consolidation (isotropic or K0) and shear mode (triaxial compression or extension) applied in the test. For the materials included in the database, the strength mobilization parameters obtained from a triaxial compression test can be used to predict the corresponding triaxial extension parameters to a reasonable accuracy.

Skirted semi-deep foundations behaviour on deposits with variable undrained shear strength

ABSTRACT Skirted semi-deep foundation becomes an increasingly prevalent option for offshore and onshore structures. Behavior of these foundations on clay with constant and variable undrained shear strength is required to be investigated. In this study, finite element analyses are conducted to evaluate vertical bearing capacity. The effect of different factors, including embedment depth ratio, soil-skirt interface property, and shear strength profile have been studied and outcomes compared to previous researches. The results showed that load carrying behavior enhances with increasing the skirt depth and roughness and decreasing the degree of soil heterogeneity. Foundation capacity for typical skirt roughness condition in practical design can be calculated assuming rough soil-skirt interface due to the negligible disparity of bearing capacity factors for skirt friction coefficients of 0.5 to 1. Furthermore, a new solution based on vertical bearing capacity ratio of semi-deep to surface foundation (VBCR) is proposed which indicates the efficiency of utilizing skirt.