Bayesian approach for calibrating transformation model from spatially varied CPT data to regular geotechnical parameter

Cone Penetration Test (CPT) is widely utilized to gain regular geotechnical parameters such as compression modulus, cohesion coefficient and internal friction angle by transformation model in the site investigation. However, it is challenging to obtain simultaneously the unknown coefficients and error of a transformation model, given the intrinsic uncertainty (i.e., spatial variability) of geomaterial and the epistemic uncertainty of geotechnical investigation. A Bayesian approach is therefore proposed calibrating the transformation model based on spatial random field theory. The approach consists of three key elements: (1) three-dimensional anisotropic spatial random field theory; (2) classifications of measurement and error, and the uncertainty propagation diagram of geotechnical investigation; and (3) the unknown coefficients and error calibration of the transformation model given Bayesian inverse modeling method. The massive penetration resistance data from CPT, which is denoted as a spatial random field variable to account for the spatial variability of soil, are classified as type A data. Meanwhile, a few laboratory test data such as the compression modulus are defined as type B data. Based on the above two types of data, the unknown coefficients and error of the transformation model are inversely calibrated with consideration of intrinsic uncertainty of geomaterial, epistemic uncertainties such as measurement errors, prior knowledge uncertainty of transformation model itself, and computing uncertainties of statistical parameters as well as Bayesian method. Baseline studying indicates the proposed approach is applicable to calibrate the transformation model between CPT data and regular geotechnical parameter within spatial random field theory. Next, the calibrated transformation model was compared with classical linear regression in cross-validation, and then it was implemented at three-dimensional site characterization of the background project.     

Response of Vertically Loaded Pile in Clay: A Probabilistic Study

This study presents the response of a vertically loaded pile in undrained clay considering spatially distributed undrained shear strength. The probabilistic study is performed considering undrained shear strength as random variable and the analysis is conducted using random field theory. The inherent soil variability is considered as source of variability and the field is modeled as two dimensional non-Gaussian homogeneous random field. Random field is simulated using Cholesky decomposition technique within the finite difference program and Monte Carlo simulation approach is considered for the probabilistic analysis. The influence of variance and spatial correlation of undrained shear strength on the ultimate capacity as summation of ultimate skin friction and end bearing resistance of pile are examined. It is observed that the coefficient of variation and spatial correlation distance are the most important parameters that affect the pile ultimate capacity.     

基于多源试验数据空间变异土体参数概率反演及边坡可靠度更新

岩土工程现场勘察试验通常只能获得有限的试验数据,据此难以真实地量化土体参数的空间变异性。提出了考虑土体参数空间变异性的概率反演和边坡可靠度更新方法,基于室内和现场两种不同来源的试验数据概率反演空间变异参数统计特征和更新边坡可靠度水平,并给出了计算流程。此外为合理地描述土体参数先验信息,发展了不排水抗剪强度非平稳随机场模型。最后通过不排水饱和黏土边坡算例验证了提出方法的有效性,并探讨了试验数据和钻孔位置对边坡后验失效概率的影响。结果表明：提出方法实现了空间变异土体参数概率反演与边坡可靠度更新的一体化,基于有限的多源试验数据概率反演得到的土体参数均值与试验数据非常吻合,明显降低了对参数不确定性的估计,更新的边坡可靠度水平显著增加。受土体参数空间自相关性的影响,试验数据对钻孔取样点附近区域土体参数统计特征更新的影响明显大于距离取样点较远区域。     

Undrained Shear Strength in Cohesive Soils Estimated by Directional Modes of In-Situ Shear Wave Velocity

The estimated undrained shear strength (s_u) is often not a unique value because it can be evaluated by various test types and/or procedures, such as different failure modes, shear strain rates, and boundary conditions. This study explores (1) the relationship between reference undrained shear strength and in situ shear wave velocity in terms of the effective overburden stress, and (2) the independent relationships to evaluate the undrained shear strength with special consideration of different directional and polarization modes (VH, HV, HH shear waves), which has not been reported. This evaluation is done via a worldwide database compiled from 43 well-documented geotechnical test sites associated with soft ground. Finally, new correlation models are proposed to estimate the undrained shear strength based on the in situ shear wave velocity as well as the plasticity index or the overconsolidation ratio. The application of the shear wave velocity–undrained shear strength relation is illustrated through two independent case studies. The proposed relationships are expected to contribute to reasonable estimates of undrained shear strength as well as offer practical guidance on even extrapolation beyond the data that is available to geotechnical engineers.     

NGI‐ADP: Anisotropic shear strength model for clay

Many geotechnical problems involve undrained behavior of clay and the capacity in undrained loading. Most constitutive models used today are effective stress based and only indirectly obtain values for the undrained shear strength. To match the design profiles of undrained shear strengths, in active (A), direct simple shear (D) and passive (P) modes of loading are complicated. This paper presents the elastoplastic constitutive model NGI‐ADP which is based on the undrained shear strength approach with direct input of shear strengths. Consequently, exact match with design undrained shear strengths profiles is obtained and the well‐known anisotropy of undrained shear strength and stiffness is accounted for in the constitutive model. A non‐linear stress path‐dependent hardening relationship is used, defined from direct input of failure strains in the three directions of shearing represented by triaxial compression, direct simple shear and triaxial extension. With its clear input parameters the model has significant advantages for design analysis of undrained problems. The constitutive model is implemented, into finite element codes, with an implicit integration scheme. Its performance is demonstrated by a finite element analysis of a bearing capacity problem. Copyright © 2011 John Wiley & Sons, Ltd.     

深海浅表层沉积物不排水剪切强度的多探头原位测试系统及评价方法研究

海洋工程建设已步入深海,但与之匹配的浅表层沉积物不排水剪切强度原位测试技术尚不成熟。为此,本文开发了可用于评估深海浅表层沉积物土力学性质的多探头原位测试系统,包括锥形触探仪、球形贯入仪和十字板剪切仪,可实现对深海沉积物土力学性质的快速、准确和智能化评价。进一步,通过CEL大变形数值模拟和足尺土工模型试验确定锥形触探仪的锥尖阻力系数,基于离心模型试验给出球形贯入仪的贯入阻力系数,从而完善深海浅表层沉积物不排水剪切强度的评价方法;在此基础上,探讨3种特定仪器各自适合的强度测试区间。结果表明:对于深海浅表层沉积物不排水剪切强度的评估,锥形触探仪和球形贯入仪的阻力系数建议分别取值为9.5和11.1。     

Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations

ABSTRACT

Field data is commonly used to determine soil parameters for geotechnical analysis. Bayesian analysis allows combining field data with other information on soil parameters in a consistent manner. We show that the spatial variability of the soil properties and the associated measurements can be captured through two different modelling approaches. In the first approach, a single random variable (RV) represents the soil property within the area of interest, while the second approach models the spatial variability explicitly with a random field (RF). We apply the Bayesian concept exemplarily to the reliability assessment of a shallow foundation in a silty soil with spatially variable data. We show that the simpler RV approach is applicable in cases where the measurements do not influence the correlation structure of the soil property at the vicinity of the foundation. In other cases, it is expected to underestimate the reliability, and a RF model is required to obtain accurate results.     

Reliability-based design of spread footings on fibre-reinforced clay

The potential use of fibres in a number of geotechnical engineering applications is gaining more interest in the geotechnical community. A select application consists of the improvement of soft grounds to mitigate their problematic shear strength characteristics. Extensive experimental work has been reported on the response/behaviour of fibre-reinforced clay (FRC) and was recently complemented by several strength prediction models. The effectiveness of these models has not been thoroughly evaluated yet. The objectives of this study are to (1) quantify the model uncertainty of a newly developed FRC model that is aimed exclusively at predicting the “undrained” shear strength of FRCs, (2) combine the model uncertainty with other conventional sources of uncertainty to assess the reliability levels that are inherent in the ultimate limit state design of spread footings that rest on a top FRC layer underlain by weaker natural soft clay, and (3) recommend factors of safety that would ensure a target reliability level for these footings. Results indicate that the traditional safety factor of 3 should be used with caution as it may not be sufficient to yield the desired level of reliability, particularly for smaller footings, lower applied stresses, larger scales of fluctuation, and larger target reliability indices.     

考虑土体参数空间变异性的边坡大变形破坏模式研究

边坡失稳是涉及土体大变形的动态演化过程,该过程往往决定了滑坡失事后果。传统的边坡稳定分析方法如极限平衡方法与有限元方法难以模拟边坡失稳演化过程,尤其是失稳后的土体变形破坏过程。边坡失稳受到多重不确定性因素影响,其中一个重要因素是土体参数的空间分布不均匀性。在考虑土体参数的空间不均匀分布情况下,本文采用一种随机极限平衡-物质点法研究边坡不同破坏模式的动态演化过程,同时利用极限平衡方法简单、高效的优点和物质点方法模拟土体大变形破坏的能力。以一个两层不排水土坡算例为例,识别了4种不同的边坡破坏模式（即浅层、中层、深层和渐进）,研究了它们的演化过程与土体参数的空间分布之间的关系。结果表明边坡的破坏模式演化过程与土体参数的空间分布密切相关,强调了岩土工程勘察信息对充分表征土体参数空间变异性的重要作用。     

SBPT测定饱和黏土不排水强度的数值分析

自钻式旁压试验（SBPT）因其扰动小、测试深度大、可以获得应力-应变、超孔隙水压力-时间等数据,在确定地基土性参数和地基承载力上有广阔的应用前景。然而由于用以解释SBPT的柱孔扩张理论（Gibson解）所采用的平面应变假设与实际旁压腔几何特征存在差异,导致试验所确定的黏土不排水剪切强度su与其他原位试验或室内试验结果存在差别。针对旁压腔几何尺寸及应变区间的选择对确定su的影响,基于修正剑桥模型,采用低渗透系数控制加载过程中不排水条件,利用有限元法模拟SBPT,建议了不同应力历史下确定su的应变区间,并给出考虑几何尺寸影响时相应应变区间上su的修正系数。     

Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods

A long slope consisting of spatially random soils is a common geographical feature. This paper examined the necessity of three-dimensional(3 D) analysis when dealing with slope with full randomness in soil properties. Although 3 D random finite element analysis can well reflect the spatial variability of soil properties, it is often time-consuming for probabilistic stability analysis. For this reason, we also examined the least advantageous(or most pessimistic) cross-section of the studied slope. The concept of"most pessimistic" refers to the minimal cross-sectional average of undrained shear strength. The selection of the most pessimistic section is achievable by simulating the undrained shear strength as a 3 D random field. Random finite element analysis results suggest that two-dimensional(2 D) plane strain analysis based the most pessimistic cross-section generally provides a more conservative result than the corresponding full 3 D analysis. The level of conservativeness is around 15% on average. This result may have engineering implications for slope design where computationally tractable 2 D analyses based on the procedure proposed in this study could ensure conservative results.     

Effect of rod friction on vane shear tests in very soft organic harbour mud

Very soft organic harbour mud is increasingly used as a filling and construction material in harbour construction and reorganization. The undrained shear strength of such soft sediments is the critical geotechnical soil parameter with regard to any specific construction design. Field and laboratory vane shear testing is a standard method to quickly determine this important parameter. So far, the effect of rod friction on vane shear tests in very soft organic soils is unclear. In this study we present results from laboratory experiments on harbour mud from a construction site in northern Germany. Relations among vane and rod geometry, penetration depth, water content, rod friction and undrained shear strength are derived. Based on these relations the influence of rod friction on vane shear test results is investigated. The results indicate that field and laboratory vane shear test measurements may be significantly influenced by rod friction. Methods are proposed to correct for the rod influence, which is shown to increase with rising water contents.     

Effects of anisotropy in correlation structure on the stability of an undrained clay slope

Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.     

Estimation of undrained shear strength in moderately OC clays based on field vane test data

The undrained shear strength (s _u) of cohesive soils is a crucial parameter for many geotechnical engineering applications. Due to the complexities and uncertainties associated with laboratory and in situ tests, it is a challenging task to obtain the undrained shear strength in a reliable and economical manner. In this study, a probabilistic model for the s _u of moderately overconsolidated clays is developed using the Bayesian model class selection approach. The model is based on a comprehensive geotechnical database compiled for this study with field measurements of field vane strength (s _u), plastic limit (PL), natural water content (W _n), liquid limit (LL), vertical effective overburden stress (\(\sigma_{\nu }^{\prime }\)), preconsolidation pressure (\(\sigma_{\text{p}}^{\prime }\)) and overconsolidated ratio (OCR). Comparison study shows that the proposed model is superior to some well-known empirical relationships for OC clays. The proposed probabilistic model not only provides reliable and economical estimation of s _u but also facilitates reliability-based analysis and design for performance-based engineering applications.     

扁铲侧胀试验在软土地基评价中的应用研究

在回顾分析国内外利用扁铲侧胀试验评价地基土性参数基础上,介绍了应用扁铲侧胀试验（DMT）和其它试验手段进行高速公路软土地基综合分析评价所取得的一些成果。根据扁铲侧胀试验结果估算的不排水抗剪强度与十字板试验结果基本一致,并能够反映土的强度随深度增长的规律,也分析了造成扁铲侧胀试验结果与室内试验结果之间差异的因素,研究结果可为扁铲侧胀试验在我国岩土工程领域的应用提供参考。     

Reliability-based design of spread footings on clays reinforced with aggregate piers

ABSTRACT

The economical and safe design of footings supported on aggregate-pier-reinforced clay could benefit from the implementation of a reliability-based approach that incorporates the different sources of uncertainty. Monte Carlo simulations are conducted to quantify the probability distribution of the ultimate bearing capacity for practical design scenarios. A reliability analysis is then conducted to propose design charts that yield the required factor of safety as a function of the major input parameters. The novelty in the proposed methodology is the incorporation of a lower bound shear strength that is based on the remoulded undrained shear strength in the reliability analysis.     

Modeling uncertainty in stability analysis for design of embankment dams on difficult foundations

A probabilistic 3-D slope stability analysis model (PTDSSAM) is developed to evaluate the stability of embankment dams and their foundations under conditions of staged construction taking into consideration uncertainty, spatial variabilities and correlations of shear strength parameters, as well as the uncertainties in pore water pressure. The model has the following capabilities: (1) conducting undrained shear strength analysis (USA) and effective stress analysis (ESA) slope stability analysis of staged construction, (2) incorporation of field monitored data of pore water pressure, and (3) incorporation of increase of undrained shear strength with depth, effective stress, and pore water pressure dissipation. The PTDSSAM model is incorporated in a computer program that can analyze slopes located in multilayered deposits, considering the total slope width.

The main outputs of the program are the geometric parameters of the most critical sliding surface (i.e., center of rotation/radius of rotation and critical width of failure), mean 2-D safety factor, mean 3-D safety factor, squared coefficient of variation of resisting moment, and the probability of slope failure. The program is applied to a case study, Karameh dam in Jordan. Monitored data of induced pore water pressure in the dam embankment and soft foundation were gathered during dam construction.

The stability of Karameh dam embankment and foundation was evaluated during staged construction using deterministic and probabilistic analysis. Foundation stability was evaluated based on the monitored data of pore water pressure.

The study showed that the mean values of the corrective factors which account for the discrepancies between the in situ and laboratory-measured values of soil properties and for the modeling errors have significant influence on the 2-D safety factor, 3-D safety factor, slope probability of failure, and on the expected failure width.

The degree of spatial correlation associated with shear strength parameters within a soil deposit also influences the probability of slope failure and the expected failure width. This correlation is quantified by scale of fluctuation. It is found that a larger scale of fluctuation gives an increase in the probability of slope failure and a reduction in the critical failure width.     

Probabilistic analysis of simple slopes with cohesive soil strength using RLEM and RFEM

The 2D random finite element method and the one-dimensional and 2D random limit equilibrium method are used to investigate the influence of spatial variability of soil strength parameters on the probability of failure of simple soil slopes with cohesive undrained shear strength. The combined influence of spatial variability of soil properties and cross-correlation between undrained soil strength and unit weight on the computed probability of failure is explored. The paper identifies conditions where numerical outcomes are similar and where they are not. The limitations of each analysis method are described and implications to analysis and design are identified.

Abbreviations: FEM: finite element method; LEM: limit equilibrium method; RFEM: random finite element method; RLEM: random limit equilibrium method     

Probability distribution for mobilised shear strengths of spatially variable soils under uniform stress states

This paper studies the probability distribution for the mobilised shear strength of a spatially variable soil mass that is subjected to a uniform stress state. Based on the mechanisms identified in two previous studies conducted by the authors, this study further proposes a probability distribution model for the mobilised shear strength that is based on the extreme value of normal random variables. It is concluded that the probability distribution of the mobilised shear strength of a spatially variable soil mass is affected by the line averaging effect along the potential slip plane and the number of independent potential slip planes. These two factors depend on the stress state and the orientation of the potential slip planes. With this model, the mobilised shear strength of a spatially variable soil mass can be simulated without the need of conducting random-field finite-element analyses. In addition, the strength characteristic value that is the 5% quantile in the Eurocodes can be easily derived from this model.     

Undrained Strength of Deposited Mine Tailings Beds: Effect of Water Content, Effective Stress and Time of Consolidation

An understanding of the geotechnical behaviour of mine tailings is imperative when evaluating the stability and erosional resistance of sedimented tailings beds; as well as for the design and long-term management of tailings disposal facilities. Laboratory testing was conducted on mine tailings beds of various ages and thicknesses, deposited from concentrated slurries. Measured index properties allowed classifying the tailings as a coarse grained and non-cohesive material. The results obtained from the performed sedimentation experiments showed that the primary consolidation of the tailings beds was complete in approximately 1 h and negligible volume changes occurred in the beds during secondary compression. The undrained shear strength of the tailings beds was measured using an automated fall cone device at a depth interval of 1 cm and a profile of the shear strength variation with depth was obtained. At each tested surface, moisture content specimens were taken to determine the moisture content profile of the tested tailings beds. The undrained shear strength of the beds varied between 0.008 and 0.975 kPa for effective stresses below 1.19 kPa and increased with depth. Correspondingly, the moisture content decreased with depth and varied between 17 and 27%. The factor controlling the undrained shear strength of the tested beds was the vertical effective stress, with the water content also having some secondary effect. The correlation between the undrained shear strength and the vertical effective stress was expressed with a second order polynomial function. Consolidation time did not appear to influence the observed shear strength.