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1.
Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion
A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross‐correlated non‐Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non‐intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
2.
G. Y. Sheu 《Geotechnical and Geological Engineering》2013,31(5):1453-1464
Originating an attempt of understanding the reliability and serviceability of foundations, an interest of comparing the difference between settlements predicted with and without considering the uncertainty in such as the spatial variability of soil properties is born. This study selectively compares between settlements predicted with and without considering the uncertainty in the spatial variability of Young’s modulus. The tool is a coupling of perturbation expansions of Young moduli and a two-dimensional meshfree weak-strong form in elastostatics. Two further examples show that the spatial variability of Young’s modulus causes apparent difference between probabilistic and deterministic settlement components along the direction of a surcharge. We can derive an autocorrelation function to describe the spatial variability of Young’s modulus and understand how it affects predicted settlements depending upon autocorrelation function values. In addition, the spectral stochastic meshless local Petrov–Galerkin method is a time-saving tool for predicting probabilistic settlements with the uncertainty in the spatial variability of soil properties. 相似文献
3.
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. 相似文献
4.
为了解漓江流域土壤水分空间变化特征及其影响因素,基于2'经纬网格,采用地统计学方法对该流域表层（0~10 cm）土壤水分物理性质的空间变异进行分析。结果表明:从空间结构比上,漓江流域表层土壤含水量、容重、最大和最小持水量均具有高度的空间自相关性（各指标空间结构比均大于0.87）,且其空间分布趋势基本一致,由流域上游向中下游逐渐变化。土地利用对流域表层土壤水分物理性质及其空间变异具有显著影响。受时间尺度和土地利用类型等因素的影响,漓江流域表层土壤含水量相比其他土壤水分物理性质,其空间异质性由随机引起的空间变异增加,空间自相关减小,为0.87;而土壤容重最大,为0.92。相关结果对于漓江流域土壤水分动态模拟与预测研究具有一定参考价值。 相似文献
5.
《Geomechanics and Geoengineering》2013,8(2):91-97
Directional variability of spatial correlation is observed in natural soils due to their depositional characteristics and it influences the response of structures founded on these deposits. Nonetheless, the results presented in most of the available literature are based on the assumption of either isotropic spatial correlation or perfect spatial correlation of soil properties in horizontal and vertical directions. It is also observed from past studies that the effect of transformation model on the total uncertainty is quite significant. Hence, an effort has been made in this paper to study the effect of anisotropy of autocorrelation characteristics of cone tip resistance (qc) and the transformation model on the bearing capacity of a shallow strip footing, founding on the surface of a spatially varying soil mass. The statistics in the vertical direction of the soil mass are taken from 8 Cone Penetration Test (CPT) records and statistics in the horizontal direction are assumed. For the case considered, it is observed that the transformation model significantly influences the degree of variability of design parameter. The results also show that isotropic correlation structure based on the vertical autocorrelation distance underestimates the variability of design parameter. On the other hand, perfect correlation in horizontal or vertical, or both directions, overestimates the variability of design parameters, and produces conservative estimates of allowable bearing capacity. 相似文献
6.
The failure probability of geotechnical structures with spatially varying soil properties is generally computed using Monte Carlo simulation (MCS) methodology. This approach is well known to be very time-consuming when dealing with small failure probabilities. One alternative to MCS is the subset simulation approach. This approach was mainly used in the literature in cases where the uncertain parameters are modelled by random variables. In this article, it is employed in the case where the uncertain parameters are modelled by random fields. This is illustrated through the probabilistic analysis at the serviceability limit state (SLS) of a strip footing resting on a soil with a spatially varying Young's modulus. The probabilistic numerical results have shown that the probability of exceeding a tolerable vertical displacement (P e) calculated by subset simulation is very close to that computed by MCS methodology but with a significant reduction in the number of realisations. A parametric study to investigate the effect of the soil variability (coefficient of variation and the horizontal and vertical autocorrelation lengths of the Young's modulus) on P e was presented and discussed. Finally, a reliability-based design of strip footings was presented. It allows one to obtain the probabilistic footing breadth for a given soil variability. 相似文献
7.
Ghazal Rezaie Soufi Mehran Karimpour Fard 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2020,14(1):69-89
ABSTRACTProbabilistic methods in geotechnical engineering have received a lot of attention during the last decade and different methodologies are used to capture the inherent variability of soil in different geotechnical engineering problems. In this paper, numerical simulations are conducted to obtain the bearing capacity factor, Nγ, for a purely frictional heterogenous soil where the friction angle is modelled as randomly distributed throughout the domain and the effect of its spatial variability on Nγ is investigated. A finite element method, based on the upper bound limit analysis was combined with random field theory and linear programming to develop a probabilistic analysis. Monte Carlo simulations were performed and the effect of the variability of the friction angle defined by statistical parameters on the bearing capacity factor was investigated. Results show that the mean bearing capacity factor Nγ of a footing on a spatially variable cohesionless soil is generally higher than the deterministic Nγ obtained from a constant mean value. Increasing the heterogeneity of the friction angle by an increase in the coefficient of variation generally increases this deviation. This can be explained by the nonlinearity of the relationship between Nγ and the friction angle. 相似文献
8.
The sparse polynomial chaos expansion (SPCE) methodology is an efficient approach that deals with uncertainties propagation in case of high‐dimensional problems (i.e., when a large number of random variables is involved). This methodology significantly reduces the computational cost with respect to the classical full PCE methodology. Notice however that when dealing with computationally‐expensive deterministic models, the time cost remains important even with the use of the SPCE. In this paper, an efficient combined use of the SPCE methodology and the Global Sensitivity Analysis is proposed to solve such problem. The proposed methodology is firstly validated using a relatively non‐expensive deterministic model that involves the computation of the PDF of the ultimate bearing capacity of a strip footing resting on a weightless spatially varying soil where the soil cohesion and angle of internal friction are modeled by two anisotropic non‐Gaussian cross‐correlated random fields. This methodology is then applied to an expensive model that considers the case of a ponderable soil. A brief parametric study is presented in this case to show the efficiency of the proposed methodology. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation 
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下载免费PDF全文 This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability ksat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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11.
Thanh Son Nguyen Suched Likitlersuang Hiroyasu Ohtsu Takafumi Kitaoka 《Arabian Journal of Geosciences》2017,10(16):369
Rainfall-induced landslides frequently occur in humid temperate regions worldwide. Research activity in understanding the mechanism of rainfall-induced landslides has recently focused on the probability of slope failure involving non-homogeneous soil profiles. This paper presents probabilistic analyses to assess the stability of unsaturated soil slope under rainfall. The influence of the spatial variability of shear strength parameters on the probability of rainfall-induced slope failure is conducted by means of a series of seepage and stability analyses of an infinite slope based on random fields. A case study of shallow failure located on sandstone slopes in Japan is used to verify the analysis framework. The results confirm that a probabilistic analysis can be efficiently used to qualify various locations of failure surface caused by spatial variability of soil shear strength for a shallow infinite slope failure due to rainfall. 相似文献
12.
Mohammad Wasiul Bari Mohamed A. Shahin 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2015,9(1):37-48
A stochastic approach that investigates the effects of soil spatial variability on stabilisation of soft clay via prefabricated vertical drains (PVDs) is presented and discussed. The approach integrates the local average subdivision of random field theory with the Monte Carlo finite element (FE) technique. A special feature of the current study is the investigation of impact of spatial variability of soil permeability and volume compressibility in the smear zone as compared to that of the undisturbed zone, in conjunction with uncoupled three-dimensional FE analysis. A sensitivity analysis is also performed to identify the random variable that has the major contribution to the uncertainty of the degree of consolidation achieved via PVDs. The results of this study indicate that the spatial variability of soil properties has a significant impact on soil consolidation by PVDs; however, the spatial variability of soil properties in the smear zone has a dominating impact on soil consolidation by PVDs over that of the undisturbed zone. It is also found that soil volume compressibility has insignificant contribution to the degree of consolidation estimated by uncoupled stochastic analysis. 相似文献
13.
Acta Geotechnica - The prime objective of this paper is to study the effect of soil spatial variability on the three-dimensional probabilistic bearing capacity of a circular footing resting on the... 相似文献
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土体具有显著的空间变异性,描述土体空间变异性的重要指标是自相关距离。提出基于土体微结构模拟的方法来求解土体的自相关距离。在生成土体的微结构数值模型时,对四参数随机生长法（QSGS法）进行改进,考虑土体的粒径分布信息,使得生成的土体微结构更加合理。改进的四参数随机生长法（MQSGS法）所需的输入参数可以结合土体的扫描电镜试验及粒径分析试验获取。基于生成的土体微结构数值模型,即可计算土体的2点自相关函数,再通过曲线拟合即可求解土体的自相关距离。研究表明：与QSGS法相比,采用MQSGS法生成的土体微结构更加符合自然界的真实土体;基于MQSGS法生成的微结构数值模型计算得到的土体自相关距离略小于QSGS法得出的自相关距离。 相似文献
16.
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。 相似文献
17.
约束随机场下的边坡可靠度随机有限元分析方法 总被引：2，自引：1，他引：1
目前边坡可靠度中常用的简化分析方法,不考虑边坡土体的空间变异性,每次计算整个边坡都取用相同的强度参数,由离散点试样试验得到的土体参数统计特性只能反映点特性,而边坡的稳定性受滑面上平均抗剪强度特性控制,因此,需要考虑空间范围内的平均特性。描述空间变异性的随机场理论对变异性较高的土体,实际上高估了其空间变异性。把随机场理论和地质统计中的区域化变量理论结合起来,建立约束随机场,并在此基础上进行Monte-Carlo随机有限元分析。计算实例表明,在高变异性条件下约束随机场能有效降低完全随机场的模拟方差,得到更低的破坏概率。对比了随机有限元和简化法的计算结果表明,简化法在土体强度变异性很高时其结果并非偏于保守。另外也指出了可靠度分析中存在的边坡尺度效应和简化法的适用条件。 相似文献
18.
Reliability analysis of bearing capacity of a strip footing at the crest of a simple slope with cohesive soil was carried out using the random finite element method (RFEM). Analyses showed that the coefficient of variation and the spatial correlation length of soil cohesion can have a large influence on footing bearing capacity, particularly for slopes with large height to footing width ratios. The paper demonstrates cases where a footing satisfies a deterministic design factor of safety of 3 but the probability of design failure is unacceptably high. Isotropic and anisotropic spatial variability of the soil strength was also considered. 相似文献
19.
Reza Jamshidi Chenari Reza Alaie 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2015,9(2):109-123
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. 相似文献
20.
Pinom Ering G. L. Sivakumar Babu 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2017,11(4):285-298
The study presents a recent slope failure in India which resulted in the burial of a village and claimed large number of lives. Current methods of probabilistic back analysis incorporate uncertainty in the analysis but do not consider spatial variability. In this study, back analysis is performed using Bayesian analysis in conjunction with random field theory. The probabilistic method is shown to be efficient in back-analysing a slope failure. It also provides confidence in parameter values to be used for post-failure slope design. The back analysis method which does not consider spatial variability overestimates the uncertainty in analysis, which can lead to uneconomical slope remediation design and measures. 相似文献