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1.
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   

2.
The subset simulation (SS) method is a probabilistic approach which is devoted to efficiently calculating a small failure probability. Contrary to Monte Carlo Simulation (MCS) methodology which is very time-expensive when evaluating a small failure probability, the SS method has the advantage of assessing the small failure probability in a much shorter time. However, this approach does not provide any information about the probability density function (PDF) of the system response. In addition, it does not provide any information about the contribution of each input uncertain parameter in the variability of this response. Finally, the SS approach cannot be used to calculate the partial safety factors which are generally obtained from a reliability analysis. To overcome these shortcomings, the SS approach is combined herein with the Collocation-based Stochastic Response Surface Method (CSRSM) to compute these outputs. This combination is carried out by using the different values of the system response obtained by the SS approach for the determination of the unknown coefficients of the polynomial chaos expansion in CSRSM. An example problem that involves the computation of the ultimate bearing capacity of a strip footing is presented to demonstrate the efficiency of the proposed procedure. The validation of the present method is performed by comparison with MCS methodology applied on the original deterministic model. Finally, a probabilistic parametric study is presented and discussed.  相似文献   

3.
ABSTRACT

Probabilistic 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   

4.
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   

5.
Geotechnical engineering problems are characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for a probabilistic analysis that considers the spatial variability of cross‐correlated soil properties is presented and applied to study the bearing capacity of spatially random soil with different autocorrelation distances in the vertical and horizontal directions. The approach integrates a commercial finite difference method and random field theory into the framework of a probabilistic analysis. Two‐dimensional cross‐correlated non‐Gaussian random fields are generated based on a Karhunen–Loève expansion in a manner consistent with a specified marginal distribution function, an autocorrelation function, and cross‐correlation coefficients. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses was performed to study the effects of uncertainty due to the spatial heterogeneity on the bearing capacity of a rough strip footing. The simulations provide insight into the application of uncertainty treatment to geotechnical problems and show the importance of the spatial variability of soil properties with regard to the outcome of a probabilistic assessment. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

6.
This paper presents a probabilistic analysis to compute the probability density function of the bearing capacity of a strip footing resting on a spatially varying rock mass. The rock is assumed to follow the generalised Hoek–Brown failure criterion. The uniaxial compressive strength of the intact rock (σc) was considered as a random field and the geological strength index was modelled as a random variable. The uncertainty propagation methodology employed in the analysis is the sparse polynomial chaos expansion. A global sensitivity analysis based on Sobol indices was performed. Some numerical results were presented and discussed.  相似文献   

7.
ABSTRACT

A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design.  相似文献   

8.
Two advanced Kriging metamodeling techniques were used to compute the failure probability of geotechnical structures involving spatially varying soil properties. These methods are based on a Kriging metamodel combined with a global sensitivity analysis that is called in literature Global Sensitivity Analysis-enhanced Surrogate (GSAS) modeling for reliability analysis. The GSAS methodology may be used in combination with either the Monte Carlo simulation (MCS) or importance sampling (IS) method. The resulting Kriging metamodeling techniques are called GSAS-MCS or GSAS-IS. The objective of these techniques is to reduce the number of calls of the mechanical model as compared with the classical Kriging-based metamodeling techniques (called AK-MCS and AK-IS) combining Kriging with MCS or IS. The soil uncertain parameters were assumed as non-Gaussian random fields. EOLE methodology was used to discretize these random fields. The mechanical models were based on numerical simulations. Some probabilistic numerical results are presented and discussed.  相似文献   

9.
This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.  相似文献   

10.
This paper develops a risk de-aggregation and system reliability approach to evaluate the slope failure probability, pf, using representative slip surfaces together with MCS. An efficient procedure is developed to strategically select the candidate representative slip surfaces, and a risk de-aggregation approach is proposed to quantify contribution of each candidate representative slip surface to the pf, identify the representative slip surfaces, and determine how many representative slip surfaces are needed for estimating the pf with reasonable accuracy. Risk de-aggregation is performed by collecting the failure samples generated in MCS and analyzing them statistically. The proposed methodology is illustrated through a cohesive soil slope example and validated against results from previous studies. When compared with the previous studies, the proposed approach substantially improves the computational efficiency in probabilistic slope stability analysis. The proposed approach is used to explore the effect of spatial variability on the pf. It is found that, when spatial variability is ignored or perfect correlation assumed, the pf of the whole slope system can be solely attributed to a single representative slip surface. In this case, it is theoretically appropriate to use only one slip surface in the reliability analysis. As the spatial variability becomes growingly significant, the number of representative slip surfaces increases, and all representative slip surfaces (i.e., failure modes) contribute more equally to the overall system risk. The variation of failure modes has substantial effect on the pf, and all representative surfaces have to be incorporated properly in the reliability analysis. The risk de-aggregation and system reliability approach developed in this paper provides a practical and efficient means to incorporate such a variation of failure modes in probabilistic slope stability analysis.  相似文献   

11.
Multiple response surfaces for slope reliability analysis   总被引：1，自引：0，他引：1       下载免费PDF全文
This paper develops a multiple response surfaces approach to approximate the limit state function for slope failure by second‐order polynomial functions, to incorporate the variation of the most probable slip surfaces, and to evaluate the slope failure probability pf. The proposed methodology was illustrated through a cohesive soil slope example. It is shown that the pf values estimated from multiple response surfaces agree well with those pf values that have been obtained by searching a large number of potential slip surfaces in each Monte Carlo simulation (MCS) sample. The variation of number of the most probable slip surfaces is studied at different scale of fluctuation (λ) values. It is found that when full correlation assumed for each of random fields (i.e., spatial variability is ignored), the number of the most probable slip surfaces is equal to the number of random fields (in this study, it is 3). When the spatial variability grows significantly, the number of the most probable slip surfaces or number of multiple response surfaces firstly increases evidently to a higher value and then varies slightly. In addition, the contribution of a specific most probable slip surface varies dramatically at different spatial variability level, and therefore, the variation of the most probable slip surfaces should be accounted for in the reliability analysis. The multiple response surfaces approach developed in this paper provides a limit equilibrium method and MCS‐based means to incorporate such a variation of the most probable slip surfaces in slope reliability analysis. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

12.
By using the method of characteristics, the effect of footing–soil interface friction angle (δ) on the bearing capacity factor Nγ was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance Bt from the footing edge. For a given footing width (B), the value of Bt increases continuously with a decrease in δ. For δ=0, no trapped wedge exists below the footing base, that is, Bt/B=0.5. On the contrary, with δ=?, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in ?. The magnitude of Nγ increases substantially with an increase in δ/?. The maximum depth of the plastic zone becomes higher for greater values of δ/?. The results from the present analysis were found to compare well with those reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

13.
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   

14.
The ultimate bearing capacity of a group of equally spaced multiple rough strip footings was determined due to the contribution of soil unit weight. The analysis was performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. Along the interfaces of all the triangular elements, velocity discontinuities were considered. The value of ξγ was found to increase continuously with a decrease in S/B, where (i) ξγ is the ratio of the failure load of an interfering strip footing of a given width (B) to that of a single isolated strip footing having the same width and (ii) S is the clear spacing between any two adjacent footings. The effect of the variation of spacing on ξγ was found to be very extensive for small values of S/B; ξγ approaches infinity at S/B=0. In all the cases, the velocity discontinuities were found to exist generally in a zone only around the footing edge. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

15.
A probabilistic framework to perform inverse analysis of geotechnical problems is presented. The formulation allows the incorporation of existing prior information on the parameters in a consistent way. The method is based on the maximum likelihood approach that allows a straightforward introduction of the error structure of field measurements and prior information. The difficulty of ascribing definite values to the uncertainties associated with the various types of observations is overcome by including the corresponding variances in the set of parameters to be identified. The inverse analysis results in a minimization problem that is solved by coupling the optimization technique to the finite element method. Two examples are presented to illustrate the performance of the method. The first one corresponds to a synthetic case simulating the excavation of a tunnel. Young's modulus, K0 value and measurements variances are identified. The second case concerns the excavation of a large underground cavern in which again Young's modulus and K0 are identified. It is shown that introduction of prior information permits the estimation of parameters more consistent with all available informations that include not only monitored displacements but also results from in situ tests carried out during the site investigation stage.  相似文献   

16.
ABSTRACT

A fact that is generally overlooked in many geotechnical uncertainty analyses is that input data of the model may be correlated. While this correlation may influence the system response, epistemic uncertainties i.e. lack of knowledge of this correlation appears as a risk factor. This paper discusses how a negative correlation between cohesion (c’) and friction angle (Ø’) with their associated uncertainties can influence both the bearing resistance of a shallow strip foundation footing and the estimation of its safety. A probabilistic approach that considers both the negative correlation and the uncertainty is used in this work as a reference. This method is compared to Eurocode 7 variants that do not for the correlation. These variants, resistance and material factoring methods appears to be more or less conservative depending on the negative correlation degree between (c’–Ø), their associated uncertainties and soil configurations. Finally, the proposed probabilistic comparison shows that the material factoring method is more conservative than the resistance one.  相似文献   

17.
By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξγ) was determined, where ξγ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξγ at S/B = 0 becomes equal to 2.0, and the maximum ξγ occurs at S/B = Scr/B. For S/B?Scr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>Scr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξγ for S/B>Scr/B. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

18.
System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.  相似文献   

19.
An advanced hypoplastic constitutive model is used in probabilistic analyses of a typical geotechnical problem, strip footing. Spatial variability of soil parameters, rather than state variables, is considered in the study. The model, including horizontal and vertical correlation lengths, was calibrated using a comprehensive set of experimental data on sand from horizontally stratified deposit. Some parameters followed normal, whereas other followed lognormal distributions. Monte-Carlo simulations revealed that the foundation displacement uy for a given load followed closely the lognormal distribution, even though some model parameters were distributed normally. Correlation length in the vertical direction θv was varied in the simulation. The case of infinite correlation length was used for evaluation of different approximate probabilistic methods (first order second moment method and several point estimate methods). In the random field Monte-Carlo analyses with finite θv, the vertical correlation length was found to have minor effect on the mean value of uy, but significant effect on its standard deviation. As expected, it decreased with decreasing θv due to spatial averaging of soil properties.  相似文献   

20.
In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (quE) is expressed in terms of single coefficient NγE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (df/B0), seismic acceleration (kh, kv) are studied on the variation of seismic bearing capacity co-efficients.  相似文献   

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