Effects Of Soil Spatial Variability Research Articles

Effect of soil spatial variability on the stability of pipelines under horizontal loading

Submarine pipeline has been utilized more and more widely in offshore oil and gas transportation engineering. Given that these pipelines frequently subject horizontal loading during operation, thus precise predicting their horizontal bearing capacity is essential. However, most previous studies employ deterministic analysis without considering soil spatialvariability. This article introduces a two-dimensional (2D) random finite element analysis to study the horizontal pullout behaviour and failure mechanisms of a pipeline in a spatial variability soil. It is observed that the effect of soil spatial variability on the horizontal bearing capacity factor and failure mechanisms is remarkably substantial, with the distribution of the former showing a close approximation to a log-normal distribution. Furthermore, the average horizontal bearing capacity typically falls below the corresponding deterministic value. Consequently, the deterministic estimation of the horizontal bearing capacity tends to be inflated. Eventually, a reliability-based approach is formulated, where a factor of safety is incorporated to account for the uncertainties arising from spatial variability and ensure a sufficient safety margin. This methodology enables engineers to determine appropriate factor of safety tailored to the specific requirements of each project.

Effects of soil spatial variability on the behaviour of the embankment supported with a combined retaining structure

In this study, the effects of soil spatial variability on the behaviour of the embankment supported with a combined retaining structure (CRS) were investigated. The numerical model of the CRS embankment was established and validated with the field data. An application programming interface (API) was developed to deal with the data exchanging issue between the numerical model and the spatial variability characterization model. Based on the verified numerical model and the API, the probabilistic analysis with 500 Monte Carlo simulations was automatically computed. Three influencing factors of the retained soil (the mean of the friction angle, the variation of the friction angle and the vertical correlation length of the random field) are analysed by parametric analysis. The results show that the vertical correlation length of the random field is most important in the earth pressure calculation process, while the mean of the friction angle is the factor with least impact. On the whole, the spatial variability of soil properties has minimal impact on the distribution and magnitude of earth pressure behind the retaining structure.

Predicting ground vibrations from railway tunnels using an improved 2.5D FEM-PML model with soil spatial variability

PurposeThis study establishes a method for predicting ground vibrations caused by railway tunnels in unsaturated soils with spatial variability.Design/methodology/approachFirst, an improved 2.5D finite-element-method-perfect-matching-layer (FEM-PML) model is proposed. The Galerkin method is used to derive the finite element expression in the ub-pl-pg format for unsaturated soil. Unlike the ub-v-w format, which has nine degrees of freedom per node, the ub-pl-pg format has only five degrees of freedom per node; this significantly enhances the calculation efficiency. The stretching function of the PML is adopted to handle the unlimited boundary domain. Additionally, the 2.5D FEM-PML model couples the tunnel, vehicle and track structures. Next, the spatial variability of the soil parameters is simulated by random fields using the Monte Carlo method. By incorporating random fields of soil parameters into the 2.5D FEM-PML model, the effect of soil spatial variability on ground vibrations is demonstrated using a case study.FindingsThe spatial variability of the soil parameters primarily affected the vibration acceleration amplitude but had a minor effect on its spatial distribution and attenuation over time. In addition, ground vibration acceleration was more affected by the spatial variability of the soil bulk modulus of compressibility than by that of saturation.Originality/valueUsing the 2.5D FEM-PML model in the ub-pl-pg format of unsaturated soil enhances the computational efficiency. On this basis, with the random fields established by Monte Carlo simulation, the model can calculate the reliability of soil dynamics, which was rarely considered by previous models.

Effects of soil spatial variability on the seismic response of multi-span simply-supported highway bridges

Effects of soil spatial variability on the seismic response of multi-span simply-supported highway bridges

Effect of soil spatial variability on characteristics of depth-varying multi-support seismic motions at offshore sites

The purpose of this study is to evaluate the influence of soil spatial variability (SSV) on the simulation of depth-varying multi-support seismic motions (DMSMs) at offshore sites. Firstly, the random field theory is used to quantify the extent of SSV, and a series of random field models with different characteristics are established for an offshore site by changing the coefficient of variation (COV) and correlation distance of soil parameters. Then, the simulation approach for random ground motion transfer functions (GMTFs) and DMSMs at offshore sites are introduced. The sensitivity of each uncertain soil parameter on the offshore seismic motions is explored using the single variable method. Finally, the effects of SSV on the GMTFs and DMSMs are investigated, in which the effects of COV and correlation distance are studied in detail. The results demonstrate that SSV has a remarkable influence on the GMTFs of offshore sites, which results in a large intensity variation of DMSMs. The sensitivity analysis indicates that the soil density and shear modulus are influential factors for the horizontal components of DMSMs; except these two parameters, the Poisson’s ratio also significantly affects the vertical DMSMs. Moreover, both COV and correlation distance can lead to certain variability in the GMTFs and DMSMs, and the effect of COV is more prominent than the correlation distance. This study provides an effective approach for the simulation of DMSMs at random offshore sites, which is valuable for rational probabilistic seismic performance assessment of offshore engineering structures.

Probabilistic hazard analysis of rainfall-induced landslides at a specific slope considering rainfall uncertainty and soil spatial variability

A key index for assessing landslide risk quantitatively is annual slope failure probability, PFA, induced by rainfalls at a specific slope. Although PFA is expected to be significantly influenced by both spatial variability of soil properties and rainfall uncertainty, previous studies seldom estimate PFA with simultaneous consideration of both soil spatial variability and rainfall uncertainty. Most previous studies focused on the effect of soil spatial variability and ignored rainfall uncertainty, and the estimated slope failure probability is not associated with a reference time period (e.g., a year for PFA). This study aims to assess PFA considering both soil spatial variability and rainfall uncertainty by developing a fully Monte Carlo simulation (MCS)-based method. To bypass the high-dimensional integration in estimation of PFA and high computational costs of MCS, a semi-analytical method is further developed for enhancing computational efficiency in estimating a small failure probability. Results show that the semi-analytical and fully MCS-based methods produce consistent PFA. Using the proposed semi-analytical method, a small number (e.g., 30) of random samples is sufficient for estimating a small failure probability (e.g., 10−4) accurately. When the variability of soil properties is negligible, PFA is dominated by rainfall uncertainty and converges to a constant failure probability.

Optimize characteristic value of SPT for seismic design of offshore wind turbines in liquefiable soils by stochastic models

Dynamic numerical analyses on an offshore wind turbine (OWT) supported by a suction bucket foundation were performed to investigate the effects of soil spatial variability on the ground liquefaction and tilts of OWT, and to provide suggestions on selecting a representative percentile of the random distributions of a clean sand equivalent SPT blow count, (N1)60cs, for deterministic models. The material parameters of an elastoplastic constitutive model (Cyclic Mobility model) in the numerical model were derived from the (N1)60cs (spatial variability). Monte Carlo simulations were used to describe the seismic responses of the laterally loaded suction bucket foundation in spatially variable soil. Simulation results for deterministic models (uniform properties of soil) were compared to results for random models (spatially variable properties of soil). Tilts of OWT and liquefaction potential index of ground are chosen as criteria, and those obtained from the random models and deterministic models were compared to identify the representative (N1)60cs, based on the principle that the deterministic models produce reasonable consistency with the upper limit of the random model responses. The effects of site conditions, seismic conditions, and other factors were evaluated, and it is found that the coefficient of variation (COV), (N1)60cs, acceleration, and frequency have significant influence.

Stochastic analysis of excavation-induced wall deflection and box culvert settlement considering spatial variability of soil stiffness

In this study, a three-dimensional (3D) finite element modelling (FEM) analysis is carried out to investigate the effects of soil spatial variability on the response of retaining walls and an adjacent box culvert due to a braced excavation. The spatial variability of soil stiffness is modelled using a variogram and calibrated by high-quality experimental data. Multiple random field samples (RFSs) of soil stiffness are generated using geostatistical analysis and mapped onto a finite element mesh for stochastic analysis of excavation-induced structural responses by Monte Carlo simulation. It is found that the spatial variability of soil stiffness can be described by an exponential variogram, and the associated vertical correlation length is varied from 1.3 m to 1.6 m. It also reveals that the spatial variability of soil stiffness has a significant effect on the variations of retaining wall deflections and box culvert settlements. The ignorance of spatial variability in 3D FEM can result in an underestimation of lateral wall deflections and culvert settlements. Thus, the stochastic structural responses obtained from the 3D analysis could serve as an effective aid for probabilistic design and analysis of excavations.

Irrigation management zone strategies impact assessment on potential crop yield, water and energy savings

In irrigated agriculture, soil spatial variability is a primary factor for low irrigation efficiency. In regions such as the Brazilian Cerrado, where there is a continuous growth of irrigated agriculture and limited water supplies, it is important to seek alternatives to reach an efficient and sustainable irrigated agriculture. In this context, precision irrigation has great potential. Better strategies must be established, especially for center pivot irrigation conditions. Irrigation considering management zones is a promising option; however, criteria must be set to delimitate management zones and evaluate irrigation performance in such situations. This study aims to assess the impact of the use of management zones on irrigation performance. Therefore, two center pivots, PivoBHBV and PivoBHALPA, with distinct soil water physical traits, were evaluated. Two management zones strategies were considered to carry out the simulations. One of the strategies was based on regions in the format of square grids with areas of 25, 100 and 225 m2. In the other strategy, the unsupervised grouping algorithm Fuzzy C-Means was used to create management zones. The irrigation performed on those management zones was assessed by comparing their performance with the irrigation conducted in the grid areas. The irrigation management zones were delimited based on the interpolated maps of soil available water capacity (AWC), and the management was conducted individually for each zone. The simulations were made through a model developed with the Python language. The results indicate similarity between the irrigation with management zones and the grid irrigation, as it did not significantly increase water and energy demands or reduce soybean yield. Precision irrigation practiced management zones increased irrigation efficiency, reducing the effect of soil spatial variability. The total irrigation depth applied was, on average, 1.47 % lower than the irrigation by grids. Comparing the grid and the management zones irrigations, water and energy savings potential and the average yield increase potential were 1.85 %, 1.75 %, and 0.41 %.

General 3D solution to the free vibration of offshore wind turbines supported on multiple foundations

Dynamic characterization of offshore wind turbines (OWTs) is an important design consideration dictating two Limit States: Serviceability Limit State (SLS), and the Fatigue Limit State (FLS). Hence determining the natural frequency of the system considering Soil-Structure-Interaction, is an important design parameter and is also necessary in preliminary concept design. Currently, OWTs are planned to be installed in deeper waters where support structures (for example Jackets and seabed frames) are founded on multiple foundations. This paper presents a general 3D solution to obtain the natural frequencies of OWTs supported on multiple foundations. A mechanical idealization is presented, and mass and stiffness matrices were derived using the Euler-Lagrange method. This method will enable designers to study the natural frequency of the system under different conditions where the foundation supports may have different mass and stiffness properties and is compared to the Finite Element method. Using the derived formulations critical front-end design considerations are provided such as the effect of soil spatial variability, the effect of aspect ratio, and effect of foundation mass.

A semi-analytical random shakedown solution for pavements with spatial variability

ABSTRACT The present paper proposes a step-by-step random shakedown solution, by considering uncertainty in soil parameters explicitly, to meet the safety requirements of road pavement systems design rationally. To this aim, theoretical-based random analysis, called Random Analytical Shakedown Analysis, is established and then validated through comparison of the obtained predictions with the known Random Mesh-free Shakedown Analysis results. It has been shown that the developed theoretical model can effectively capture the effects of soil spatial variability on the pavement shakedown behaviour in a shakedown analysis model. The difference between the deterministic shakedown limit loads obtained by the proposed method and the mesh-free model is within 2%, which shows the comparable accuracy of the suggested theoretical model with the mesh-free method which comprises hundreds of variables and constraints in the optimisation problem. Another advantage of the developed theoretical solution is the prevention of non-convergence situations occurrence in the mesh-free shakedown analysis. Accordingly, the introduced scheme can be efficiently used for rapid evaluation of the shakedown capacity of spatially-varying pavements.

Accounting for Soil Spatial Variability in Plate Anchor Design

AbstractThe effect of soil spatial variability on the undrained vertical uplift capacity of plate anchors has been examined using the three-dimensional random finite-element approach. Multiple dire...

Reply to the discussion on “Effect of soil spatial variability on failure mechanisms and undrained capacities of strip foundations under uniaxial loading” by Zhe Luo

Reply to the discussion on “Effect of soil spatial variability on failure mechanisms and undrained capacities of strip foundations under uniaxial loading” by Zhe Luo

Discussion on “Effect of soil spatial variability on failure mechanisms and undrained capacities of strip foundations under uniaxial loading”

It is a widely accepted practice to use finer meshes at soil domains of stronger interest and coarser meshes at other domains of less interest on a finite element model (FEM) to simultaneously save computational resources and achieve accuracy. But when the random field modeling is implemented into FEM consisting of unequal element sizes, the local averaging of soil property across the elements needs to be consistently applied on elements of various sizes. The mesh-dependent variance reduction factors are required in the statistics of a random field. Otherwise, the generated random field will not be stationary as desired, and the actual statistics of soil property mapped onto the FEM mesh will no longer be constant.

Effect of soil spatial variability on failure mechanisms and undrained capacities of strip foundations under uniaxial loading

This paper mainly investigates the effect of soil spatial variability on failure mechanisms and capacities of strip foundations under uniaxial loading on marine clay deposits with linearly increasing undrained shear strength using random finite element analysis. The soil spatially variable feature is characterised by a non-stationary random field where the ratio of the standard deviation and mean of undrained shear strength is maintained. The effect of soil parameters, including the dimensionless soil heterogeneity index, the coefficient of variation of shear strength and the dimensionless autocorrelation distance, on the uniaxial capacities are discussed. In addition, shapes of failure envelopes for combined loading in the probabilistic analysis are compared to those shapes in deterministic analysis. Results demonstrate that the difference in shapes of failure envelopes between deterministic and probabilistic cases is minimal and can be neglected for practical purposes. Probabilistic uniaxial capacities derived in this study can be employed to scale probabilistic failure envelopes, which represent sizes of probabilistic failure envelopes. The obtained results offer insights into how soil spatial variability can be comprehensively considered in the design of an offshore shallow foundation.

Effect of Soil Spatial Variability on the Structural Reliability of a Statically Indeterminate Frame

AbstractThis paper presents a probabilistic procedure for assessing the structural responses of a statically indeterminate frame caused by soil spatial variability. Neglecting the soil spatial vari...

An Analytical Random Field Solution for the Reliability of Axially Loaded Piles in the Ultimate Limit State Considering the Effect of Soil Sampling

The present work is concerned with the effect of soil spatial variability on estimating the ultimate soil resistance of floating axially loaded piles from point measurements of soil properties along the pile. The ultimate limit state is considered. In particular, closed form formulae for (i) determining the optimal sampling depth for minimizing statistical uncertainty and (ii) the optimal—minimum required—safety factor for a desired failure probability level are derived. A dimensionless parameter, the cohesion-to-friction parameter Λ, is introduced which quantifies the weight of soil’s cohesion contribution relative to that of soil’s friction in the linear trend of the ultimate soil strength. The analysis shows that the probability of failure profile with the sampling depth attains a minimum, designating the optimal sampling point. This depends on the scaled spatial correlation length of the soil Θ (i.e., the spatial correlation length of soil over the length of the pile) and the parameter Λ, but not on the coefficient of variance of the ultimate soil strength (covu) or the safety factor. Furthermore, it was found that the optimal depth is always at the lower half of the pile, approaching the mid-point or the bottom end of the pile for Λ>>1 or Λ<<1, respectively. In addition, it was found that for large Θ, the optimal depth tends to be closer to the mid-point of the pile, while for small Θ, the optimal sampling depth arises closer to the bottom end. The practical usefulness of the results is related to a suitable choice of the safety factor. Inverting the probability of failure formula at its minimum value, an optimal safety factor is obtained as a function of the desired (acceptable) probability of failure, and the parameters Θ, Λ and covu. The optimal safety factor is the minimum value required for a desired level of the probability of failure.

Effects of soil spatial variability on structural reliability assessment in excavations

In this study, the effects of soil spatial variability in braced excavations are investigated by focusing on three structural responses: wall bending moments, wall shear forces, and strut forces. The soil spatial variability is modeled using random field theory, and the generated soil parameters are mapped onto a finite element model. A procedure for automating the Monte Carlo simulation, which is used for probabilistic analysis, is described. A case study demonstrates that the soil spatial variability has a considerable effect on the excavation-induced structural responses. Furthermore, a reliability analysis is performed to estimate the failure probability for three structural failure modes. The results demonstrate the importance of considering soil spatial variability in the structural assessment of braced excavations.

An analytical method for quantifying the correlation among slope failure modes in spatially variable soils

An efficient analytical method for quantifying the correlation between performance functions of different slope failure modes in spatially variable soils is proposed, and its performance in slope system reliability analysis is investigated. First, a new correlation coefficient (NCC) is proposed to evaluate the correlation among slope failure modes considering spatial variability. For comparison and verification, the simulation-based correlation coefficient (SCC) is also presented. Second, appying these two types of correlation coefficients, the effects of soil spatial variability on the representative slip surfaces (RSSs) and the system probability of slope failure are investigated using different system reliability methods, including a probabilistic network evaluation technique, a risk aggregation approach, and a bimodal bounds method. A single-layered cohesive slope is investigated to illustrate the validity of the proposed NCC. The results indicate that the proposed NCC can efficiently and accurately quantify the correlation among slope failure modes considering soil spatial variability. The number of RSSs indicated by the NCC is in good agreement with the number obtained using the SCC. The system failure probabilities of slope stability obtained with the SCC and the NCC using a risk aggregation approach are generally comparable. Also, the system reliability bounds of slope stability obtained using the NCC are relatively close together and comparable to those obtained using the SCC. Thus, the NCC shows good performance when evaluating the correlation among slope failure modes, and was effectively applied to analyze a single-layered cohesive slope considering soil spatial variability.

Effects of soil spatial variability at the hillslope and catchment scales on characteristics of rainfall‐induced landslides

AbstractSpatial variations in soil properties affect key hydrological processes, yet their role in soil mechanical response to hydro‐mechanical loading is rarely considered. This study aims to fill this gap by systematically quantifying effects of spatial variations in soil type and initial water content on rapid rainfall‐induced shallow landslide predictions at the hillslope‐ and catchment‐scales. We employed a physically‐based landslide triggering model that considers mechanical interactions among soil columns governed by strength thresholds. At the hillslope scale, we found that the emergence of weak regions induced by spatial variations of soil type and initial water content resulted in early triggering of landslides with smaller volumes of released mass relative to a homogeneous slope. At the catchment scale, initial water content was linked to a topographic wetness index, whereas soil type varied deterministically with soil depth considering spatially correlated stochastic components. Results indicate that a strong spatial organization of initial water content delays landslide triggering, whereas spatially linked soil type with soil depth promoted landslide initiation. Increasing the standard deviation and correlation length of the stochastic component of soil type increases landslide volume and hastens onset of landslides. The study illustrates that for similar external boundary conditions and mean soil properties, landslide characteristics vary significantly with soil variability, hence it must be considered for improved landslide model predictions.