Determining the burial depth for offshore pipelines to resist impact load is challenging owing to the spatial variability of soil strengths, which proves to significantly affect failure behaviours of soils and pipelines. To facilitate the design, accurate and fast evaluation on pipeline damage is required. Here, an integrated surrogate model was developed to forecast impact damage of pipelines buried in spatially varied soils. Through coupling the random field and numerical simulation, a stochastic finite element analysis framework was derived and verified to yield the datasets; Based on the scheme of feature extraction - integration from convolution neural network, the surrogate model was established, which mapped the three-dimensional soil spatial field to the structural response. Prediction mechanism of the developed model was explored, where correlations among soil spatial distribution patterns, failure mechanisms and feature recognitions were discussed. The models enabled to capture the key features representing the failure mechanisms under random soil conditions, including the local failure mode of soil and pipe-soil interactions, which theoretically explained its feasibility in damage estimation. Further, model performance was comprehensively evaluated with regard to prediction accuracy, uncertainty quantification, and transfer learning, and the corresponding causes were investigated. Satisfactory performance and high computation efficiency were demonstrated.

Soil-water characteristics, which vary with hydrological events such as rainfall, significantly influence soil strength properties. These properties are crucial determinants of the bearing capacity of foundations. Moreover, shear strength characteristics of soils are inherently spatially variable, and considering them as homogeneous parameters can result in unreliable design. This paper presents a probabilistic study of the two-dimensional bearing capacity of a strip footing on spatially random, unsaturated fine-grained soil using Monte Carlo simulation. The study employs the hydro-mechanical random finite difference method through MATLAB programming along with FLAC2D software. The undrained shear strength under saturated conditions is modelled as random fields using a log-normal distribution. The generated random values are then made depth-dependent by correlating them with matric suction. Initially, matric suction is assumed to be under a hydrostatic condition and decreases linearly with depth to zero at the groundwater level. Afterward, unsaturated soil is subjected to rainfall with different durations, resulting in the non-linear distribution of matric suction and, consequently, the mean value of undrained shear strength in depth. The results showed that rainfall infiltration impacts the strength characteristics of near-surface heterogeneous strata, leading to significant effects on the bearing capacity and failure mechanism of footing.

The mechanical properties of soil, resulting from the weathering of rocks through physical and chemical processes, exhibit spatial variability. This variability introduces uncertainties in the design and characteristics of excavation projects. To address these uncertainties caused by soil spatial variability, safety factors are commonly used in excavation design. However, using the same safety factor for different indicators of soil spatial variability is illogical. Therefore, specialized research on the characteristics of deep excavations in the context of soil spatial variability is necessary, as it provides the theoretical basis for rational excavation design. In this study, we assumed that soil parameters follow a lognormal distribution, while spatial correlation adheres to a Gaussian function. We developed a random finite element algorithm for deep excavations, which incorporated Python programming and the ABAQUS computational platform. This algorithm was created within the framework of random field theory and Monte Carlo simulation. The results of our study indicate that, influenced by soil spatial variability, the lateral wall movements and ground surface settlements exhibit discrete distributions near the deterministic results. The maximum deformation of the excavation follows a normal distribution, while the pattern of ground surface settlements demonstrates diversity and chaotic characteristics. The extent to which soil spatial variability affects deep excavations is correlated with indicators of this variability. As the coefficient of soil spatial variability increases, the diversity and chaotic characteristics of ground surface settlements become more prominent. The locations of maximum ground surface settlement and maximum deformation becomes more scattered. Consequently, the probability of excavation failure increases, and the reliability index of the excavation decreases. In summary, soil spatial variability significantly impacts deformation prediction and safety control during the design and construction stages of deep excavations. Therefore, it is crucial to consider the influence of soil spatial variability when designing deep excavations, based on the variability indicators.

Burial is an effective approach to offshore pipeline protection for impact loads. However, few studies address the influences of inherent soil spatial variabilities on failure behaviour of soil covers and pipelines, causing deviations. Therefore, a random field-large deformation finite element analysis framework is developed to explore the failure mechanisms of buried pipelines in spatially varying soils. The failure mode of soil cover is conformed to a local mode, where the failure path is insensitive to soil variability. The failure mechanism of pipelines depends on the competition mechanism between soil strengths and pipe-soil interactions, based on which two typical failure modes are summarized. Soil variability not only aggravates the impact damage but also stimulates the diversity of structural responses. Correlations between probabilistic damage degrees and multiple influential factors are discussed. Further, inspired by the principle of energy dissipation, an integrated quantitative risk assessment model is derived to reveal the failure risk evolution, where uncertainties from soil variabilities and structure-related factors are considered. The latter shows a significant influence, which may pose an additional failure probability of over 50 %. Different safety design approaches are compared, and spatial failure probability surfaces are configured for burial depth determination.

The influence of a firm stratum on the stability of a slope under undrained conditions has long been of interest to geotechnical investigators, which has been studied in a number of previously important works in relation to slope stability analyses without considering soil spatial variability. This paper proposes another look at such a problem in the context of probabilistic slope stability analyses considering soil spatial variability. Here, the random field (RF) is used to simulate the spatially variable undrained soil strength. It is found that under stationary RF and non-stationary RF with the soil strength at the top ground surface (s(u0)) larger than 0, the depth of the firm stratum (H-f) has a significant influence on the mean and standard deviation of factor of safety (i.e., mu [FS] and 6 [FS], respectively). By contrast, under non-stationary RF with s(u0) = 0, H-f has a slight influence on mu [FS], but its influence on 6 [FS] is non-negligible. In addition, the autocorrelation distance is found to have an insignificant impact on the influential effect of H-f f on mu [FS]. However, for 6 [FS], this impact is not negligible. When the autocorrelation distance is smaller, the influence of Hf f on 6 [FS] would be more significant. Under non-stationary RF, the influence of H-f on 6 [FS] would be slight if the autocorrelation distance is large enough. Furthermore, the impacts of slope ratio, su0, u0 , isotropic and anisotropic features on the influential effects of H-f are also investigated and discussed.