Seismic loading can significantly affect the safety and serviceability of structures supported by piles, making seismic performance a key consideration in pile foundation design. The coupling between slope effect and dynamic loading can significantly alter pile-soil interaction and consequently influence the response of laterally loaded piles. In the present study, a dynamic extension of the static p-y curve model for piles near clay slopes is developed for analyzing the response of laterally loaded piles under dynamic loading, based on adjustment of the real stiffness component, and the spring and dashpot model. A computational program based on the Beam on Dynamic Winkler Foundation (BDWF) model is developed for analyzing the dynamic response of piles near a slope. Comparison with finite element simulation results shows that the complex stiffness scheme provides accurate response predictions, thereby validating the effectiveness of the proposed model. Finally, parametric analyses are carried out to investigate the effects of loading parameters (excitation frequency and load amplitude), pile parameters (pile diameter, pile length, and adhesion coefficient), boundary conditions (pile-head and pile-tip constraints), and slope parameter (slope angle). The pile-soil system exhibits a characteristic frequency governed by the soil shear-wave velocity and pile diameter, while being essentially independent of slope angle and pile length. Near this frequency, the pile-head stiffness and damping ratio change significantly. The proposed method provides a practical tool for steady-state dynamic analysis of laterally loaded piles near clay slopes.

The cyclic lateral response of piles is a key research priority for ensuring the safety and long-term serviceability of structures subjected to cyclic lateral loads, such as wind turbines. This study presents an artificial neural network-based cyclic p-y curve model for analyzing cyclically laterally loaded piles in sand. The cyclic stress-strain response of sand under complex stress sequences is predicted using recurrent neural networks. This prediction is incorporated into the development of the cyclic p-y curve model through the scaling factor. A cyclic stress-strain dataset for sand is obtained through a comprehensive series of discrete element method simulations of cyclic triaxial tests. A computational framework for analyzing pile response is developed based on the finite difference method, incorporating artificial neural network predictions into the cyclic p-y curve portion to reduce simplifying assumptions and empirical parameters. Comparison with centrifuge test results demonstrates the validity of the proposed method and supports the incorporation of artificial neural network predictions. Further analysis of the soil resistance also shows the capability of the model to capture cyclic pile-soil interaction.

Rock-socketed piles are commonly used in coastal engineering, and their bearing capacity has attracted extensive attention. To study the bearing capacity of rock-socketed piles near slopes, this paper develops an analytical method for determining the ultimate end-bearing capacity of piles based on the method of characteristics and the Hoek–Brown criterion. This method modifies the calculation procedures for piles embedded in level and inclined rock. A new proportionality coefficient is introduced to characterize the relationship between the distance of the pile from the slope crest and the characteristic lines. To solve for the coefficient, a specific geometric relationship is found. The proposed method is verified against published experimental results, existing analytical solutions, and three-dimensional finite element analyses. The mean relative error with respect to the experimental data is 22.3%, the maximum relative error is 34.6%, and the deviation from the finite element results is within 10%. Finally, the influence of the distance of the pile from the slope crest on the limiting embedment ratios and the ultimate end-bearing capacity of piles is studied by using this method.

Aiming at the fatigue damage and the synergistic effect of dry and wet action triggered by the cyclic construction of dams in reservoir areas and the rise and fall of the water level, this study systematically reveals the acoustic emission (AE) response characteristics and the fracture behavior evolution law of the red sandstone through the multistage fatigue loading and unloading test and the dry and wet cycles. Results show that the AE activity is characterized by three phases: intermittent-active-surge, and the dry and wet cycles significantly aggravate the sudden increase of AE counts before the rock samples are destabilized. The AE b-values decreased continuously, but the strain softening effect weakened the decrease before the damage, and the cumulative energy curve was accelerated in stages with the increase of the number of cycles. In addition, the intelligent crack recognition model (ICRM) based on machine learning showed a positive correlation between the percentage of shear cracks and the number of dry and wet cycles. The damage mode gradually evolved from a single dominant type to a high-density network type. Based on Critical Deceleration Theory (CDT), variance and autocorrelation coefficients are constructed as fatigue signals and employed as critical failure warning indicators, providing quantitative basis for assessing the long-term stability of reservoir rock engineering.

Frost heaving and fatigue disturbances affect the stability of geotechnical engineering in cold regions. This paper discussed the fatigue fracture behaviour and energy evolution law of sandstone at the mesoscopic level. First, via the discrete element method, the water-ice phase change coupling expansion process of pore water particles was realized. Second, the S-N curves of the samples under different numbers of freeze-thaw cycles were obtained. Then, the normal contact force and anisotropy of the sample were analysed via 3D fabric. Finally, a damage model of the sample under the coupling of freeze-thaw cycles and fatigue loading was established. The results show that the sample failed after 180 freeze-thaw cycles and that there was no freeze-thaw limit. The increase in the number of freeze-thaw cycles results in the initiation stress of tensile and shear cracks approaching 0 MPa and 22 MPa, respectively, during the loading process. The macroscopic cracks diffuse from the end of the sample to the middle. Freeze-thaw cycles affect the anisotropy of a sample and reduce the maximum normal contact force at the peak load. As the number of freeze-thaw cycles increases, the energy storage limit of the elastic energy decreases. The cementation strain energy decreases faster than the particle strain energy does.

Offshore wind turbine pile foundations, primarily steel pipe piles, are critical components in the design and operation of offshore wind farms, but their long-term performance is increasingly threatened by non-uniform corrosion in harsh marine conditions. Based on a non-probabilistic ellipsoidal model, this study presents a reliability assessment framework for laterally loaded offshore monopiles subjected to degradation induced by non-uniform corrosion. The framework incorporates an improved HL-RF algorithm and accounts for the timedependent variation of pile-soil interaction throughout the service life. Results show that an increase in the number of uncertain parameters leads to a decrease in initial reliability, a shorter fully reliable phase, and a longer transition reliability period. Among the performance functions considered, the rotation-controlled function exhibits the highest correlation with the variation in the reliability index. Moreover, the correlation among uncertain parameters has a significant impact on the reliability results, and neglecting such correlations may introduce errors in the service life assessment of pile foundations. In conclusion, the proposed method provides theoretical support for time-variant reliability assessment and resilient design of pile foundations under corrosion conditions.

Pile foundations are frequently used in the construction of bridges, offshore platforms, and offshore wind turbines, which are often subjected to complex lateral cyclic loading from wind, wave, or current. These lateral loads usually come from different directions or constantly change their direction, which is ignored by most existing calculation models. A two-dimensional p-y model is proposed in this study for the lateral response of the pile subjected to multi-directional cyclic loading in sand. Without introducing additional parameters, the p-y response in two dimensions is coupled by developing the model within the framework of the bounding surface p-y model. Combined with the collapse and recompression model, the effect of sand collapse around the pile during cyclic loading is considered to approach reality. The pile lateral displacement and soil resistance are obtained in incremental form using the finite difference method in the two-dimensional case. By comparing with the model test results, it is demonstrated that the proposed model is able to reasonably predict the lateral cyclic response of the pile as well as the effects of multi-directional cyclic loading. The distribution and variation characteristics of the soil resistance are further discussed by analyzing the results calculated by the proposed model.

Asperities within discontinuities play a critical role in contributing to shear resistance. However, their influence on the shear fracture behavior of discontinuities is constrained by size effects. Revealing and predicting the fracture process of discontinuities with multi-scale asperities is crucial for guiding engineering stability assessment. In this study, PFC2D was employed to simulate the microscopic fracture process of discontinuities with multi-scale asperities under shear loading conditions. The simulation revealed that first-order asperities predominantly experience wear failure, whereas second-order asperities primarily undergo shear failure. Based on these findings, the damage evolution equation for the microscopic elements of first-order asperities was formulated using classical wear theory, while the equation for second-order asperities employed Weibull distribution statistical theory. Consequently, an analytical model was developed that considers the influence of multi-scale asperities on the shear behavior of discontinuities incorporating the damage element method. Subsequently, this analytical model was validated against experimental data and numerical results, demonstrating its capability to accurately predict the rapid stress decrease following the peak point. Finally, the sensitivity of the model parameters was discussed.

As a common geological structure in engineering, the current research on the shear deformation characteristics of grouted joints remains confined to laboratory experiments. Establishing a shear analytical model for grouted joints holds significant theoretical value. Focusing on thin-layer grouted joints, this work investigated the macro-mechanical properties and micro-fracture behavior of thin-layer grouted joints under shear loads numerically by generating discrete element method (DEM) models with the particle flow code in two dimensions (PFC2D). The shear process was divided into three phases: compressive and elastic deformation (Phase I), strain hardening and softening (Phase II), and residual deformation (Phase III). Subsequently, by decomposing the shear deformation in Phase I into closure compression of the grout layer and elastic deformation of the composite load-bearing structure composed of the cement mortar skeleton and rock, an analytical solution for the shear behavior in Phase I was derived. In Phase II, homogenization theory was utilized to model the thin-layer grouted joint as a macroscopically isotropic material composed of multiple anisotropic composite elements. To predict strain hardening and softening behavior, a three-parameter modified damage model was developed using damage theory. Finally, the proposed analytical model was validated through comparisons with numerical simulation results and direct shear test results from other studies, accompanied by a discussion of the model parameters.

The lateral response of pile groups used to support offshore structures differs significantly from that of single piles. The cyclic lateral loads induced by waves, tides, and winds complicate the study of the calculation method for cyclic pile response. A cyclic p-y curve model is developed to address the cyclic lateral response of a two-pile group in this study. The strain wedge model is introduced and modified to account for the shadow effect of a laterally loaded pile group and to derive the backbone p-y curves. The cyclic p-y curves framework for a two-pile group is constructed using the improved collapse and recompression model to represent cyclic pile-soil interaction in sand. A program is developed for the model based on the finite difference method to solve the incremental pile governing equation. The model is evaluated by comparison with the results of existing centrifuge model tests and the discrete element method-finite difference method (DEM-FDM) coupled simulation of this work. The proposed model is effective in predicting the cyclic lateral response of two-pile group. Based on the results, the characteristics of the shadow effect, cyclic p-y curves, and sand movement are discussed.

Pile foundations supporting wind turbines and offshore platforms are always subjected to asymmetric lateral cyclic loads from wind and waves. To calculate the lateral response of the pile in sand under asymmetric cyclic loading, this paper proposes a p- y curve model to deal with different levels of load reversal. According to the state of the soil around the pile under asymmetric cyclic loading, the scaling factor of the reloading curve is modified. The soil collapse-recompression model is also extended to apply to different cases of asymmetric cyclic loading according to the characteristics of soil convection during asymmetric cyclic loading. By modifying the shape and position of the p- y curves to different degrees, the lateral response of the pile under asymmetric cyclic loading can be obtained in combination with the improved finite difference method. The validity of the proposed model is demonstrated by comparing the results with the centrifuge model tests. Then, the pile displacement accumulation, the variation of the bending moment, and the soil resistance under asymmetric cyclic loading, are further discussed.

Cylindrical cavity exhibits non-self-similarity during contraction process following expansion. Previous studies solve this problem with total strain approach and simple constitutive models, but the approach is not applicable when using an advanced constitutive model. This paper presents a semi-analytical solution for a cylindrical cavity undergoing expansion-contraction in undrained soils with auxiliary variable approach, incorporating the Modified Cam-Clay (MCC) model. The stress states around the cavity are formed by the superposition of initial and superimposed stress states. By treating superimposed effective stresses as self-similar, a semi-analytical solution is derived for solving the cavity expansion-contraction problem. The elastoplastic stress-strain relationship is formulated as a set of first-order differential equations, which can be solved as an initial value problem though Runge-Kutta (RK) method. Then the stress distribution around the cavity during expansion-contraction process can be determined. To validate the proposed approach, a series of well-conduced self-boring pressuremeter (SBP) tests are used to verify the proposed approach, which shows good agreements. Additionally, a FEM simulation incorporating the MCC model is performed, and the simulation results are presented to carry out parametric studies on soil parameters. A significant influence on the range of the plastic and reverse plastic zones is shown for overconsolidation ratio, while the in-situ coefficient of the earth pressure only quantitatively affects the stress distribution.

The cyclic response in saturated sand is gaining increasing interest owing to the soil-structure interaction in seismic regions. The evolution of the pore water pressure in liquefiable soil can significantly reduce soil strength and impact the structural dynamic response. This paper proposes a semi-analytical solution for a cylindrical cavity subjected to cyclic loading in saturated sands, incorporating an anisotropic, non-associated SANISAND model. The problem is formulated as a set of first-order partial differential equations (PDEs) by combining geometric equations, equilibrium equations, stress–strain relationships and boundary conditions. Due to the non-self-similar nature of this problem, these PDEs are solved by the hybrid Eulerian–Lagrangian approach to determine the cyclic response of the cavity. Then finite-element simulations with a user-defined subroutine are performed to validate the proposed solution. Finally, parametric studies are presented with the focus on soil parameters and cyclic loading history. It is found that the cyclic responses of the cavity in saturated sands are sensitive to the initial void ratio, and the at-rest coefficient of earth pressure primarily affects the monotonic response but marginally affects the cyclic response. Cylindrical cavities are more likely to liquefy when the sands are compacted in a loose state and under lower displacement amplitudes. The proposed solution has potential use for future research on the cyclic response of the soil-structure interaction in geotechnical engineering.

The installation of many pile foundations near slopes inevitably exposes them to the influence of the slopes on the stiffness and strength of the soil-pile system, which is a significant issue involving geomechanics and worthy of concern. Therefore, a modified failure wedge model with an optimal base angle is developed to address the impact of slopes on laterally loaded piles in sand, drawing insights from previous experimental results and finite-element analyses. The objective of this model is to provide a more comprehensive and universal analysis of the lateral behavior of piles while considering a limited height slope, compared with previous models applicable in relatively limited cases. In this modified model, factors such as edge distance from the slope crest and slope height are taken into consideration. The proposed theoretical method demonstrates its capability to accurately predict the lateral response of a pile. Based on this method, an analysis is conducted to examine how slope inclination, edge distance from the slope crest, and slope height affect the soil-pile system.

The application of large-diameter rigid monopiles is a growing trend in offshore wind turbine projects. Among the various models used to simulate the lateral response of these monopiles, the {' p - y ' +' M R - O R ' ) model has emerged as an effective choice. However, this model has certain limitations, such as its inability to capture the rotation flow mechanism above the pile rotation center and its neglect of vertical friction at soil-pile interface. To address these limitations and enhance our understanding of soil-pile interaction mechanisms for large-diameter rigid monopiles, we develop a modified {' p - y ' +' M R - O R ' +' m s - O R ' ) model that accurately captures all three components of soil-pile interaction. This improved model expands the upper range dominated by the concentrated rotation spring to include depths where shear force on the pile section approaches zero, and incorporates distributed moment resistance from vertical shaft friction into consideration. We present several validation cases that demonstrate its superiority over previous methods such as API method and {' p - y ' +' M R - O R ' ) method. Additionally, through parametric analysis based on our proposed method, we investigate how pile diameter and eccentricity influence internal mechanisms of soil-pile interaction. Our findings reveal that vertical friction at the soil-pile interface plays a significant role in large-diameter cases while rotation flow mechanism dominates in situations with large-eccentricity. Furthermore, we provide a concise empirical expression for estimating lateral bearing capacity of large-diameter rigid monopiles at serviceability limit state which can be conveniently applied during preliminary design stages in practical engineering.

This study proposes a nonlinear analytical method to predict the response of combined loaded offshore rigid monopiles near sandy slopes. Considering the slope effect, the method discusses the ultimate soil resistance before and behind the pile separately. The method assumes that the subgrade reaction modulus varies nonlinearly with relative density but linearly with depth. The equilibrium equation for the pile-soil system is obtained from the balance of forces and moments. By analyzing four mechanical models of rigid monopiles under combined loading and selecting three of them as the basis, a failure mode determination method is provided. The accuracy of this method is verified by comparing with indoor model test, 3D FEA model test and centrifugal test.

To extend the hyperbolic p-y curve model for level ground to the design of offshore piles near sandy slopes, three modifications must be incorporated: the curve framework, the ultimate soil resistance, and the initial stiffness. A new curve framework is developed, in which the displacement that determines the soil resistance is changed to the sum of the soil compression instead of the pile deflection, by considering the soil-pile-slope deformation mechanism. The ultimate soil resistance, affected by the slope angle and near-slope distance, is derived using the failure wedge (FW) model. A modified initial stiffness is obtained by considering the reduction in effective overburden pressure. The accuracy of the modified model is verified through centrifuge tests and model tests. Finally, the effects of the slope angle, near-slope distance, and soil-pile-slope deformation mechanism on the pile response and the modified model are discussed. The modified model provides practicing engineers with a simple yet comprehensive theoretical approach, without the need for additional pile tests or numerical analysis.

This paper presents an analytical solution for combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam‐Clay. The governing partial differential equations for the cylindrical cavity are established in the polar coordinate. The problem is formulated as a set of first‐order differential equations by using the axisymmetric condition, equilibrium equations, and elastic‐plastic constitutive relationship. The influence of the second shear loading on the initial shear strain is considered in the plastic state. Then the stress‐strain distributions can be calculated by integrating within the elastic and plastic zones around the cavity. A finite element method simulation of the cavity under combined shear loading is established to verify the proposed approach, and the results are in good agreement with the proposed analytical solution. Parametric analyses are carried out on the effects of clay overconsolidation ratios and in situ stress coefficients under different loading paths and loading ratios. The results show that the combined shear loading on the cavity wall has a significant effect on the stress distribution of the surrounding soil, and the influence of the loading path cannot be neglected.

Using a two-order profile to characterize the concrete/rock interface, this paper proposes an analytical solution for the shear behavior of the concrete/rock interface under constant normal stiffness (CNS), taking into account the interlocking effect and wear behavior. The interlocking effect of second-order asperities is reflected by considering the work and energy, and the analytical expression of wear behavior is obtained by geometrically decomposing the worn rock asperity into finite tiny triangles. Subsequently, the proposed analytical model, consisting of the elastic stage, the sliding stage, and the progressive damage stage, is substituted into the load-transfer governing equation, and the bearing characteristics of rock-socketed piles are figured out by taking advantage of the finite-difference method. Finally, a parametric analysis is conducted to investigate the effects of second-order asperity distribution parameter η , wear coefficient ξ , and first-order asperity angle α_0 . Both laboratory CNS direct shear tests and field vertical load pile tests are selected to verify the reliability of the proposed analytical model. The results indicate that the proposed analytical model can effectively reflect the variation characteristics of the shear stress-displacement curve and the normal stress-displacement curve under CNS conditions, and its application in the load-transfer behavior of rock-socketed piles can well predict the bearing characteristics.

Revealing lateral soil bearing mechanism around an offshore monopile is critical for understanding and solving soil-pile interactions. In this paper, the lateral bearing mechanism around an offshore monopile in sand is analyzed and a corresponding analytical method is established. Three soil bearing mechanisms, including wedge-type flow, triaxial extension and volume compression, near mudline under working load level are proposed by analyzing the distribution of the Lode's angle (θL) and soil displacement vectors. A corresponding analytical method to calculate the lateral response of the monopile is developed based on the strain wedge (SW) model. The proposed model is verified through three pile tests. Finally, the effect of the parameters of Duncan-Chang model on the monopiles in dry and saturated sand is discussed.