Abstract The expansion of offshore wind energy is essential to meet rising energy demands and reduce fossil fuel dependence. This demands next-generation extra-large offshore wind turbines (XL-OWTs) with robust foundations. Conventional monopiles may not withstand significant lateral environmental loading, necessitating innovative, practical foundation systems with enhanced lateral load capacity. This study introduces a Plate with Ribs–Monopile (PRM) foundation developed for XL-OWTs. The National Renewable Energy Laboratory (NREL) offshore wind turbine was adopted as the prototype in this study. Physical model tests were conducted to determine the ultimate load capacity of the PRM foundation, and its performance was compared with that of the Conventional Monopile (CM). Compared with the CM foundation, the PRM foundation exhibited a 65.7 percent increase in lateral load capacity, a 113 percent increase in initial stiffness, and a 74.3 percent reduction in lateral displacement. Numerical simulations were carried out using the finite-element method to investigate the mechanisms involved. The study also presents an extensive parametric analysis to determine the effects of various important parameters, such as load eccentricity, soil properties, and stratification of seabed soils. In addition, sensitivity analyses were conducted to determine the effects of the orientation of ribs in the PRM foundation. The study also presents a field installation procedure for the PRM, thereby providing installation guidelines for its practical application by the offshore wind industry. Finally, a comparative cost-capacity index was obtained, and the proposed PRM foundation was found to have greater cost efficiency. Therefore, the developed PRM foundation not only increases lateral load capacity but is also economical.
Abstract Seepage erosion is a common yet concealed internal degradation process in saturated soils under sustained seepage, and its mechanical consequences strongly depend on the soil grading because particle migration alters the load-bearing skeleton in fundamentally different ways. Seepage erosion driven by internal hydraulic gradients can selectively remove fine particles and reorganize the grain skeleton and contact network, leading to strength differential effects and changes in cyclic stiffness, but the micromechanical mechanisms behind the contrasting responses of gap-graded and well-graded soils remain unclear. This study employs the coupled computational fluid dynamics–discrete-element method to simulate seepage erosion in two representative soils, gap-graded sand and well-graded silt. Monotonic and cyclic triaxial tests are conducted to quantify the macroscopic consequences, including strength differences and cyclic degradation, before and after seepage erosion. The associated microstructural evolution during loading is analyzed to reveal the mechanisms responsible for the grading-dependent strength differential effects. Results show that the static strength and cyclic stiffness of gap-graded sand decrease after seepage erosion, whereas those of well-graded silt increase. Microscopic analysis indicates that in gap-graded sand, fine particles are essential for filling voids and stabilizing the coarse grain skeleton, and their removal produces a looser pore structure and weakened internal stability. In well-graded silt, the remaining fines preserve a load-bearing skeleton after seepage erosion, increasing effective contacts and interlocking, thereby enhancing internal stability. These findings provide a microstructure-informed basis for evaluating seepage erosion–induced strength variation and cyclic performance in soils with different gradations and support more reliable assessment and design of seepage-prone geotechnical systems.
Abstract Ignoring the uncertainty of mechanical properties in frozen soil roadbed stability analysis may cause uneven settlement and cracking. Therefore, evaluating the uncertainty of frozen soil mechanical properties is essential for reliable engineering design. Considering that temperature fluctuations and limited sample data affect the estimation of true statistical characteristics, this study investigates the dependence between the strength and elastic modulus of warm frozen soil using copula theory. Uniaxial compressive strength and elastic modulus data of warm frozen clay from the Beiluhe test section of the Qinghai–Tibet Railway at different temperatures are first statistically analyzed, and their bivariate joint distribution models are established. Second, the model's ability to characterize the uncertainty of bivariate parameter data is analyzed. This serves to verify the feasibility of judging the optimal function based on N -fold cross-validation. Moreover, the performance of different copula types in capturing parameter dependence is compared, emphasizing the effect of temperature and sample size on correct function selection for warm frozen soil. Finally, the simulation capability of the model is evaluated by the proportion of simulated data within the confidence interval of safety values. The results provide reliable parameter support for stability analysis and risk assessment of frozen ground engineering.
Abstract A back-analysis of rock mass parameters in deep-buried tunnels with complex coal-bearing strata is often limited when only displacement monitoring is used, because support loading and local stress transfer may not be sufficiently constrained. In this study, a surrogate-assisted biobjective inversion framework is developed to integrate displacement and pressure monitoring data for a rock mass parameter back-analysis. A sensitivity analysis identifies the elastic modulus, Poisson’s ratio, and internal friction angle as the key inversion variables. Latin hypercube sampling and FLAC3D (version 7.0) simulations are used to generate training samples, and Gaussian process regression is adopted to establish the parameter–response mapping. Nondominated Sorting Genetic Algorithm II (NSGA-II) optimizes displacement and pressure errors in parallel, and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) selects representative Pareto solutions under safety-oriented, balanced, and deformation-control preferences. The relative root-mean-square error serves as the scale-fair fitness metric, and the error contribution ratio (ECR) is introduced to quantify objective contributions and confirm scale invariance. The resulting Pareto front reveals the displacement–pressure trade-off, while the TOPSIS provides preference-dependent parameter sets and the ECR identifies the dominant source of error. Under three preference settings, the mean relative errors are 1.94%–3.28% for displacement and 4.61%–6.57% for pressure. The proposed framework provides decision-oriented parameter sets for design verification and construction control in deep-buried tunnels with multisource monitoring.
Abstract A method is presented to determine the average Poisson’s ratio ( ν ) of partly saturated sand up to any hysteresis loop while conducting a series of consolidated undrained (CU) strain-controlled cyclic triaxial shear tests; neither air nor water was allowed to drain from the specimen while cyclic deviatoric stress was applied. The effect of the number of loading cycles and degree of saturation ( S r ) on the average Poisson’s ratio up to any hysteresis loop for partly saturated sand has been examined. The average value of Young’s modulus ( E ) for any loop has also been determined. Experiments were performed for (1) two different effective confining pressures ( σ ′ 3 ), namely, 100 and 300 kPa; (2) two different values of relative density (RD), namely, 40 and 60 percent; and (3) three different amplitudes of axial strain, namely, 0.5, 1.0, and 2.0 percent. The measurements reveal that, for the chosen sand with the selected relative densities, an increase in the number of loading cycles invariably increases the value of E because of soil densification, whereas it decreases the value of ν . An increase in S r invariably leads to an increase in ν , and for fully saturated sand, the value of ν approaches 0.5. The magnitude of E , however, was found to reach a maximum corresponding to a certain optimum value of S r , which was approximately 50–55 percent for the chosen sand. The existence of the optimum degree of saturation ( S r −opt ) is due to the maximum observed increase in contractive volumetric strain at S r = S r −opt , which leads to the maximum relative density of the specimen. An increase in the magnitude of σ ′ 3 as well as in RD leads to a reduction in the value of ν . On the other hand, an increase in the axial strain leads to an increase in the value of ν and a reduction in the magnitude of E . The results obtained from the present research were also compared with data reported in the literature, and the observed trends in the results were found to be generally in line with those reported by other researchers. The observations drawn from the present research will be useful for determining the response of partly saturated sand during cyclic loading, and the proposed method for evaluating Poisson’s ratio, based on the measurement of axial and volumetric strains, appears to be reasonably acceptable.
Abstract Constitutive relationships for soils including anisotropy are, nowadays, quite common and, in some cases, implemented in numerical codes. These are usually elastic–plastic models characterized by anisotropic strain hardening. They very often enable both yield function and plastic potential to pseudorotate about their pseudoaxes in the effective stress space. Many strategies have been suggested to describe such an evolution, but, independently of the rule chosen, they all introduce, as a side effect, parasite distortions of surfaces. Only very recently, the authors introduced a rigorous approach to describe a pure rotational hardening. In the light of that work, in this paper, the authors reconsider a series of approaches introduced in the literature; they critically discuss them, in both triaxial and deviatoric planes, also presenting as evidence the consequences of the anisometry of the triaxial plane with respect to the effective stress space.
Abstract Understanding the mechanical behavior of cemented granular materials under multiaxial stress conditions is essential for the safe and efficient design of filtered tailings disposal systems, yet their anisotropic response remains insufficiently characterized. This study examines the strength anisotropy of iron ore tailings and natural sand blends stabilized with ordinary portland cement through low- and high-pressure true triaxial testing. Mixtures were designed using the porosity-to-volumetric cement content index ( η / C i v 0.16 ) to achieve equivalent initial conditions across varying dry unit weights and cement contents. The experimental program comprised unconfined compressive strength tests and true triaxial tests covering stress paths ( b = 0, 0.5, and 1), mean effective stresses (100, 2,000, and 4,000 kPa), and loading orientations ( θ = 0°–180°). The results show that cementation can suppress compaction-induced anisotropy under stresses below the yield threshold, promoting near-isotropic behavior in all directions; however, anisotropy reappears when cement bonds degrade beyond yielding. While both strength and stiffness improved with increasing cement content and dry density, stiffness was controlled primarily by cement dosage and strength by confining stress. Iron ore tailings displayed a larger normalized yield surface ( q / p ′ = 1.2) compared with natural sand ( q / p ′ = 0.8 at 2 MPa). These findings validate the η / C i v 0.16 index as a practical design parameter, enabling engineers to balance compaction effort and cement content to meet performance targets under complex field stress paths.
Abstract The dynamic compression fracture of brittle rock under seepage pressure is a critical issue for deep underground engineering. It directly influences the stability and safety of the surrounding rock during blasting or seismic loading. However, research on the mechanisms of microcrack evolution under these coupled conditions is still lacking. The relationship between microcrack evolution and macroscopic mechanical properties also remains poorly understood. This study develops a micro–macrofracture model grounded in the wing microcrack propagation framework, integrating both mechanical and chemical interactions between free water and rock. Mechanically, it incorporates seepage pressure, dynamic Stefan force, and dynamic fracture toughness. Chemically, it accounts for the effects of saturated water on rock mechanical parameters. This model characterizes the total stress–strain constitutive behavior of brittle rock under varying seepage pressures during dynamic compression failure, encompassing both strain-hardening and strain-softening phases. This result is validated against experimental data. It accounts for the influence of seepage pressure on both the initial crack and the newly formed wing crack. The seepage pressure weakens the wedging force F W on the initial crack while enhancing the seepage tensile force F P on the wing crack, which constitutes the seepage pressure-driven crack growth mechanism. Furthermore, under the combined effects of dynamic loading and free water, the dynamic Stefan force F S and the dynamic fracture toughness K ICD serve as the mechanism for inhibiting crack growth. The combined influences of seepage pressure, confining pressure and initial crack characteristics on the dynamic mechanical behavior of brittle rock under seepage pressure are discussed.
Abstract Deep rock masses in geothermal engineering, nuclear waste disposal, and deep mining are often subjected to the coupled effects of high temperatures and dynamic disturbances, leading to a significant deterioration in their long-term mechanical stability. However, existing research has rarely explored the coupled effects of thermal damage and impact loading on creep characteristics, and there is a lack of constitutive models capable of capturing the evolution of such coupled damage. In this study, uniaxial compressive strength tests and physical measurements were conducted on red sandstone after heat treatment (200°C–800°C), followed by impact creep tests under various temperatures and impact energies. A critical thermal threshold of approximately 400°C was identified, above which mass loss, volume expansion, and density reduction accelerated significantly, and the failure mode transitioned from splitting to shear-dominated patterns. Under impact loading, the first impact contributed the largest proportion of creep deformation, and cumulative creep deformation increased exponentially with rising temperature, while the steady-state creep rate exhibited a gradually slowing growth trend. Based on the Burgers model, a fractional-order nonlinear damage-creep constitutive model was developed by introducing a viscoplastic element and replacing the Newtonian dashpot with a fractional-order Abel dashpot. This model can effectively capture the entire creep process under coupled thermal and impact effects. The identified critical temperature of 400°C provides a practical reference for assessing the thermal stability of underground engineering, while the proposed constitutive model offers an effective tool for predicting time-dependent deformation of rock masses under the coupled effects of high temperatures and dynamic loads.
Abstract The shear strength of rock masses is a critical parameter in assessing the stability of rock engineering structures. Although the three-dimensional (3D) generalized Hoek–Brown (H-B) criterion captures the nonlinear strength of rock masses, including the influence of the intermediate principal stress, its adoption remains limited compared with the Mohr–Coulomb (M-C) criterion because it does not provide an explicit relationship between normal and shear stresses. To address this limitation, this study introduces an intermediate principal-stress coefficient ( λ ) and recasts the 3D criterion into a quasi-two-dimensional representation. Building on this reformulation and leveraging the geometric relationship between the M-C strength envelope and the Mohr circle, together with an equivalent-envelope transformation, a general framework is developed to compute rock-mass shear strength and the corresponding instantaneous shear parameters (internal friction angle and cohesion). To solve the resulting highly nonlinear implicit equations, a dual-layer iterative algorithm is proposed that couples an outer bisection loop with an inner fixed-point iteration. This scheme mitigates convergence difficulties and enables stable and efficient evaluation of rock-mass shear strength under the 3D generalized H-B criterion. Validation on four representative rock-mass cases demonstrates practical applicability, and sensitivity analyses indicate low sensitivity to rock-mass quality and disturbance factor. Moreover, three characteristic λ -dependent patterns are identified—symmetric, eccentric, and unidirectional distributions—clarifying the mechanistic basis of the intermediate principal-stress influence. Overall, the results provide theoretical support and practical tools for applying the 3D generalized H-B criterion in engineering practice.
Abstract To address the degradation of dynamic properties in subgrade engineering of cold-region loess under wetting–drying–freezing–thawing (WDFT) cycles, this study quantifies the evolution of physical damage characteristics through mass loss rate and volumetric change rate under varying cycle numbers. Integrated with the Box–Behnken response surface methodology, systematic dynamic tests were conducted to investigate the interactive effects of WDFT cycles, confining pressure, and deviator stress on the dynamic resilient modulus and associated damage variables. Quadratic polynomial models were established to predict these parameters, with significance validated by analysis of variance (ANOVA). Quantitatively, confining pressure accounts for over 70% of the variance in the dynamic resilient modulus model, while the damage variable model reveals a significant interaction between cycle number and confining pressure ( P < 0.05). Key findings reveal that mass loss and volumetric change accumulate progressively with WDFT cycles, exhibiting distinct stage-wise characteristics. Significant nonlinear interactions among cyclic parameters dominantly govern both dynamic resilient modulus and damage variables. ANOVA-optimized models identify confining pressure as the dominant factor for resilient modulus, while damage variables highlight synergistic mechanisms in cycle–pressure interactions. This research elucidates the physicomechanical damage mechanisms of loess under WDFT cycles, providing quantitative tools for dynamic stability assessment of cold-region loess subgrades.
This research develops a numerical model to simulate the thermal performance of energy tunnels in cold regions, with validation through laboratory-scale model tests. Using the Daban Mountain Tunnel as a prototype, a full-scale numerical model incorporating energy tunnel technology was constructed to perform a detailed parametric study. Key factors such as wind speed, seasonal temperature variations, and design/operational parameters were examined to assess their influence on the heat exchange efficiency at the tunnel portal. The findings reveal that: (1) the temperature of the heat transfer fluid at the inlet and the insulation layer thickness considerably affect heat transfer efficiency in the entrance segment of cold-region energy tunnels; (2) wind speed at the tunnel entrance also notably affects heat transfer performance-when wind speed increases from 2.5 to 4.5 m/s, the heat exchange efficiency rises by 94.6%, but further increases beyond 4.5 m/s only lead to a 5.1% improvement due to convective saturation; and (3) from the perspective of engineering application, the influence of wind speed on heat transfer efficiency cannot be ignored in the design of cold-region energy tunnels.
The propagation morphology of hydraulic fractures plays a critical role in the stimulation effectiveness of unconventional oil and gas reservoirs. Based on the displacement discontinuity method (DDM) within a boundary element framework, this study establishes the transformation relationship between the global and local coordinate systems for fracture elements. The induced stress field generated by an arbitrary fracture element and the corresponding theoretical stress-displacement relationships are subsequently derived, enabling the numerical solution of stress intensity factors at the fracture tip. By introducing a circular-arc fracture model, analytical solutions for the stress intensity factor and energy release rate are further obtained. The error between the numerical and analytical solutions is < 5%, validating the reliability of the DDM. Furthermore, the numerical solutions for fracture width obtained via the DDM are verified against the analytical solutions derived from the Khristianovic-Geertsma-de Klerk (KGD) model, with the error in peak width remaining within 5%. This study systematically analyzes the width distribution in both single fractures and T-shaped fractures during hydraulic fracturing. The results indicate that within the T-shaped configuration, the single fracture and the branch fractures exhibit an arch-shaped width distribution, whereas the main fracture demonstrates a tower-shaped profile with a peak width significantly larger than that of the branch fractures. These findings provide theoretical and numerical insights for understanding fracture propagation mechanisms and optimizing fracturing design.
The particle size, morphology, and mineralogy of fines all contribute to the flow instability of mixed soils. However, few experimental studies have isolated the influence of particle size from the morphology and mineralogy when investigating the impact of clay-sized fines content on the flow instability of mixed soils. To fill this research gap, in this study, red mud-characterized by its clay-sized fine fraction and the consistent morphology and mineralogy of both its fine and coarse particles-was employed for such investigation and examined using monotonic undrained triaxial tests prepared via moist tamping. The results indicated that the changing fines content resulted in parallel translation and rotation of the critical state lines in the volumetric plane. Three regions of the critical state friction angle were identified with increasing fines content; the liquefaction potential, LP, first increased at lower fines content, then decreased as the fines content continued to rise, before increasing again at very high fines content. An analysis of the intergranular microstructure under the framework of critical state soil mechanics provided a rational explanation for the observations described previously. The sieve size adopted in moist tamping was also proven to influence the critical state due to the cementitious nature of the red mud.
The deterioration of jointed rock mass strength induced by cyclic water-level fluctuations constitutes a critical issue affecting the stability of shallow rock slope engineering. To study the influence of cyclic water intrusion on joint shear rock mechanical characteristics, direct shear tests were conducted on joint samples with varying degrees of roughness subjected to cyclic water intrusion. The shear critical angle icr1 and tensile critical angle icr2 were proposed by analyzing the stress state of the asperities. Based on the joint failure modes, a joint surface shear strength model for the jointed rock mass was proposed that considered the failure modes of the joint surface under cyclic water intrusion. The findings indicate that (1) as the number of water intrusion cycles increases, the degree of stress softening exhibits an initially steep, followed by a gradual declining trend, with the decline magnitude positively correlated to the joint roughness coefficient; stress-displacement curves transition from postpeak drop type to platform type, while both the compressive strength of the jointed rock mass and the basic friction angle show an exponential downward; (2) as the number of water intrusion cycles increases, the shear critical angle icr1 decreases, while the tensile critical angle icr2 increases, and asperities become more prone to shear-cutting failure. Based on this, a shear strength model was established by considering the failure modes of the joint surface; and (3) model validation via MATLAB (version R2021b) programming quantified failure mode contributions to shear strength. The contribution ratios for the cutting failure in the J5 and J10 joints are about 14% and 37%, respectively. Ignoring this contribution will lead to significant deviations in the predicted values of shear strength. The relevant research methodologies and findings can provide significant references for stability analysis and analogous model testing in shallow water-related geotechnical engineering.
A formulation is presented to incorporate the friction stresses exerted by the soil on diaphragm walls modeled using the subgrade reaction method (SRM). The wall structure is discretized with beam finite elements, and the soil-structure friction is represented by equivalent distributed moments and axial forces. The coupling between axial and lateral displacements is introduced at the soil-structure interaction level through the constitutive law for tangential stresses. The resulting nonlinear problem is solved using the Newton-Raphson method, and the adopted iteration strategies are discussed. A benchmark case of an embedded cantilever wall is analyzed. The SRM predictions are compared with results from the FEM, reduced-scale laboratory experiments, and field measurements of a monitored wall. A sensitivity analysis highlights the influence of interface parameters on the mechanical response of the embedded wall. A large data set is generated to quantify the impact of including or neglecting skin friction along the wall. Neglecting these effects leads to conservative (safer) designs but also to significant oversizing of diaphragm walls.
Current research on one-dimensional consolidation of soft soils rarely systematically incorporates the simultaneous effects of soil nonlinearity, heterogeneity, and multistage linear loading. To investigate the nonlinear consolidation behavior of a one-dimensional double-layered heterogeneous soft soil foundation under multistage linear loading, this paper develops a comprehensive consolidation model. The model explicitly accounts for soil nonlinearity based on the e-log sigma ' and e-log kv relationships established by Mesri and Rokhsar, as well as for soil heterogeneity following Louis's principle that permeability and compressibility coefficients attenuate with depth. The solution to the governing consolidation equation was derived using the finite-difference method, and the accuracy of the solution was verified through comparisons with field-measured data and existing theoretical solutions. Additionally, the study analyzes the influence of the attenuation coefficient, the ratio of the compression index to the permeability index, the form of the surcharge loading, and the soil nonlinearity coefficient on consolidation characteristics. The results indicate that, compared to single-stage loading, multistage linear loading can effectively reduce the peak excess pore-water pressure. The first loading stage is identified as having the most significant impact on the overall consolidation process. Therefore, in engineering applications, controlling the loading magnitude and rate of the first stage is crucial to avoid potential soil damage.
Cemented soil-rock mixtures (CSRMs) consist of a bonded soil matrix embedded with rigid rock blocks. The shear behavior exhibits pronounced anisotropy depending on block geometry and orientation. In this study, a three-dimensional (3D) heterogeneous discrete-element method framework is developed to perform numerical direct-shear simulations of CSRM with rock blocks oriented at 0 degrees, 30 degrees, 60 degrees, and 90 degrees to the shear plane. At the macroscale, after precise microstructural reconstruction and parameter calibration, block-induced anisotropy in CSRM shear behavior is captured by the 3D model. At the microscale, 3D heterogeneous statistics of contact forces and crack networks elucidate the anisotropic shear failure mechanisms in CSRM. Additionally, fracture-surface topology is reconstructed from particle slip data to illustrate how block orientation governs stress transmission. Results reveal a two-stage response: an initial peak-strength hardening followed by residual softening. Block inclination significantly influences residual strength, which increases with inclination, whereas peak strength remains relatively insensitive to block angle. At the mesoscopic level, residual strength arises from a combination of high-stiffness block-block contacts and geometrical interlocking induced by block inclination. These findings illuminate multiscale mechanisms, crack propagation, volumetric dilation, and force-chain distribution, providing the insight basis for improved anisotropic strength models and assessing engineering stability.
The present study utilizes the coupled Eulerian-Lagrangian finite-element modeling technique to simulate three-dimensional piles with true helices in sand under axial compression. The aim is to develop a numerical methodology that accounts for installation-induced disturbances of the helices, evaluate the influence of the true-helix geometry, and investigate the axial failure mechanisms of helical piles in sand. The models include single-helix and double-helix piles with interhelix spacing ratios of 1.5 and 2.5. The results are validated against centrifuge model tests of helical piles in sand. The disintegration of axial loads between the helices and the shaft suggests higher loads in the helix in single-helix piles and lower helix loads in double-helix piles. The structural integrity of the helix, assessed against the ultimate axial load capacity, validates the assumption of elastic pile behavior and confirms its adequacy. The axial behavior of multihelix piles in sand was governed by an individual bearing mode (IBM). IBM failure also dominates for larger helix wings, while larger-diameter shafts lead to global failure, accompanied by ground surface heave. As pile embedment increases, the failure envelope around the upper helix of a double-helix pile transitions from a near-circular to a funnel-shaped pattern. A shaft-to-helix ratio of 1-to-3 presents an ideal selection for pile design.
