Landslide dams form when landslides, rock avalanches, debris flows, or related geological hazards obstruct mountain rivers. Because they commonly consist of loose, heterogeneous, and poorly compacted materials, they are highly susceptible to erosion and instability. Once overtopping occurs, rapid breach incision and lateral enlargement may release an extreme flood, threatening downstream communities and critical infrastructure. Reliable predictions of breach discharge, reservoir drawdown, and breach morphology are therefore essential for emergency risk assessment and disaster mitigation. However, empirical models cannot explicitly represent the water-sediment interactions and physical mechanisms controlling breach development. Simplified physically based models usually assume regular dam and breach geometries and estimate discharge using broad-crested weir relationships. Although detailed numerical models can reproduce hydrodynamics, sediment transport, and topographic evolution, their application is often restricted by high computational costs. In particular, repeated corrections of unstable breach side slopes require extensive sequential searches and constitute a major computational bottleneck. An efficient numerical model was therefore developed to simulate overtopping-induced landslide dam breaching with explicit consideration of breach side-slope instability.The model was established by coupling the depth-averaged shallow-water equations with non-equilibrium sediment-transport and bed-evolution equations. Conservation equations for water-sediment mixture mass and momentum were incorporated into a unified system, including density variations caused by changing sediment concentrations. Bed erosion and deposition were determined from the difference between the actual sediment-transport rate and equilibrium transport capacity. The transition toward equilibrium transport was represented by a sediment adaptation length. Sediment transport was separated into suspended-load and bed-load components, whose equilibrium capacities were evaluated from hydraulic and sediment properties. A topographic stability constraint was imposed because landslide dams are generally composed of non-cohesive materials. Accordingly, each local breach side-slope angle was required to remain below the internal friction angle of the dam material. A rapid parallel algorithm was designed to resolve intermittent side-slope instability. Conventional methods correct unstable cells sequentially, but each correction modifies neighboring topography and may reactivate previously processed cells. In the proposed method, each unstable slope was corrected by only a small angular increment during each iteration. Every cell was examined against its eight neighbors, and excessive slopes were identified by comparison with the corresponding internal friction angle. Soil was transferred between adjacent cells using a mass-conservative relationship, while bed lowering was restricted by the prescribed fixed-bed elevation. Small incremental corrections allowed simultaneous cell updates without interference from intermediate topographic changes. After the first global iteration, searches were restricted to previously unstable cells and their neighbors, thereby reducing unnecessary calculations. The governing equations were solved using a finite-volume method on an orthogonal structured grid. Interface variables were reconstructed using the MUSCL scheme with the MINMOD limiter, while surface reconstruction was applied near wet-dry fronts and steep terrain. Hydrodynamic fluxes were evaluated using the HLLC approximate Riemann solver, and sediment fluxes were coupled to the fluid flux. Source terms were discretized using stable formulations, and a variable time step satisfied the Courant-Friedrichs-Lewy condition with a Courant number of 0.25. The model was implemented in Taichi, with computationally intensive grid operations executed on a graphics processing unit.The side-slope algorithm was first examined using idealized collapse tests involving a conical soil pile and a compound channel-bank topography. Numerical solutions were compared with analytical solutions using angular correction increments of 0.1°, 0.5°, and 1.0°. When the increment did not exceed 1.0°, numerical errors remained within ±3%. Smaller increments required more iterations but produced slightly greater accuracy. An increment of 1.0° was therefore selected to balance accuracy and efficiency. The coupled model was then validated against a laboratory overtopping experiment involving a non-cohesive landslide dam. Sensitivity analyses were conducted using particle diameters of 1.0, 1.25, and 1.5 mm and sediment adaptation lengths of 0.02-0.05 m. Increasing the adaptation length delayed the initial sediment response but accelerated subsequent vertical incision and lateral enlargement, producing higher peak discharges and stronger fluctuations. Increasing particle diameter raised the critical entrainment stress, suppressed erosion, and reduced peak discharge. The influence of adaptation length also weakened with increasing particle diameter. Using a particle diameter of 1.5 mm and an adaptation length of 0.03 m, the measured peak breach discharge was 0.00 328 m³/s at 67 s. The proposed model predicted 0.00 325 m³/s at the same time, resulting in a discharge error of only -0.9% and no timing error. A conventional model predicted 0.00 316 m³/s at 69 s and generated strong oscillations around the peak. By contrast, the proposed model produced a smoother hydrograph and reproduced the observed erosion and breach morphology. Under identical conditions, the conventional model required 365 063 s, the serial proposed model required 178 260 s, and the GPU-parallel model required 6708 s. The parallel implementation was 26.6 times faster than its serial counterpart and 54.4 times faster than the conventional method. Field-scale applicability was further evaluated through back-analysis of the 2018 Baige landslide dam breach on the Jinsha River. A field domain was constructed from surveyed terrain and discretized into 400 200 cells at a 3 m resolution. The landslide deposit was represented as erodible material, whereas the surrounding mountains were treated as non-erodible terrain. A particle diameter of 5 mm was adopted, and above-water and underwater internal friction angles were set to 35° and 30°, respectively. A dynamic upstream water-level boundary was updated using water balance and the observed stage–storage relationship, avoiding explicit simulation of the entire lake. Suspended-load adaptation coefficients of 2, 5, and 10 were evaluated. Larger coefficients produced faster reservoir drawdown, earlier peak occurrence, and higher peak discharge. The best agreement was obtained with a coefficient of 2, which predicted a peak discharge of 32 538 m³/s at 17:54. The observed peak was 31 000 m³/s at 18:00, giving a discharge error of 5.0% and a timing difference of six minutes. The calculated final breach-bottom width was 140.5 m, compared with the measured 119.3 m, resulting in an error of 17.8%. All key breaching parameters remained within ±20% of observations. The simulated evolution reproduced headcut erosion, longitudinal erosion, and final breach stabilization. Reservoir-level discrepancies were attributed to uncertainty in inflow, the stage-storage relationship, material heterogeneity, grid resolution, and simplified bank-collapse representation. Overall, the proposed framework balanced physical representation, numerical accuracy, and computational efficiency. It can provide physically based estimates of breach discharge, reservoir drawdown, and breach morphology for emergency response and downstream flood-hazard assessment.
Accurately understanding the mechanical response behaviors of deep shale is one of the key factors for optimizing reservoir fracturing stimulation. Currently, significant breakthroughs have been achieved in shale oil and gas exploration and development, with the main burial depth below 4000 m. However, the in-situ conditions and physical properties of shale reservoirs at different depths vary considerably, and the influences of burial depth and core physical properties on the mechanical response behaviors remain unclear, making it difficult to implement refined stimulation in different reservoirs, which leads to low efficiency in deep exploitation. Consequently, the exploitation theories and technologies developed for shallow formations can no longer meet the current demands. To this end, based on the shale gas development project in the Z201 well area, core samples were collected from reservoirs at various depths. Triaxial compression failure mechanical tests were conducted on these cores, with the in-situ high-temperature and high-pressure conditions of deep strata being synchronously considered. Combined with physical property analyses and CT scanning techniques, the anisotropic mechanical response behaviors of shale at different depths and their intrinsic controlling factors were clarified. Furthermore, a novel brittleness evaluation method was proposed, and the differences in brittleness indices among different sub-layers under deep in-situ conditions were revealed, so as to provide scientific interpretation and theoretical guidance for deep shale gas development.The results showed that: (1) With increasing burial depth, significant differences were observed in the physical properties of the QZS shale cores, and both the peak stress and the initiation stress exhibited increasing trends. Higher elastic modulus and peak stress were exhibited by the 90° bedding samples compared to the 0° bedding ones, whereas lower initiation stress was obtained for the former. The failure mode of the deepest shale was dominated by a single shear fracture, while "Y"-shaped shear failures were identified for the other depths. Slightly larger fracture area was observed for the 0° bedding samples than for the 90° bedding ones. The largest fracture area was found in the middle 5 sub-layer, which possessed high brittle mineral content and high porosity, and this area was 1.5 times that of the deep 3 sub-layer. (2) With increasing depth, both the elastic energy and the total energy exhibited increasing trends. At the peak stress, the minimum total energy and elastic energy, along with the maximum dissipated energy, were recorded for the shallowest cores. After failure, the largest dissipated energy was transformed to be that of the deepest cores, and the dissipated energy per unit fracture area was significantly higher than that of the other sub-layers. For the shallowest cores, due to high clay mineral content and large plastic deformation, the dissipated energy still remained relatively large, and the dissipated energy per unit fracture area was slightly higher than that of the middle 5 sub-layer. This indicated that the energy allocation and fracturing difficulty were controlled synergistically by the in-situ environment and physical properties. (3) Based on the plastic strain and energy distribution characteristics from ideal plastic to ideal brittle materials, a new evaluation method was proposed by linearly superimposing the pre-peak and post-peak brittleness indices, and its good universality was verified. Meanwhile, it was found that with increasing burial depth, the brittleness index of the QZS shale tended to increase, which was mainly controlled by the brittle mineral content; this result was significantly different from the conclusion drawn by most scholars that the brittleness of rocks decreases with increasing burial depth for the same lithology. Moreover, the brittleness index of the 90° bedding samples was consistently greater than that of the 0° ones, but the difference exhibited a decreasing trend, indicating that for shale with low porosity and high brittle mineral content, the anisotropy of brittleness index was weakened under high geo-stress and high temperature.
Objective Reservoir safety deficiencies are shaped by coupled effects of service degradation, engineering scale, dam type, geographic setting, reservoir function, and operation and maintenance conditions. Conventional statistical analysis and grade based assessment methods have difficulty describing these nonlinear relationships, especially when deficiency patterns need to be identified for a group of reservoirs rather than for a single project. A structured and interpretable machine learning framework was developed to quantify deficiency severity, identify dominant driving factors, and clarify the response mechanisms of large and medium sized deficient reservoirs in Southwest China.Methods Safety assessment data from 544 large and medium sized deficient reservoirs in Yunnan, Sichuan, Tibet, Guizhou, and Chongqing were used to construct a multidimensional database. Seven explanatory variables were considered, including administrative city, dam type, dam height, storage capacity, elevation, dam age, and reservoir function. Six safety evaluation indicators were used as target dimensions: operation management, flood control safety, seepage safety, structural safety, seismic safety, and metal structure safety. The original A, B, and C evaluation grades were converted into unequal interval deficiency scores according to their engineering meanings. Random Forest, eXtreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), and Categorical Boosting (CatBoost) were trained and compared under the same input variables, target scores, and data partitioning conditions. Separate prediction models were built for the six safety indicators. Model performance was evaluated using mean absolute error, absolute accuracy after grade restoration, conservative accuracy for distinguishing severe and non severe deficiency states, Lift at the top 20% samples, and cost consistency rate. The best model was interpreted using Shapley additive explanations (SHAP), and global importance, marginal contribution trends, nonlinear responses, and interaction effects were examined.Results and Discussions CatBoost achieved the best comprehensive performance among the four ensemble models, with a mean absolute error, absolute accuracy, conservative accuracy, Lift at the top 20%, and cost consistency rate of 2.036, 0.657, 0.898, 1.878, and 0.883, respectively. The SHAP results revealed stable explanatory patterns, including the inverted U shaped response of dam age, the heterogeneous effect of engineering scale, elevation sensitivity, and relative differences among dam types. Dam age was the dominant time related factor controlling deficiency evolution. Its SHAP response showed an inverted U shaped pattern across all six safety indicators. At low dam ages, SHAP values were mostly negative or close to zero, indicating that material ageing, structural damage, seepage deterioration, and equipment degradation had not yet accumulated enough to raise the predicted deficiency score. With increasing service time, SHAP values rose rapidly and reached high positive ranges at approximately 30 to 50 years, identifying this period as a critical stage for the exposure of latent deficiencies. For reservoirs older than about 50 to 60 years, SHAP values tended to decline. This decline should not be interpreted as natural safety improvement, but is more plausibly related to previous reinforcement, structural differences, and the stabilization of deformation and seepage behavior in some earth rockfill dams. Engineering scale showed dimension dependent effects. Dam height and storage capacity generally made negative SHAP contributions to operation management, flood control safety, structural safety, and seismic safety, suggesting that larger reservoirs tend to have lower deficiency scores in these dimensions. This may be related to higher design standards, stronger regulation capacity, better construction control, and more complete management resources. However, this scale advantage was not uniform. Seepage safety showed more scattered responses, indicating joint control by dam type, seepage control system, foundation condition, operation mode, and service age. For metal structure safety, dam height contributed positively in some medium to high ranges, implying that high head operation and complex hydraulic structures may increase fatigue, corrosion, and maintenance pressure on gates, hoists, and related components. Geographic conditions also regulated deficiency responses. Elevation was one of the most sensitive geographic variables. The deficiency contributions of operation management and flood control safety generally increased with elevation, especially in middle and high elevation areas where terrain incision, traffic accessibility, flash flood processes, and emergency response conditions become more restrictive. Seepage safety showed earlier sensitivity, with SHAP values increasing even at relatively low elevations. Seismic safety and structural safety also increased with elevation, reflecting the influence of active tectonic settings, deeply incised valleys, steep slopes, and complex foundation conditions. Dam type and reservoir function further modified the deficiency patterns. Earth rockfill dams generally had higher SHAP values than rigid concrete dams for structural and seismic safety. Within the studied samples, concrete face rockfill dams tended to show lower SHAP values than homogeneous earth dams and core wall dams, whereas gravity dams showed lower SHAP values than arch dams in several indicators. These results indicate relative tendencies derived from the present dataset and model, rather than absolute rankings of dam type safety. Reservoirs with flood control functions showed higher deficiency contributions in some indicators, suggesting that high water level operation, frequent discharge regulation, and stricter emergency requirements may increase safety pressure.Conclusions The proposed framework transformed categorical dam safety grades into unequal interval deficiency scores with explicit engineering meaning and combined ensemble machine learning with SHAP interpretation to analyses regional deficiency mechanisms. Dam age was identified as the dominant driver, and the 30 to 50 year service period was the key stage for concentrated deficiency exposure. Engineering scale generally reduced deficiency contributions in flood control, structural, seismic, and operation management indicators, but its influence was heterogeneous for seepage safety and metal structure safety. Elevation and related geographic conditions imposed clear constraints on deficiency evolution, with different safety indicators showing different sensitive ranges. Dam type and function further affected deficiency responses through structural form, material behaviour, seepage control mode, force transmission mechanism, and operational task. The framework provides data driven evidence for regional deficiency trend identification, key reservoir screening, classified management, and reinforcement planning.
SignificanceIn recent years, the rapid advancement of industrial digitalization and intelligentization has extended the boundaries of cyberspace into the physical world, and urban rail transit systems, as critical national information infrastructure, have been exposed to increasingly severe cybersecurity threats. The network environment of urban rail industrial control systems is characterized by wide-area deployment, dynamic evolution, and strong heterogeneity. Extensive network coverage, dynamically changing operating conditions, and diverse equipment types and communication protocols impose higher requirements on the timeliness, accuracy, adaptability, and coordination capabilities of cybersecurity defenses. Conventional cybersecurity defenses often lack sufficient awareness and remain reactive in these environments, making timely and accurate discovery and identification of wide-area network threats difficult. Static and passive protection mechanisms cannot be readily adjusted to changes in network conditions and threats, while unified management and coordination of heterogeneous cybersecurity devices remain insufficient. Consequently, limited accuracy and timeliness in threat monitoring, static and passive defense mechanisms, and weak unified management and coordination capabilities remain major technical challenges. These challenges are further complicated by the interconnection of control centers, stations, train networks, and cloud platforms, through which threats may be propagated across different operational domains. Meanwhile, strict requirements for train operation safety, real-time control, and service continuity must be satisfied during security monitoring and defensive operations. Timely threat discovery must therefore be reconciled with accurate identification, and defensive policies must be adapted to changing network conditions and threat patterns. Research on artificial immunity and large language models is consequently needed to support the recognition of unfamiliar threats, the dynamic optimization of defensive policies, and the coordinated management of heterogeneous cybersecurity devices.ProgressTo address these challenges, artificial immunity and large language models were incorporated into a research framework for complex urban rail industrial control networks. Timely and accurate wide-area threat discovery, proactive defense against dynamically evolving threats, and collaborative orchestration of heterogeneous cybersecurity devices were identified as the three principal research problems. Three core techniques together with an integrated prototype system were included in the proposed framework. Specifically, an artificial-immune-recognition-based risk monitoring method was proposed to enable rapid threat detection and precise identification. Multisource heterogeneous data were considered for feature fusion and representation in a unified immune feature space. Traffic, logs, alerts, protocol commands, and equipment states were included among the information sources. Hierarchical clustering and detector tolerance training were incorporated into the detector generation scheme, and rapid responses within detector clusters were proposed to improve monitoring efficiency. A dual-verification mechanism was introduced, in which preliminary screening with self detectors was followed by further identification with non-self detectors. An artificial-immune-evolution-based proactive defense framework was then proposed to enhance protection against persistent and multistage attacks. Clonal proliferation and hierarchical differential evolution were incorporated into threat gene evolution to support the exploration of potential threat patterns. Stochastic attack-defense games and deep learning were combined in the proposed technical route for defense policy generation and adaptive dynamic optimization. Successive states, available actions, immediate rewards and costs, and expected future returns were considered in the game-based modeling of attack-defense interactions. A large-language-model-based collaborative management approach was also presented to coordinate diverse security devices for joint defense. Heterogeneous threat intelligence was organized within a cloud-edge-endpoint architecture for collection, aggregation, compression, and storage. The knowledge reasoning and generation capabilities of large language models were incorporated into intelligence analysis and the generation of cross-domain coordination plans. Risk monitoring systems, proactive defense systems, firewalls, and cryptographic appliances were included among the intended managed devices. Policy consistency checks, coordinated distribution, execution verification, and audit records were incorporated into the system design. Building upon this foundation, a prototype intelligent cybersecurity defense architecture was presented for urban rail transit systems, and system integration, deployment arrangements, and technical validation were outlined.Conclusions and ProspectsAn integrated research framework was proposed for cybersecurity defense in urban rail transit systems, with risk monitoring, proactive defense, and coordinated device management connected through three complementary technical directions. Artificial immune recognition was introduced for timely threat discovery and accurate identification, immune evolution was incorporated into adaptive defense policy generation, and large language models were introduced for heterogeneous threat intelligence analysis and collaborative device management. A technical route beyond traditional patch-based passive defense was thereby outlined to support the secure and reliable operation of national critical information infrastructure. Further research should be directed toward the adaptation of these techniques to actual urban rail operating conditions. Dynamic self-boundary modeling and unknown-threat recognition should be refined in response to changes in operating schedules, equipment conditions, and maintenance activities. Defense policy generation and optimization should be investigated under the constraints of train operation safety, real-time control, and service continuity. The explainability and traceability of generated management plans, cross-device policy consistency, and coordinated execution should also be strengthened. Prototype integration should be advanced, followed by system simulation, attack-defense evaluation, and third-party performance testing. Threat detection accuracy, response latency, dynamic defense policy generation, and coordinated handling across multiple devices should be evaluated, and application feedback should be used to refine the proposed technologies and methods.
Objective The vertical bearing behavior of batter pile groups is influenced by pile-head boundary conditions and pile-soil-pile interaction, but the combined effects of pile-cap restraint and depth-dependent pile spacing in outward-inclined pile groups remain insufficiently investigated. This study examined the effects of pile-cap restraint and depth-dependent pile spacing on the deformation modes, bending moment distributions, pile-group efficiency coefficients, and load-sharing ratios of batter pile foundations, and clarified the combined roles of individual pile capacity, pile-soil-pile interaction, and pile-cap coordination.Methods Three-dimensional finite element models were established in ABAQUS. Sand was represented by the Mohr-Coulomb constitutive model, and piles and soil were discretized using eight-node reduced-integration solid elements. Pile-soil interfaces were modeled using hard normal contact and Coulomb friction, with the interface friction angle taken as 0.75 times the internal friction angle of the sand. The numerical approach was assessed against a reported prototype-scale static loading test on a single batter pile and model tests on 2 × 2 batter pile groups. The former evaluated the load-settlement response under field stress conditions, whereas the latter examined the overall influence of batter angle on pile-group settlement. Prototype-scale parametric analyses were subsequently conducted for single piles with a diameter of 1.0 m, an elastic modulus of 30 GPa, length-to-diameter ratios of 10, 15, 25, and 50, and batter angles of 0°, 5°, 10°, 15°, 20°, and 25°. Free-head and pile-cap-restrained conditions were compared. For free-head piles, the characteristic vertical bearing capacity was taken as the smaller of 0.5 times the load producing 40 mm of settlement and 0.75 times the load producing 10 mm of horizontal pile-head displacement. For pile-cap-restrained piles, 0.5 times the load producing 40 mm of settlement was adopted. The 3 × 3 pile groups consisted of one central vertical pile and eight outward-inclined peripheral piles, with a length-to-diameter ratio of 15 and pile-head center-to-center spacings of 3 D, 5 D, and 7 D. The pile cap was separated from the soil surface to eliminate direct pile-cap-soil contact. The restrained single-pile model imposed horizontal and rotational restraint, whereas the elastic cap in the group model coordinated settlement and redistributed load; these two boundary conditions were not treated as mechanically identical. Group efficiency was evaluated relative to the summed capacities of individual piles under comparable pile-head restraint, with the capacities of the eight peripheral piles approximated using the edge-pile batter angle.Results and Discussions The numerical model reproduced the general load-settlement trends of the prototype-scale single-pile test and the 2 × 2 pile-group tests. However, the minimum group settlement occurred at a batter angle of 10° in the model test and approximately 20° in the numerical analysis. The validation therefore supported overall response trends rather than accurate prediction of the optimum batter angle or direct verification of load sharing in 3 × 3 pile groups. For free-head batter piles, vertical loading produced horizontal pile-head displacement and pronounced shallow bending. The combined settlement and horizontal displacement criterion reduced the assessed vertical bearing capacity of longer piles, particularly at larger batter angles. Nevertheless, the bearing capacity of piles with a length-to-diameter ratio of 50 also decreased with increasing batter angle when settlement alone was considered, indicating that this trend was not caused exclusively by the horizontal displacement limit. Pile-cap restraint restricted horizontal pile-head displacement and rotation, changing the deformation mode from bending dominated by free pile-head rotation to shallow reverse bending. Under pile-cap restraint, vertical bearing capacity increased slightly with batter angle for length-to-diameter ratios of 10, 15, and 25, but decreased slightly for a ratio of 50. Compared with free-head conditions, the increase in the vertical bearing ratio was more pronounced for ratios of 25 and 50. For piles with a length-to-diameter ratio of 15 subjected to a vertical load of 3 MN, bending moments were concentrated within approximately 9 D below the pile head. The peak bending moment of free-head piles occurred approximately 3 D below the pile head but migrated toward the pile head under pile-cap restraint. At batter angles of 5°, 10°, 15°, 20°, and 25°, the maximum absolute bending moments under pile-cap restraint were 69.8%, 54.5%, 49.3%, 45.8%, and 46.7%, respectively, of those under free-head conditions. Although the maximum absolute bending moment along the pile decreased, the pile-head bending moment increased, indicating increased structural demand at the connection between the pile head and pile cap. For regular 3 × 3 outward-inclined pile groups, vertical bearing capacity generally increased with batter angle. Increasing pile-head spacing from 3 D to 5 D increased group capacity, whereas increasing the spacing from 5 D to 7 D provided a smaller additional increase. The pile-group efficiency coefficient remained close to that of vertical pile groups for batter angles not exceeding 15° and increased at larger angles. For a pile-head spacing of 3 D, the summed capacities of the individual constituent piles increased by 3.4%, 5.8%, 7.8%, 9.1%, and 8.4% at batter angles of 5°, 10°, 15°, 20°, and 25°, respectively, whereas the corresponding group capacities increased by 3.4%, 4.7%, 9.0%, 11.8%, and 16.0%. Therefore, the increase in group capacity could not be attributed solely to changes in individual pile capacity or depth-dependent pile spacing. Under a vertical group load of 16 MN, corner piles exhibited the highest load-sharing ratios, followed by edge piles and the central pile. Increasing the batter angle reduced the differences in load-sharing ratios among pile positions. Vertical displacement contours also showed an expanded shallow soil deformation zone around outward-inclined pile groups; however, they did not directly quantify stress overlap or interaction intensity at different depths.Conclusions Pile-cap restraint changed the deformation mode and bending moment distribution of single batter piles, shifted the peak bending moment toward the pile head, and increased the structural demand at the pile-head connection. In outward-inclined pile groups, depth-dependent pile spacing was associated with changes in pile-group efficiency and load sharing. Vertical bearing behavior resulted from the combined effects of individual pile capacity, pile-soil-pile interaction, and pile-cap coordination. These findings are limited to fully drained sand represented by the adopted soil parameters, regular 3 × 3 outward-inclined pile groups with a length-to-diameter ratio of 15, batter angles of 0°–25°, pile-head spacings of 3 D–7 D, and pile caps without direct soil contact. The results should be interpreted as comparative response trends rather than directly applicable engineering design capacities.
