Fiber optic monitoring of an anti-slide pile in a retrogressive landslide

Anti-slide piles are one of the most important reinforcement structures against landslides,and evalu-ating the working conditions is of great significance for landslide mitigation.The widely adopted analytical methods of pile internal forces include cantilever beam method and elastic foundation beam method.However,due to many assumptions involved in calculation,the analytical models cannot be fully applicable to complex site situations,e.g.landslides with multi-sliding surfaces and pile-soil interface separation as discussed herein.In view of this,the combination of distributed fiber optic sensing(DFOS)and strain-internal force conversion methods was proposed to evaluate the working conditions of an anti-sliding pile in a typical retrogressive landslide in the Three Gorges reservoir area,China.Brillouin optical time domain reflectometry(BOTDR)was utilized to monitor the strain distri-bution along the pile.Next,by analyzing the relative deformation between the pile and its adjacent inclinometer,the pile-soil interface separation was profiled.Finally,the internal forces of the anti-slide pile were derived based on the strain-internal force conversion method.According to the ratio of calculated internal forces to the design values,the working conditions of the anti-slide pile could be evaluated.The results demonstrated that the proposed method could reveal the deformation pattern of the anti-slide pile system,and can quantitatively evaluate its working conditions.

Experimental Study of Local Scour Around Four Piles Under Different Attack Angles and Gap Ratios

In an effort to investigate and quantify the patterns of local scour,researchers embarked on an in-depth study using a systematic experimental approach.The research focused on the effects of local scour around a set of four piles,each subjected to different hydromechanical conditions.In particular,this study aimed to determine how different attack angles—the angles at which the water flow impinges on the piles,and gap ratios—the ratios of the spacing between the piles to their diameters,influence the extent and nature of scour.A comprehensive series of 35 carefully designed experiments were orchestrated,each designed to dissect the nuances in how the gap ratio and attack angle might contribute to changes in the local scour observed at the base of pile groups.During these experimental trials,a wealth of local scour data were collected to support the analysis.These data included precise topographic profiles of the sediment bed around the pile groups,as well as detailed scour time histories showing the evolution of scour at strategic feature points throughout the test procedure.The analysis of the experimental data provided interesting insights.The study revealed that the interplay between the gap ratio and the attack angle had a pronounced influence on the scouring dynamics of the pile groups.One of the key observations was that the initial phases of scour,particularly within the first hour of water flow exposure,were characterized by a sharp increase in the scour depth occurring immediately in front of the piles.After this initial rapid development,the scour depth transitioned to a more gradual change rate.In contrast,the scour topography around the piles continuously evolved.This suggests that sediment displacement and the associated sculpting of the seabed around pile foundations are sustained and progressive processes,altering the underwater landscape over time.The results of this empirical investigation have significant implications for the design and construction of offshore multi-pile foundations,providing a critical reference for engineers and designers to estimate the expected scour depth around such structures,which is an integral part of decisions regarding foundation design,selection of structural materials,and implementation of scour protection measures.

Pile foundation in alternate layered liquefiable and non-liquefiable soil deposits subjected to earthquake loading

Pile foundations are still the preferred foundation system for high-rise structures in earthquake-prone regions.Pile foundations have experienced failures in past earthquakes due to liquefaction.Research on pile foundations in liquefiable soils has primarily focused on the pile foundation behavior in two or three-layered soil profiles.However,in natural occurrence,it may occur in alternative layers of liquefiable and non-liquefiable soil.However,the experimental and/or numerical studies on the layered effect on pile foundations have not been widely addressed in the literature.Most of the design codes across the world do not explicitly mention the effect of sandwiched non-liquefiable soil layers on the pile response.In the present study,the behavior of an end-bearing pile in layered liquefiable and non-liquefiable soil deposit is studied numerically.This study found that the kinematic bending moment is higher and governs the design when the effect of the sandwiched non-liquefied layer is considered in the analysis as opposed to when its effect is ignored.Therefore,ignoring the effect of the sandwiched non-liquefied layer in a liquefiable soil deposit might be a nonconservative design approach.

Thermal performance of cast-in-place piles with artificial ground freezing in permafrost regions

During the construction of cast-in-place piles in warm permafrost,the heat carried by concrete and the cement hydration reaction can cause strong thermal disturbance to the surrounding permafrost.Since the bearing capacity of the pile is quite small before the full freeze-back,the quick refreezing of the native soils surrounding the cast-in-place pile has become the focus of the infrastructure construction in permafrost.To solve this problem,this paper innovatively puts forward the application of the artificial ground freezing(AGF)method at the end of the curing period of cast-in-place piles in permafrost.A field test on the AGF was conducted at the Beiluhe Observation and Research Station of Frozen Soil Engineering and Environment(34°51.2'N,92°56.4'E)in the Qinghai Tibet Plateau(QTP),and then a 3-D numerical model was established to investigate the thermal performance of piles using AGF under different engineering conditions.Additionally,the long-term thermal performance of piles after the completion of AGF under different conditions was estimated.Field experiment results demonstrate that AGF is an effective method to reduce the refreezing time of the soil surrounding the piles constructed in permafrost terrain,with the ability to reduce the pile-soil interface temperatures to below the natural ground temperature within 3 days.Numerical results further prove that AGF still has a good cooling effect even under unfavorable engineering conditions such as high pouring temperature,large pile diameter,and large pile length.Consequently,the application of this method is meaningful to save the subsequent latency time and solve the problem of thermal disturbance in pile construction in permafrost.The research results are highly relevant for the spread of AGF technology and the rapid building of pile foundations in permafrost.

Theoretical investigation on axial cyclic performance of monopile in sands using interface constitutive models

Cyclic loads generated by environmental factors,such as winds,waves,and trains,will likely lead to performance degradation in pile foundations,resulting in issues like permanent displacement accumulation and bearing capacity attenuation.This paper presents a semi-analytical solution for predicting the axial cyclic behavior of piles in sands.The solution relies on two enhanced nonlinear load-transfer models considering stress-strain hysteresis and cyclic degradation in the pile-soil interaction.Model parameters are calibrated through cyclic shear tests of the sand-steel interface and laboratory geotechnical testing of sands.A novel aspect involves the meticulous formulation of the shaft loadtransfer function using an interface constitutive model,which inherently inherits the interface model’s advantages,such as capturing hysteresis,hardening,degradation,and particle breakage.The semi-analytical solution is computed numerically using the matrix displacement method,and the calculated values are validated through model tests performed on non-displacement and displacement piles in sands.The results demonstrate that the predicted values show excellent agreement with the measured values for both the static and cyclic responses of piles in sands.The displacement pile response,including factors such as bearing capacity,mobilized shaft resistance,and convergence rate of permanent settlement,exhibit improvements compared to non-displacement piles attributed to the soil squeezing effect.This methodology presents an innovative analytical framework,allowing for integrating cyclic interface models into the theoretical investigation of pile responses.

Centrifuge modeling of unreinforced and multi-row stabilizing piles reinforced landslides subjected to reservoir water level fluctuation

With the construction of the Three Gorges Reservoir dam,frequent reservoir landslide events have been recorded.In recent years,multi-row stabilizing piles(MRSPs)have been used to stabilize massive reservoir landslides in China.In this study,two centrifuge model tests were carried out to study the unreinforced and MRSP-reinforced slopes subjected to reservoir water level(RWL)operation,using the Taping landslide as a prototype.The results indicate that the RWL rising can provide lateral support within the submerged zone and then produce the inward seepage force,eventually strengthening the slope stability.However,a rapid RWL drawdown may induce outward seepage forces and a sudden debuttressing effect,consequently reducing the effective soil normal stress and triggering partial pre-failure within the RWL fluctuation zone.Furthermore,partial deformation and subsequent soil structure damage generate excess pore water pressures,ultimately leading to the overall failure of the reservoir landslide.This study also reveals that a rapid increase in the downslope driving force due to RWL drawdown significantly intensifies the lateral earth pressures exerted on the MRSPs.Conversely,the MRSPs possess a considerable reinforcement effect on the reservoir landslide,transforming the overall failure into a partial deformation and failure situated above and in front of the MRSPs.The mechanical transfer behavior observed in the MRSPs demonstrates a progressive alteration in relation to RWL fluctuations.As the RWL rises,the mechanical states among MRSPs exhibit a growing imbalance.The shear force transfer factor(i.e.the ratio of shear forces on pile of the n th row to that of the first row)increases significantly with the RWL drawdown.This indicates that the mechanical states among MRSPs tend toward an enhanced equilibrium.The insights gained from this study contribute to a more comprehensive understanding of the failure mechanisms of reservoir landslides and the mechanical behavior of MRSPs in reservoir banks.

Determination of the Pile Drivability Using Random Forest Optimized by Particle Swarm Optimization and Bayesian Optimizer

Driven piles are used in many geological environments as a practical and convenient structural component.Hence,the determination of the drivability of piles is actually of great importance in complex geotechnical applications.Conventional methods of predicting pile drivability often rely on simplified physicalmodels or empirical formulas,whichmay lack accuracy or applicability in complex geological conditions.Therefore,this study presents a practical machine learning approach,namely a Random Forest(RF)optimized by Bayesian Optimization(BO)and Particle Swarm Optimization(PSO),which not only enhances prediction accuracy but also better adapts to varying geological environments to predict the drivability parameters of piles(i.e.,maximumcompressive stress,maximum tensile stress,and blow per foot).In addition,support vector regression,extreme gradient boosting,k nearest neighbor,and decision tree are also used and applied for comparison purposes.In order to train and test these models,among the 4072 datasets collected with 17model inputs,3258 datasets were randomly selected for training,and the remaining 814 datasets were used for model testing.Lastly,the results of these models were compared and evaluated using two performance indices,i.e.,the root mean square error(RMSE)and the coefficient of determination(R2).The results indicate that the optimized RF model achieved lower RMSE than other prediction models in predicting the three parameters,specifically 0.044,0.438,and 0.146;and higher R^(2) values than other implemented techniques,specifically 0.966,0.884,and 0.977.In addition,the sensitivity and uncertainty of the optimized RF model were analyzed using Sobol sensitivity analysis and Monte Carlo(MC)simulation.It can be concluded that the optimized RF model could be used to predict the performance of the pile,and it may provide a useful reference for solving some problems under similar engineering conditions.

Longitudinal vibration characteristics of a tapered pipe pile considering the vertical support of surrounding soil and construction disturbance

This research is concentrated on the longitudinal vibration of a tapered pipe pile considering the vertical support of the surrounding soil and construction disturbance.First,the pile-soil system is partitioned into finite segments in the vertical direction and the Voigt model is applied to simulate the vertical support of the surrounding soil acting on the pile segment.The surrounding soil is divided into finite ring-shaped zones in the radial direction to consider the construction disturbance.Then,the shear complex stiffness at the pile-soil interface is derived by solving the dynamic equilibrium equation for the soil from the outermost to innermost zone.The displacement impedance at the top of an arbitrary pile segment is obtained by solving the dynamic equilibrium equation for the pile and is combined with the vertical support of the surrounding soil to derive the displacement impedance at the bottom of the upper adjacent segment.Further,the displacement impedance at the pile head is obtained based on the impedance function transfer technique.Finally,the reliability of the proposed solution is verified,followed by a sensitivity analysis concerning the coupling effect of the pile parameters,construction disturbance and the vertical support of the surrounding soil on the displacement impedance of the pile.

Effects of cement-enhanced soil on the ultimate lateral resistance of composite pile in clayey soil

The composite pile consisting of core-pile and surrounding cement-enhanced soil is a promising pile foundation in recent years.However,how and to what extent the cement-enhanced soil influences the ultimate lateral resistance has not been fully investigated.In this paper,the ultimate lateral resistance of the composite pile was studied by finite element limit analysis(FELA)and theoretical upper-bound analysis.The results of FELA and theoretical analysis revealed three failure modes of laterally loaded composite piles.The effects of the enhanced soil thickness,strength,and pile-enhanced soil interface characteristics on the ultimate lateral resistance were studied.The results show that increasing the enhanced soil thickness leads to a significant improvement on ultimate lateral resistance factor(N P),and there is a critical thickness beyond which the thickness no longer affects the N P.Increasing the enhanced soil strength induced 6.2%-232.6%increase of N P.However,no noticeable impact was detected when the enhanced soil strength was eight times higher than that of the natural soil.The maximum increment of N P is only 30.5%caused by the increase of interface adhesion factor(a).An empirical model was developed to calculate the N P of the composite pile,and the results show excellent agreement with the analytical results.

Aero-Hydro-Elastic-Servo Modeling and Dynamic Response Analysis of A Monopile Offshore Wind Turbine Under Different Operating Scenarios

This paper constructs a coupled aero-hydro-elastic-servo simulation framework for a monopile offshore wind turbine(OWT).In this framework,a detailed multi-body dynamics model of the monopile OWT including the gearbox,blades,tower and other components(nacelle,hub,bedplate,etc.)has been explicitly established.The effects of pile−soil interaction,controller and operational conditions on the turbine dynamic responses are studied systematically in time domain and frequency domain.The results show that(1)a comprehensive drivetrain model has the capability to provide a more precise representation of the complex dynamic characteristics exhibited by drivetrain components,which can be used as the basis for further study on the dynamic characteristics of the drivetrain.(2)The pile−soil interaction can influence the wind turbine dynamic responses,particularly under the parked condition.(3)The effect of the pile−soil interaction on tower responses is more significant than that on blade responses.(4)The use of the controller can substantially affect the rotor characteristics,which in turn influences the turbine dynamic responses.(5)The tower and blade displacements under the operational condition are much larger than those under the parked condition.The model and methodology presented in this study demonstrate potential for examining complex dynamic behaviors of the monopile OWTs.To ensure accuracy and precision,it is imperative to construct a detailed model of the wind turbine system,while also taking into account simulation efficiency.

NLR、PILE评分与PD-1抑制剂治疗晚期非小细胞肺癌的疗效及预后的相关性

目的 探讨中性粒细胞-淋巴细胞比值(neutrophil to lymphocyte ratio, NLR)、PILE评分与程序性细胞死亡蛋白-1(programmed cell death protein 1, PD-1)抑制剂治疗的晚期非小细胞肺癌(non-small cell lung cancer, NSCLC)患者疗效及预后的关系。方法 回顾性分析邵阳市中心医院在2020年6月至2021年12月收治的使用PD-1抑制剂治疗的109例晚期NSCLC患者的资料,计算患者治疗前的NLR、PILE评分,分析其与疗效及预后的相关性。结果 低NLR组比高NLR组有更高的疾病控制率(disease control rate, DCR)(P<0.05),PILE评分低分组较PILE评分高分组有更高的客观缓解率(objective response rate, ORR)和DCR(均P<0.05)。在多因素分析中,NLR、PILE评分是影响PFS的独立危险因素(均P<0.05)。结论 高NLR、高PILE评分与PD-1抑制剂治疗的晚期NSCLC患者的疗效更差有关,且高NLR、高PILE评分是患者预后不良的独立危险因素。

Innovative Techniques Unveiled in Advanced Sheet Pile Curtain Design

This thorough review explores the complexities of geotechnical engineering, emphasizing soil-structure interaction (SSI). The investigation centers on sheet pile design, examining two primary methodologies: Limit Equilibrium Methods (LEM) and Soil-Structure Interaction Methods (SSIM). While LEM methods, grounded in classical principles, provide valuable insights for preliminary design considerations, they may encounter limitations in addressing real-world complexities. In contrast, SSIM methods, including the SSI-SR approach, introduce precision and depth to the field. By employing numerical techniques such as Finite Element (FE) and Finite Difference (FD) analyses, these methods enable engineers to navigate the dynamics of soil-structure interaction. The exploration extends to SSI-FE, highlighting its essential role in civil engineering. By integrating Finite Element analysis with considerations for soil-structure interaction, the SSI-FE method offers a holistic understanding of how structures dynamically interact with their geotechnical environment. Throughout this exploration, the study dissects critical components governing SSIM methods, providing engineers with tools to navigate the intricate landscape of geotechnical design. The study acknowledges the significance of the Mohr-Coulomb constitutive model while recognizing its limitations, and guiding practitioners toward informed decision-making in geotechnical analyses. As the article concludes, it underscores the importance of continuous learning and innovation for the future of geotechnical engineering. With advancing technology and an evolving understanding of soil-structure interaction, the study remains committed to ensuring the safety, stability, and efficiency of geotechnical structures through cutting-edge design and analysis techniques.

Advanced Sheet Pile Curtain Design: Case Study of Cotonou East Corniche

This paper delves into the critical aspects of sheet pile walls in civil engineering, highlighting their versatility in soil protection, retention, and waterproofing, all while emphasizing sustainability and efficient construction practices. The paper explores two fundamental approaches to sheet pile design: limit equilibrium methods and numerical techniques, with a particular focus on finite element analysis. Utilizing the robust PLAXIS 2016 calculation code based on the finite element method and employing a simplified elastoplastic model (Mohr-Coulomb), this study meticulously models the interaction between sheet pile walls and surrounding soil. The research offers valuable insights into settlement and deformation patterns that adjacent buildings may experience during various construction phases. The central objective of this paper is to present the study’s findings and recommend potential mitigation measures for settlement effects on nearby structures. By unraveling the intricate interplay between sheet pile wall construction and neighboring buildings, the paper equips engineers and practitioners to make informed decisions that ensure the safety and integrity of the built environment. In the context of the Cotonou East Corniche development, the study addresses the limitations of existing software, such as RIDO, in predicting settlements and deformations affecting nearby buildings due to the substantial load supported by sheet pile walls. This information gap necessitates a comprehensive study to assess potential impacts on adjacent structures and propose suitable mitigation measures. The research underscores the intricate dynamics between sheet pile wall construction and its influence on the local environment. It emphasizes the critical importance of proactive engineering and vigilant monitoring in managing and mitigating potential hazards to nearby buildings. To mitigate these risks, the paper recommends measures such as deep foundations, ground improvement techniques, and retrofitting. The findings presented in this study contribute significantly to the field of civil engineering and offer invaluable insights into the multifaceted dynamics of construction-induced settlement. The study underscores the importance of continuous evaluation and coordination between construction teams and building owners to effectively manage the impacts of sheet pile wall construction on adjacent structures.

Construction Technology of Pile Foundation for Subway Tunnel Crossing Bridge

Urban infrastructure has become more complex with the rapid development of urban transportation networks.In urban environments with limited space,construction of facilities like subways and bridges may mutually influence each other,especially when subway construction requires passing under bridges.In such cases,pile foundation replacement technology is often necessary.However,this technology is highly specialized,with a lengthy and risky construction period,and high costs.Personnel must be proficient in key technical aspects to ensure construction quality.This article discusses the technical principle,construction process,and core technology of pile foundation replacement,along with the application of this technology in subway tunnel crossing bridge projects,supported by engineering examples for reference.

基于Pile单元改进模型的锚杆锚固角度效应数值模拟研究

为探究锚杆在不同锚固角度下的受力特征和作用机制,采用Pile单元改进模型建立具有不同锚固角度的锚固结构面数值模型,并开展一系列的单轴压缩数值试验,对锚杆的锚固角度效应进行了系统研究。结果表明:当锚固角较大时,锚固结构面试件加载过程分为4个阶段,而当锚固角较小时仅为3个阶段;随着锚固角的增加,峰值应力整体上先恒定后减小,弹性模量呈非线性降低;锚杆与试件力的相互作用主要分布在结构面与锚杆相交处以及锚杆两端;锚杆的显著变形和受力主要分布在结构面附近,大致为锚杆直径的3~4倍;随着锚固角的增大,锚杆轴力的贡献呈非线性减小,锚杆剪力的贡献呈线性增大,锚杆抗剪力呈非线性减小。

Study on the squeezing effect of open-ended pipe piles

During the installation of a pipe pile,the soil around the pile will be squeezed out. This paper deals with this squeezing effect of open-ended pipe piles using the cylindrical cavity expansion theory. The characteristics of soil with different tension and compression moduli and dilation are involved by applying the elastic theory with different moduli and logarithmic strain. The closed-form solutions of the radius of the plastic region,the displacement of the boundary between the plastic region and the elastic region and the expansion pressure on the external surface of the pipe piles are obtained. When obtaining these solutions,the soil plug in the open-ended pipe pile is considered by employing an incremental filling ratio to quantify the degree of soil plugging. Moreover,the effects of the ratio of tension and compression moduli,angle of dilation and incremental filling ratio on the radius of the plastic region and the expansion pressure on the external surface of the pipe pile are investigated. The parametric analyses show that it is necessary and important to consider the difference between the tension modulus and compression modulus,dilation angle and incremental filling ratio for studying the squeezing effect of open-ended pipe pile installation. It is concluded that the analytical solutions presented in this paper are suitable for studying the squeezing effect of open-ended pipe piles.

Seismic response comparison and sensitivity analysis of pile foundation in liquefiable and non-liquefiable soils

Case history investigations have shown that pile foundations are more critically damaged in liquefiable soils than non-liquefiable soils.This study examines the differences in seismic response of pile foundations in liquefiable and non-liquefiable soils and their sensitivity to numerical model parameters.A two-dimensional finite element(FE)model is developed to simulate the experiment of a single pile foundation centrifuge in liquefiable soil subjected to earthquake motions and is validated against real-world test results.The differences in soil-pile seismic response of liquefiable and non-liquefiable soils are explored.Specifically,the first-order second-moment method(FOSM)is used for sensitivity analysis of the seismic response.The results show significant differences in seismic response for a soil-pile system between liquefiable and non-liquefiable soil.The seismic responses are found to be significantly larger in liquefiable soil than in non-liquefiable soil.Moreover,the pile bending moment was mainly affected by the kinematic effect in liquefiable soil,while the inertial effect was more significant in non-liquefiable soil.The controlling parameters of seismic response were PGA,soil density,and friction angle in liquefiable soil,while the pile bending moment was mainly controlled by PGA,the friction angle of soil,and shear modulus of loose sand in non-liquefiable soil.

Combined load bearing capacity of rigid piles embedded in a crossanisotropic clay deposit using 3D finite element lower bound

In this study,an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition.The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium,equilibrium of shear and normal stresses along discontinuities,boundary conditions,yield function,and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure.A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment(V-H-M)space.The results of this study are compared and validated against three different cases including an isotropic lateral loading,anisotropic end bearing capacity,and a pile embedded in an isotropic soil deposit under general loading condition.A parametric study is conducted to evaluate the impact of different influencing factors.It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads,whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

Centrifuge tests for seismic response of single pile foundation supported wind turbines in sand influenced by earthquake history

This paper reports on two sets of centrifuge model tests of wind turbines in dry sand and saturated sand subjected to earthquake sequences.The wind turbine system is composed of a single pile foundation and a wind turbine.All tests were applied with liquefaction experiments and analysis projects(LEAP)waves to simplify the analysis.The objectives of the tests are to investigate:(1)the influence of earthquake history on the seismic response of wind turbines;(2)the influence of earthquake history on the dynamic pile-soil interaction;and(3)the influence of two different foundation types on the seismic response of wind turbines.The tests indicated that earthquake history has a significant influence on the natural frequency of the pile and the soil around the pile in the saturated sand,but has no obvious influence on the dry sand.The shear modulus of the soil and the acceleration amplification factor of the pile top in both tests increased and the maximum bending moment envelope of the single pile foundation shrunk.The stiffness of the p-y curve in saturated sand was increased by the earthquake history,while that in dry sand was not significantly affected.

Centrifuge and numerical modeling of h-type anti-slide pile reinforced soil-rock mixture slope

Due to the loose structure,high porosity and high permeability of soil-rock mixture slope,the slope is unstable and may cause huge economic losses and casualties.The h-type anti-slide pile is regarded as an effective means to prevent the instability of soilrock mixture slope.In this paper,a centrifuge model test was conducted to investigate the stress distribution of the h-type anti-slide pile and the evolution process of soil arching during the loading.A numerical simulation model was built based on the similar relationship between the centrifuge model and the prototype to investigate the influence factors of the pile spacing,anchored depth,and crossbeam stiffness,and some recommendations were proposed for its application.The results show that the bending moment distribution of the rear pile exhibits Wshaped,while for the front pile,its distribution resembles V-shaped.The soil arching evolution process during loading is gradually dissipated from bottom to top and from far to near.During the loading,the change of bending moment can be divided into three stages,namely,the stabilization stage,the slow growth stage,and the rapid growth stage.In engineering projects,the recommended values of the pile spacing,anchored depth,and crossbeam stiffness are 4.0d,2.0d,and 2.0EI,where d and EI are the diameter and bending stiffness of the h-type anti-slide pile respectively.