Mechanical response of bridge piles in high-steep slopes and sensitivity study

The bridge piles located in high-steep slopes not only endure the loads from superstructure, but also the residual sliding force as well as the resistance from the slope. By introducing the Winkler foundation theory, the mechanical model of piles-soils-slopes system was established, and the equilibrium differential equations of pile were derived. Moreover, an analytic solution for identifying the model parameters was provided by means of power series method. A project with field measurement was compared with the proposed method. It is indicated that the lateral loads have great influences on the pile, the steep slope effect is indispensable, and reasonable diameter of the pile could enhance the bending ability. The internal force and displacements of pile are largely based upon the horizontal loads applied on pile, especially in upper part.

Comprehensive evaluation of high-steep slope stability and optimal high-steep slope design by 3D physical modeling

High-steep slope stability and its optimal excavation design in Shuichang open pit iron mine were analyzed based on a large 3D physical simulation technique. An optimal excavation scheme with a relatively steeper slope angle was successfully implemented at the northwest wall between Nos. 4 and 5 exploration lines of Shuichang Iron Mine, taking into account the 3D scale effect. The phys-ico-mechanical properties of rock materials were obtained by laboratory tests conducted on sample cores from exploration drilling directly from the iron mine. A porous rock-like composite material was formed for the model, and the mechanical parameters of the material were assessed experimentally;specifically, the effect of water on the sample was quantitatively determined. We adopted an experimental setup using stiff modular applied static loading to carry out a visual excavation of the slope at a random depth. The setup was equipped with acous-tic emission （AE） sensors, and the experiments were monitored by crack optical acquirement, ground penetrating radar, and close-field pho-togrammetry to investigate the mechanisms of rock-mass destabilization in the high-steep slope. For the complex study area, the model re-sults indicated a clear correlation between the model＇s destabilization resulting from slope excavation and the collected monitoring informa-tion. During the model simulation, the overall angle of the slope increased by 1-6 degrees in different sections. Dramatically, the modeled excavation scheme saved over 80 million tons of rock from extraction, generating enormous economic and ecological benefits.

Deformation and failure of a high-steep slope induced by multi-layer coal mining

During underground mining,accurate revelation on the deformation and failure mechanisms of a high-steep slope under multi-layer mining conditions facilitates the prevention and control of geological disasters in mines.Numerical simulation based on discrete element theory can be used to explore the characteristics and mechanism of action of deformation and failure of a slope under complex geological and multi-layer mining conditions.By utilising PFC2 D(particle flow code) software,the deformation and failure characteristics of a high-steep slope in Faer Coal Mine in Guizhou Province,China were investigated.Additionally,the mechanism of influence of different numbers of mining layers on the deformation and failure of the high and steep slope was elucidated.The result showed that after the goaf passed by the slope toe,multi-layer mining aggravated the subsidence and deformation of the slope toe:the slope toppled forward as it sank.The toppling of the slope changed the slope structures:the strata in the front of the slope were transformed from anti-dip to down-dip features.Extruded by collapsedtoppled rock mass,the slope toe and the rock mass located in the lower part of the slope toe generally exhibited a locking effect on the slope.Multi-layer mining degraded the overall stability of the slope,in that the total displacement of the slope was much greater than the total mining thickness of the coal seams.Based on the aforementioned research,ideas for preventing and controlling geological disasters during mining operations under a high-steep slope were proposed.

Pre-stressed anchoring beam technique applicable in the reinforcement of high-steep slopes

During the construction of some large-scale rock engineering,high-steep slopes and insufficient slope stability induced by unloading fissures are often encountered.For the reinforcement of these slopes,some techniques(including conventional pre-stressed anchoring cable and unconventional anchoring hole)are usually utilized,however,having several obvious defects.Thus,it is very difficult for a designer to design an efficient reinforcement scheme for the high-steep slopes.For this reason,the authors develop the pre-stressed anchoring beam technique,in which tensile capacity of pre-stressed structures are fully utilized.It is analyzed that the new technique is characterized by multi-functions,including engineering investigation,efficient reinforcement,drainage,monitoring and urgent strength supplement,and hoped to be extensively applicable in the reinforcement of high-steep slopes.

A method to interpret fracture aperture of rock slope using adaptive shape and unmanned aerial vehicle multi-angle nap-of-the-object photogrammetry

The aperture of natural rock fractures significantly affects the deformation and strength properties of rock masses,as well as the hydrodynamic properties of fractured rock masses.The conventional measurement methods are inadequate for collecting data on high-steep rock slopes in complex mountainous regions.This study establishes a high-resolution three-dimensional model of a rock slope using unmanned aerial vehicle(UAV)multi-angle nap-of-the-object photogrammetry to obtain edge feature points of fractures.Fracture opening morphology is characterized using coordinate projection and transformation.Fracture central axis is determined using vertical measuring lines,allowing for the interpretation of aperture of adaptive fracture shape.The feasibility and reliability of the new method are verified at a construction site of a railway in southeast Tibet,China.The study shows that the fracture aperture has a significant interval effect and size effect.The optimal sampling length for fractures is approximately 0.5e1 m,and the optimal aperture interpretation results can be achieved when the measuring line spacing is 1%of the sampling length.Tensile fractures in the study area generally have larger apertures than shear fractures,and their tendency to increase with slope height is also greater than that of shear fractures.The aperture of tensile fractures is generally positively correlated with their trace length,while the correlation between the aperture of shear fractures and their trace length appears to be weak.Fractures of different orientations exhibit certain differences in their distribution of aperture,but generally follow the forms of normal,log-normal,and gamma distributions.This study provides essential data support for rock and slope stability evaluation,which is of significant practical importance.

Experimental study on instability mechanism and critical intensity of rainfall of high-steep rock slopes under unsaturated conditions

Two critical factors,namely intense precipitation and intricate excavation,can trigger rock mass disasters in mining operations.In this study,an indoor rainfall system was developed to precisely regulate the flow and intensity of precipitation.A large-scale model experiment was conducted on a self-designed physical simulation experiment platform to investigate the failure and instability of high-steep rock slopes under unsaturated conditions.The real-time reproduction of the progressive failure process in high-steep rock slopes enabled the determination of the critical rainfall intensity and revealed the mechanism underlying slope instability.Experiment results indicated that rainfall may be the primary factor contributing to rock mass instability,while continuous pillar mining exacerbates the extent of rock mass failure.The critical failure stage of high-steep rock slopes occurs at a rainfall intensity of 40 mm/h,whereas a rainfall exceeding 50 mm can induce critical instability and precipitation reaching up to 60 mm will result in slope failure.The improved region growing segmentation method(IRGSM)was subsequently employed for image recognition of rock mass deformation in underground mines.Herein an error comparison with the simple linear iterative cluster(SLIC)superpixel method and the original region growing segmentation method(ORGSM)showed that the average identification error in the X and Y directions by the method was reduced significantly(1.82%and 1.80%in IRGSM;4.70%and 6.26%in SLIC;9.45%and 12.40%in ORGSM).Ultimately,the relationship between rainfall intensity and failure probability was analyzed using the Monte Carlo method.Moreover,the stability assessment criteria of rock slope under unsaturated condition were quantitatively and accurately evaluated.

Modified Sadowski formula-based model for the slope shape amplification effect under multistage slope blasting vibration

Blasting operations,which are crucial to open-pit mine production due to their simplicity and efficiency,require precise control through accurate vibration velocity calculations.The conventional Sadowski formula mainly focuses on blast center distance but neglects the amplification effect of blasting vibration waves by terraced terrain,from which the calculated blasting vibration velocities are smaller than the actual values,affecting the safety of the project.To address this issue,our model introduces the influences of slope and time into Sadowski formula to measure safety through blast vibration displacement.In the northern section of the open-pit quartz mine in Jinchang City,Gansu Province,China,the data of a continuous blasting slope project are referred to.Our findings reveal a noticeable vibration amplification effect during blasting when a multi-stage slope platform undergoes a sudden cross-sectional change near the upper overhanging surface.The amplification vibration coefficient increases with height,while vibration waves within rocks decrease from bottom to top.Conversely,platforms without distinct crosssectional changes exhibit no pronounced amplification during blasting.In addition,the vibration intensity decreases with distance as the rock height difference change propagates.The results obtained by the proposed blast vibration displacement equation incorporating slope shape influence closely agree with real-world scenarios.According to Pearson correlation coefficient(PPMCC)analysis,the average accuracy rate of our model is 88.84%,which exceeds the conventional Sadowski formula(46.92%).

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope.The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope.The objective function of the mathematical programming problem is such as to optimize a boundary load,which is known as the limit load,resembling the ultimate bearing capacity of a strip footing.While focusing on the vertical slope,parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio,the dimensionless height ratio,and the dimensionless rock strength ratio.A comprehensive set of design charts is presented,and failure envelopes shown with the results explained in terms of three identified failure mechanisms,i.e.the face,the toe,and the Prandtl-type failures.These novel results can be used with great confidence in design practice,in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Infiltration,runoff,and slope stability behaviors of infinite slope with macropores based on an improved Green–Ampt model

Infiltration–runoff–slope instability mechanism of macropore slope under heavy rainfall is unclear.This paper studied its instability mechanism with an improved Green–Ampt(GA)model considering the dual-porosity(i.e.,matrix and macropore)and ponding condition,and proposed the infiltration equations,infiltration–runoff coupled model,and safety factor calculation method.Results show that the infiltration processes of macropore slope can be divided into three stages,and the proposed model is rational by a comparative analysis.The wetting front depth of the traditional unsaturated slope is 17.2%larger than that of the macropore slope in the early rainfall stage and 27%smaller than that of the macropore slope in the late rainfall stage.Then,macropores benefit the slope stability in the early rainfall but not in the latter.Macropore flow does not occur initially but becomes pronounced with increasing rainfall duration.The equal depth of the wetting front in the two domains is regarded as the onset criteria of macropore flow.Parameter analysis shows that macropore flow is delayed by increasing proportion of macropore domain(ω_(f)),whereas promoted by increasing ratio of saturated permeability coefficients between the two domains(μ).The increasing trend of ponding depth is sharp at first and then grows slowly.Finally,when rainfall duration is less than 3 h,ωf andμhave no significant effect on the safety factor,whereas it decreases with increasingωf and increases with increasingμunder longer duration(≥3 h).With the increase ofω_(f),the slope maximum instability time advances by 10.5 h,and with the increase ofμ,the slope maximum instability time delays by 3.1 h.

Stability analysis of loose accumulation slopes under rainfall:case study of a high‑speed railway in Southwest China

The high and steep slopes along a high-speed railway in the mountainous area of Southwest China are mostly composed of loose accumulations of debris with large internal pores and poor stability,which can easily induce adverse geological disasters under rainfall conditions.To ensure the smooth construction of the high-speed railway and the subsequent safe operation,it is necessary to master the stability evolution process of the loose accumulation slope under rainfall.This article simulates rainfall using the finite element analysis software’s hydromechanical coupling module.The slope stability under various rainfall situations is calculated and analysed based on the strength reduction method.To validate the simulation results,a field monitoring system is established to study the deformation characteristics of the slope under rainfall.The results show that rainfall duration is the key factor affecting slope stability.Given a constant amount of rainfall,the stability of the slope decreases with increasing duration of rainfall.Moreover,when the amount and duration of rainfall are constant,continuous rainfall has a greater impact on slope stability than intermittent rainfall.The setting of the field retaining structures has a significant role in improving slope stability.The field monitoring data show that the slope is in the initial deformation stage and has good stability,which verifies the rationality of the numerical simulation method.The research results can provide some references for understanding the influence of rainfall on the stability of loose accumulation slopes along high-speed railways and establishing a monitoring system.

44%of steep slope cropland in Europe vulnerable to drought

Steep-slope cropland plays a vital role in food production,economic development,ecosystem diversity,and Eu-ropean cultural heritage.However,these systems are susceptible to extreme weather events.The 2022 summer drought significantly impacted European agriculture,but the specific effects on steep-slope crops remain uncer-tain.Clarifying this is essential for comprehending similar future events and for implementing effective water management strategies to ensure the sustainability of steep-slope agriculture and associated ecosystem services.This study quantitatively analyzes the spatial distribution of twelve major European steep-slope(>12%)crops and assesses agricultural drought severity during the 2022 events using open-access spatial data.The satellite-based Vegetation Health Index(VHI)is utilized to identify critical hotspots.Results show that olive grove is the most widespread crop in steep slope agriculture(34%of total area),followed by wheat(24%),maize(16%),and vineyard(11%).Almost half of the steep-slope agriculture in Europe suffered drought during summer 2022.Vineyards were hardest affected at 79%,primarily in northern Portugal,northern Spain,southern France,and central Italy.Sunflowers followed at 62%,mainly in Spain,central Italy,southern France,and northern Roma-nia.Olive groves ranked third at 59%,with the most impact in northern Portugal,southern and central Spain,and southern Italy.Maize was also significantly affected at 54%.In this paper,we therefore highlight the need to increase steep-slope agriculture resilience by improving water management and promoting sustainable land practices.

Slope-climbing of cropland and its effects in China

In recent decades,the spatio-temporal patterns of China’s croplands have been reshaped by disturbances from anthropogenic activities,with complex changes in the topographic characteristics of croplands.Slope-climbing of croplands(SCCL)is an important issue that threatens sustainable agricultural development.While providing land with prominent location advantages,SCCL weakens the water and fertilizer retention capacity for cropland,intensifies various geological disasters,and adversely affects the ecological environment and food yield of these croplands.It is crucial to determine the spatio-temporal variation features and effects of SCCL in China to formulate more accurate cropland protection policies and to maintain food security;however,the current lack of relevant studies is detrimental for capturing trends in cropland resources and sustainable cropland use.In this study,we constructed a multi-scale slope spectrum for cropland and total terrain to explore the spatial differences and trends of SCCL from a three-dimensional view.We evaluated the natural and socioeconomic effects of SCCL in China from multiple perspectives.Results indicate that the proportion of cropland with slopes below 2°,5°,and 6°in China decreased by 0.43%,0.47%,and 0.50%from 1980 to 2020,respectively.SCCL became apparent during 1980-1990 and 2010-2020,especially over the recent decade.The cropland climbing index(CCI)and upper limited slope change(ULSC)to measure the spatio-temporal pattern of SCCL were 0.99%and 1.17°,respectively,during 2010-2020.At the agricultural regional scale,the SCCL was also concentrated in 1980-1990 and 2010-2020,and it is more pronounced in the southern areas.The proportion of provinces and prefecture-level cities with high-intensity SCCL during 1980-2020 were 87.10%and 49.73%,respectively.SCCL was comparatively more pronounced and broader from 2010 to 2020.During this period,17.84%of prefecture-level cities had no SCCL,and the average CCI for all prefecture-level cities peaked at 1.62%.In this study,we also evaluated the pros and cons of SCCL and provided targeted suggestions for decision makers and farmers to refine cropland protection policy systems and further develop the sustainable use of croplands.

Evolution model and failure mechanisms of rainfall-induced cracked red clay slopes:insights from Xinshao County,China

Red clay landslides are widely distributed worldwide,resulting in severe loss of life and property.Although rainfall-induced red clay slopes have received extensive attention,the role of cracks in the evolutionary process of red clay slopes and their connection to failure mechanisms is still poorly understood.A comprehensive approach integrating field investigation,laboratory tests,and numerical simulations was conducted to study the 168 red clay landslides in Xinshao County,China.The results show that red clay is prone to forming cracks at high moisture content due to its low swelling and high shrinkage properties.The failure mode of red clay slopes can be summarized in three stages:crack generation,slope excavation,and slope failure.Furthermore,the retrospective analysis and numerical simulations of the typical landslide in Guanchong indicated that intense rainfall primarily impacts the shallow layer of soil within approximately 0.5 m on the intact slope.However,cracks change the pattern of rainfall infiltration in the slope.Rainwater infiltrates rapidly through the preferential channels induced by the cracks rather than uniformly and slowly from the slope surface.This results in a significant increase in both the depth of infiltration and the saturated zone area of the cracked slope,reaching 3.8 m and 36.2 m^(2),respectively.Consequently,the factor of safety of the slope decreases by 13.4%compared to the intact slope,ultimately triggering landslides.This study can provide valuable insights into understanding the failure mechanisms of red clay slopes in China and other regions with similar geological settings.

Stability assessment of tree ring growth of Pinus armandii Franch in response to climate change based on slope directions at the Lubanling in the Funiu Mountains,China

Global warming will affect growth strategies and how trees will adapt.To compare the response of tree radial growth to climate warming in different slope directions,samples of Pinus armandii Franch were collected and treering chronologies developed on northern and western slopes from the Lubanling in the Funiu Mountains.Correlation analyses showed that two chronologies were mainly limited by temperatures in the previous June–August and the combination of temperatures and moisture in the current May–July.The difference of the climate response to slopes was small but not negligible.Radial growth of the LBL01 site on the northern slope was affected by the combined maximum and minimum temperatures,while that of the LBL02 site was affected by maximum temperatures.With regards to moisture,radial growth of the trees on the north slope was influenced by the relative humidity in the current May–July,while on the western slope,it was affected by the relative humidity in the previous June–August,the current May–July and the precipitation in the current May–July.With the change in climate,the effects of the main limiting factors on growth on different slopes were visible to a certain extent,but the differences in response of trees on different slopes gradually decreased,which might be caused by factors such as different slope directions and the change in diurnal temperature range.These results may provide information for forest protection and ecological construction in this region,and a scientific reference for future climate reconstruction.

Bio-cementation for tidal erosion resistance improvement of foreshore slopes based on microbially induced magnesium and calcium precipitation

In most coastal and estuarine areas,tides easily cause surface erosion and even slope failure,resulting in severe land losses,deterioration of coastal infrastructure,and increased floods.The bio-cementation technique has been previously demonstrated to effectively improve the erosion resistance of slopes.Seawater contains magnesium ions(Mg^(2+))with a higher concentration than calcium ions(Ca^(2+));therefore,Mg^(2+)and Ca^(2+)were used together for bio-cementation in this study at various Mg^(2+)/Ca^(2+)ratios as the microbially induced magnesium and calcium precipitation(MIMCP)treatment.Slope angles,surface strengths,precipitation contents,major phases,and microscopic characteristics of precipitation were used to evaluate the treatment effects.Results showed that the MIMCP treatment markedly enhanced the erosion resistance of slopes.Decreased Mg^(2+)/Ca^(2+)ratios resulted in a smaller change in angles and fewer soil losses,especially the Mg^(2+)concentration below 0.2 M.The decreased Mg^(2+)/Ca^(2+)ratio achieved increased precipitation contents,which contributed to better erosion resistance and higher surface strengths.Additionally,the production of aragonite would benefit from elevated Mg^(2+)concentrations and a higher Ca^(2+)concentration led to more nesquehonite in magnesium precipitation crystals.The slopes with an initial angle of 53°had worse erosion resistance than the slopes with an initial angle of 35°,but the Mg^(2+)/Ca^(2+)ratios of 0.2:0.8,0.1:0.9,and 0:1.0 were effective for both slope stabilization and erosion mitigation to a great extent.The results are of great significance for the application of MIMCP to improve erosion resistance of foreshore slopes and the MIMCP technique has promising application potential in marine engineering.

An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes

Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angleγlim.However,the assignment ofγlim is currently used generally based on an empirical criterion.This study aims to propose an approach for determining the value ofγlim in deterministic and probabilistic kinematic planar sliding analysis.A new perspective is presented to reveal thatγlim essentially influences the probability of forming a potential planar sliding block.The procedure to calculate this probability is introduced using the block theory method.It is found that the probability is correlated with the number of discontinuity sets presented in rock masses.Thus,different values ofγlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses;whereas a fixed value ofγlim is commonly assigned to different types of rock masses in traditional method.Finally,an engineering case was used to compare the proposed and traditional kinematic analysis methods.The error rates of the traditional method vary from 45%to 119%,while that of the proposed method ranges between 1%and 17%.Therefore,it is likely that the proposed method is superior to the traditional one.

Investigation of the block toppling evolution of a layered model slope by centrifuge test and discrete element modeling

Primary toppling usually occurs in layered rock slopes with large anti-dip angles.In this paper,the block toppling evolution was explored using a large-scale centrifuge system.Each block column in the layered model slope was made of cement mortar.Some artificial cracks perpendicular to the block column were prefabricated.Strain gages,displacement gages,and high-speed camera measurements were employed to monitor the deformation and failure processes of the model slope.The centrifuge test results show that the block toppling evolution can be divided into seven stages,i.e.layer compression,formation of major tensile crack,reverse bending of the block column,closure of major tensile crack,strong bending of the block column,formation of failure zone,and complete failure.Block toppling is characterized by sudden large deformation and occurs in stages.The wedge-shaped cracks in the model incline towards the slope.Experimental observations show that block toppling is mainly caused by bending failure rather than by shear failure.The tensile strength also plays a key factor in the evolution of block toppling.The simulation results from discrete element method(DEM)is in line with the testing results.Tensile stress exists at the backside of rock column during toppling deformation.Stress concentration results in the fragmented rock column and its degree is the most significant at the slope toe.

Failure evaluation and control factor analysis of slope block instability along traffic corridor in Southeastern Tibet

The instability of slope blocks occurred frequently along traffic corridor in Southeastern Tibet(TCST),which was primarily controlled by the rock mass structures.A rapid method evaluating the control effects of rock mass structures was proposed through field statistics of the slopes and rock mass structures along TCST,which combined the stereographic projection method,modified M-JCS model,and limit equilibrium theory.The instabilities of slope blocks along TCST were then evaluated rapidly,and the different control factors of instability were analyzed.Results showed that the probabilities of toppling(5.31%),planar(16.15%),and wedge(35.37%)failure of slope blocks along TCST increased sequentially.These instability modes were respectively controlled by the anti-dip joint,the joint parallel to slope surface with a dip angle smaller than the slope angle(singlejoint),and two groups of joints inclined out of the slope(double-joints).Regarding the control effects on slope block instability,the stabilization ability of doublejoints(72.7%),anti-dip joint(67.4%),and single-joint(57.6%)decreased sequentially,resulting in different probabilities of slope block instability.Additionally,nearby regional faults significantly influenced the joints,leading to spatial heterogeneity and segmental clustering in the stabilization ability provided by joints to the slope blocks.Consequently,the stability of slope blocks gradually weakened as they approached the fault zones.This paper can provide guidance and assistance for investigating the development characteristics of rock mass structures and the stability of slope blocks.

Stability assessment of tree ring growth of Pinus armandii Franch in response to climate change based on slope directions at the Lubanling in the Funiu Mountains,China

Global warming will affect growth strategies and how trees will adapt.To compare the response of tree radial growth to climate warming in different slope directions,samples of Pinus armandii Franch were collected and tree-ring chronologies developed on northern and western slopes from the Lubanling in the Funiu Mountains.Correlation analyses showed that two chronologies were mainly limited by temperatures in the previous June-August and the com-bination of temperatures and moisture in the current May-July.The difference of the climate response to slopes was small but not negligible.Radial growth of the LBLO1 site on the northern slope was affected by the combined maximum and minimum temperatures,while that of the LBLO2 site was affected by maximum temperatures.With regards to moisture,radial growth of the trees on the north slope was influenced by the relative humidity in the current May-July,while on the western slope,it was affected by the relative humidity in the previous June-August,the current May-July and the precipitation in the current May-July.With the change in climate,the effects of the main limiting factors on growth on different slopes were visible to a certain extent,but the differences in response of trees on different slopes gradually decreased,which might be caused by factors such as different slope directions and the change in diurnal temperature range.These results may provide information for forest protection and ecological construction in this region,and a scientific reference for future climate reconstruction.

A semi-infinite beam theoretical model on predicting rock slope subsidence induced by underground mining

When the mining goaf is close to the cliff,rock slope subsidence induced by underground mining is significantly affected by its boundary conditions.In this study,an analytical method is proposed by considering the key strata as a semi-infinite Euler-Bernoulli beam rested on a Winkler foundation with a local subsidence area.The analytical solutions of deflection are derived by analyzing the boundary and continuity conditions of the cliff.Then,the analytical solutions are verified by the results from experimental tests,FEM and InSAR,respectively.After that,the influence of changing parameters on deflections is studied with sensitivity analysis.The results show that the distance between goaf and cliff significantly affects the deflection of semi-infinite beam.The response of semi-infinite beam is obviously determined by the length of goaf and the bending stiffness of beam.The comparisons between semi-infinite beam and infinite beam illustrate the ascendancy of the improved model in such problems.