A Calculation Method of Double Strength Reduction for Layered Slope Based on the Reduction of Water Content Intensity

The calculation of the factor of safety(FOS)is an important means of slope evaluation.This paper proposed an improved double strength reductionmethod(DRM)to analyze the safety of layered slopes.The physical properties of different soil layers of the slopes are different,so the single coefficient strength reduction method(SRM)is not enough to reflect the actual critical state of the slopes.Considering that the water content of the soil in the natural state is the main factor for the strength of the soil,the attenuation law of shear strength of clayey soil changing with water content is fitted.This paper also establishes the functional relationship between different reduction coefficients.Then,a USDFLD subroutine is programmed using the secondary development function of finite element software.Controlling the relationship between field variables and calculation time realizes double strength reduction applicable to the layered slope.Finally,by comparing the calculation results of different examples,it is proved that the stress and displacement distribution of the critical slope state obtained by the improved method is more realistic,and the calculated safety factor is more reliable.The newly proposedmethod considers the difference of intensity attenuation between different soil layers under natural conditions and avoids the disadvantage of the strength reduction method with uniform parameters,which provides a new idea and method for stability analysis of layered and complex slopes.

Slope analysis based on local strength reduction method and variable-modulus elasto-plastic model

Employing an ideal elasto-plastic model,the typically used strength reduction method reduced the strength of all soil elements of a slope.Therefore,this method was called the global strength reduction method(GSRM).However,the deformation field obtained by GSRM could not reflect the real deformation of a slope when the slope became unstable.For most slopes,failure occurs once the strength of some regional soil is sufficiently weakened; thus,the local strength reduction method(LSRM)was proposed to analyze slope stability.In contrast with GSRM,LSRM only reduces the strength of local soil,while the strength of other soil remains unchanged.Therefore,deformation by LSRM is more reasonable than that by GSRM.In addition,the accuracy of the slope's deformation depends on the constitutive model to a large degree,and the variable-modulus elasto-plastic model was thus adopted.This constitutive model was an improvement of the Duncan–Chang model,which modified soil's deformation modulus according to stress level,and it thus better reflected the plastic feature of soil.Most importantly,the parameters of the variable-modulus elasto-plastic model could be determined through in-situ tests,and parameters determination by plate loading test and pressuremeter test were introduced.Therefore,it is easy to put this model into practice.Finally,LSRM and the variable-modulus elasto-plastic model were used to analyze Egongdai ancient landslide.Safety factor,deformation field,and optimal reinforcement measures for Egongdai ancient landslide were obtained based on the proposed method.

A strength reduction method based on double reduction parameters and its application

In the traditional strength reduction method,the cohesion and the friction angle adopt the same reduction parameter,resulting in equivalent proportional reduction.This method does not consider the different effects of the cohesion and friction angle on the stability of the same slope and is defective to some extent.Regarding this defect,a strength reduction method based on double reduction parameters,which adopts different reduction parameters,is proposed.The core of the double-parameter reduction method is the matching reduction principle of the slope with different angles.This principle is represented by the ratio of the reduction parameter of the cohesion to that of the friction angle,described as η.With the increase in the slopeangle,ηincreases; in particular,when the slope angle is 45°,tηis 1.0.Through the matching reduction principle,different safety margin factors can be calculated for the cohesion and friction angle.In combination with these two safety margin factors,a formula for calculating the overall safety factor of the slope is proposed,reflecting the different contributions of the cohesion and friction angle to the slope stability.Finally,it is shown that the strength reduction method based on double reduction parameters acquires a larger safety factor than the classic limit equilibrium method,but the calculation results are very close to those obtained by the limit equilibrium method.

Limit analysis of vertical anti-pulling screw pile group under inclined loading on 3D elastic-plastic finite element strength reduction method

Based on the functional theory, catastrophe theory, simultaneity principle and the idea of strength reduction method （SRM）, the bearing capacity functional anti SRM of pile group foundation were established, and the criteria of ultimate load and the concept of safety storage coefficient （Css） were advanced. The inclined ultimate loads by the static loading test, load increment method （LIM） and SRM are compared. Theoretically, the ultimate load of piles does not change with the loading levels when it is calculated by SRM. When the one strength reduction parameter is applied in the calculation boundary, there are calculating errors because the bearing capacity action of soils happened in the finite zone. The inclined 10adings are 108, 132 and 144 kN, and SSC are 1.07, 0.94 and 0.79, respectively, so the calculation values of ultimate loads are about 115.56, 124.08 and 113.76 kN, respectively. The error between calculations and observation values is less than 6%. But .the error between calculations of LIM and observations is 20%. Because of the effect of inclined loading, the push-rotation phenomenon of screw pile group appears. Under this testing, the ultimate bearing capacity of piles is mostly determined by the horizontal ultimate bearing capacity, and the effect of the vertical component of inclined load should also be considered.

Strength reduction method for slope based on a ubiquitous-joint criterion and its application

In order to expand the application of strength reduction methods with the ubiquitous-joint criterion, the corresponding program is compiled using FLAC3D software. A procedure for strength reduction in the ubiquitous-joint criterion is proposed to study the safety factor of slopes as well as the relationships of the bedding plane inclination angle β and the safety factor F. The results show that： 1） for the bedding rock slope, the various failure modes cause different variations of the safety factor F; 2） a bed- ding rock slope can be divided into two types by the angle between the bedding plane inclination and slope surface inclination a; when a_〈45~, the bedding slope can be strictly defined as the subsequent bedding rock slope; when 45°〈α〈90°, the bedding slope is defined as an oblique bedding slope; 3） for bedding rock slopes, the safety factor increases with an increase in a; for inverse bed- ding slopes, when the bedding plane inclination angle fl is small, the safety factor F of the slope increases at first, then decreases with an increase in a; when β is large, the safety factor F increases with an increase in α.

Application of strength reduction method to dynamic anti-sliding stability analysis of high gravity dam with complex dam foundation

Considering that there are some limitations in analyzing the anti-sliding seismic stability of dam-foundation systems with the traditional pseudo-static method and response spectrum method, the dynamic strength reduction method was used to study the deep anti-sliding stability of a high gravity dam with a complex dam foundation in response to strong earthquake-induced ground action. Based on static anti-sliding stability analysis of the dam foundation undertaken by decreasing the shear strength parameters of the rock mass in equal proportion, the seismic time history analysis was carried out. The proposed instability criterion for the dynamic strength reduction method was that the peak values of dynamic displacements and plastic strain energy change suddenly with the increase of the strength reduction factor. The elasto-plastic behavior of the dam foundation was idealized using the Drucker-Prager yield criterion based on the associated flow rule assumption. The result of elasto-plastic time history analysis of an overflow dam monolith based on the dynamic strength reduction method was compared with that of the dynamic linear elastic analysis, and the reliability of elasto-plastic time history analysis was confirmed. The results also show that the safety factors of the dam-foundation system in the static and dynamic cases are 3.25 and 3.0, respectively, and that the F2 fault has a significant influence on the anti-sliding stability of the high gravity dam. It is also concluded that the proposed instability criterion for the dynamic strength reduction method is feasible.

New method of designing anti-slide piles——the strength reduction FEM

At present,the thrust of an anti-slide pile can be worked out with some calculation methods. However,the resistance in front of the pile,the distributions of resistance and thrust,and appropriate pile length cannot be easily obtained. In this paper,the authors applied the strength-reduction finite element method (FEM) to several design cases of anti-slide piles. Using this method,it is possible to take the pile-soil interactions into consideration,obtain reasonable resistance in front of pile and the distributions of thrust and resistance,and reasonable lengths of anti-slide piles. In particular,the thrust and resistance imposed on embedded anti-slide piles can be calculated and composite anti-slide pile structures such as anchored piles and braced piles can be optimized. It is proved through the calculation examples that this method is more reliable and economical in the design of anti-slide pile.

A case study of multi-seam coal mine entry stability analysis with strength reduction method

In this paper,the advantage of using numerical models with the strength reduction method(SRM) to evaluate entry stability in complex multiple-seam conditions is demonstrated.A coal mine under variable topography from the Central Appalachian region is used as a case study.At this mine,unexpected roof conditions were encountered during development below previously mined panels.Stress mapping and observation of ground conditions were used to quantify the success of entry support systems in three room-and-pillar panels.Numerical model analyses were initially conducted to estimate the stresses induced by the multiple-seam mining at the locations of the affected entries.The SRM was used to quantify the stability factor of the supported roof of the entries at selected locations.The SRM-calculated stability factors were compared with observations made during the site visits,and the results demonstrate that the SRM adequately identifies the unexpected roof conditions in this complex case.It is concluded that the SRM can be used to effectively evaluate the likely success of roof supports and the stability condition of entries in coal mines.

A New Criterion for Defining Inhomogeneous Slope Failure Using the Strength Reduction Method

A new variational method treating the system as a whole with rigorous mathematical and physical derivation was presented in this paper.Combined with classical and engineering examples,variational energy expressions of slopes were derived.In addition,the calculation programs were written in the FISH language set in FLAC3D(fast Lagrangian analysis of continua in three dimensions)software.Factors of safety(FOSs)of the models were determined by the variational method based on the strength reduction method(SRM)and then compared with other criteria or methods.The result showed that the variational method reflected the process of slope plasticity and failure uniformly and was feasible to analyze the stability of inhomogeneous slopes.The method was applicable to both two-dimensional and three-dimensional heterogeneous slopes.The small error with other criteria or methods also showed the accuracy of this method.This method unified other criteria,avoided the artificial error of other criteria,and provided a logical derivation for the instability of heterogeneous slope.This method considered the system as a whole and avoided the shortcomings of the general method of one-sided instability analysis.The proposed method is of great significance as it considers the coupling effect of stress and strain of materials and gives the mechanical basis for the instability of complex slopes.

Strength reduction and step-loading finite element approaches in geotechnical engineering

The finite element limit analysis method has the advantages of both numerical and traditional limit equilibrium techniques and it is particularly useful to geotechnical engineering.This method has been developed in China,following well-accepted international procedures,to enhance understanding of stability issues in a number of geotechnical settings.Great advancements have been made in basic theory,the improvement of computational precision,and the broadening of practical applications.This paper presents the results of research on（1） the efficient design of embedded anti-slide piles,（2） the stability analysis of reservoir slopes with strength reduction theory,and（3） the determination of the ultimate bearing capacity of foundations using step-loading FEM（overloading）.These three applications are evidence of the design improvements and benefits made possible in geotechnical engineering by finite element modeling.

A new double reduction method for slope stability analysis

The core of strength reduction method(SRM) involves finding a critical strength curve that happens to make the slope globally fail and a definition of factor of safety(FOS). A new double reduction method, including a detailed calculation procedure and a definition of FOS for slope stability was developed based on the understanding of SRM. When constructing the new definition of FOS, efforts were made to make sure that it has concise physical meanings and fully reflects the shear strength of the slope. Two examples, slopes A and B with the slope angles of 63° and 34° respectively, were given to verify the method presented. It is found that, for these two slopes, the FOSs from original strength reduction method are respectively 1.5% and 38% higher than those from double reduction method. It is also found that the double reduction method predicts a deeper potential slide line and a larger slide mass. These results show that on one hand, the double reduction method is comparative to the traditional methods and is reasonable, and on the other hand, the original strength reduction method may overestimate the safety of a slope. The method presented is advised to be considered as an additional option in the practical slope stability evaluations although more useful experience is required.

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.

Application of dynamic analysis of strength reduction in the slope engineering under earthquake

At present,the methods of analyzing the stability of slope under earthquake are not accurate and reasonable because of some limitations. Based on the real dynamic tensile-shear failure mechanism of slope,the paper proposes dynamic analysis of strength reduction FEM (finite element method) and takes the reduction of shear strength parameters and tensile strength parameters into consideration. And it comprehensively takes the transfixion of the failure surface,the non-convergence of calculation and mutation of displacement as the criterion of dynamic instability and failure of the slope. The strength reduction factor under limit state is regarded as the dynamic safety factor of the slope under earthquake effect and its advantages are introduced. Finally,the method is applied in the seismic design of anchors supporting and anti-slide pile supporting of the slope. Calculation examples show that the application of dynamic analysis of strength reduction is feasible in the seismic design of slope engineering,which can consider dynamic interaction of supporting structure and rock-soil mass. Owing to its preciseness and great advantages,it is a new method in the seismic design of slope supporting.

Reinforcement strength reduction in FEM for mechanically stabilized earth structures

The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the strengths of the reinforcement members and soils are reduced with the same factor. While using the SRM, only soil strength is reduced during the calculation of the factor of safety. This causes inconsistence in calculating the factor of safety of the MSE structures. To overcome this, an iteration method is proposed to consider the strength reduction of the reinforcements in SRM. The method is demonstrated by using PLAXIS, a finite element software. The results show that the factor of safety converges after a few iterations. The reduction of strength has different effects on the factor of safety depending on the properties of the reinforcements and the soil, and failure modes.

基于均匀化理论与上限分析的膨胀土滑坡稳定性分析

在膨胀土和滑坡共同作用下,隧道洞口段施工更容易引发地表开裂甚至滑坡等工程灾害,在隧道内采用微型桩群防治滑坡比抗滑桩具有优势。本文基于均匀化理论与上限分析对某高速公路隧道洞口段膨胀土滑坡的稳定性进行计算,并评价微型桩群和削方卸载不同组合方式的处置效果,计算时将微型桩群及桩周土通过均匀化理论等效为符合摩尔库仑强度准则的等效加固体来,以此提高计算效率,最后通过对现场削方+微型桩群加固处置后的滑坡变形监测来验证计算的合理性,得出如下结论:相较于土的强度参数,等效加固体内摩擦角保持不变,黏聚力从26kPa提高到85.36kPa。处置前后的滑坡稳定性评价结果表明,不做处理时,滑坡滑动面从滑坡上方岩土交界面延续到隧道洞口前;仅采用微型桩群加固时,滑坡安全系数在1.17左右,滑动面从岩土交界面延续到隧道洞口后;同时采用微型桩群加固和削方卸载时,滑坡安全系数提高到1.26~1.28,滑动面上缘由土石交界面前移。现场变形监测表明地表变形与深层土体变形均不超过3mm,该措施能保障滑坡的稳定性,同时也验证了计算方法的合理性,可为同类工程提供参考。

基于水流牵引力的河道岸坡稳定性分析

基于极限平衡理论,结合水平条分法,将Bishop法的竖直条间力关系转换到水平土条上,推导出水流牵引力作用下均质岸坡稳定安全系数的理论计算公式,将其结果与ABAQUS有限元软件的强度折减法模拟的计算结果进行对比分析。结合工程实际,分析水流牵引力对不同坡比河流岸坡的稳定性影响规律。结果表明,理论计算公式与软件模拟的结果基本吻合,误差不超过2.1%。河流中水流牵引力会增大岸坡土体的下滑力矩,降低河流岸坡土体稳定安全系数;当岸坡土体遭受降雨、坡脚土体劣化作用等多因素作用下而处于临界稳定状态时,水流牵引力可能成为滑坡启动的关键因素;在河流岸坡失稳滑动时,水流牵引力将导致滑体向河道方向滑移更远距离,加重滑坡对河流航道安全的危害;坡度越陡,岸坡稳定安全系数受水流牵引力的影响越大。在进行高陡河流岸坡稳定性分析时,水流牵引力是与强降雨、泥石流等因素同样重要且不可忽视的导致岸坡灾变失稳的外部荷载作用。

基于离散单元法的石峁遗址东门城墙稳定性及加固方法研究

石峁遗址外城东门城墙出现了严重的外倾变形,面临倒塌风险,为对其进行科学保护,进行了城墙稳定性及加固方法的研究。提出风化折减系数表征灰缝的风化程度,利用离散单元法建立城墙模型,并验证其有效性,通过强度折减法研究在风化作用下城墙的变形及稳定性,通过反演分析法确定城墙的风化程度和灰缝的力学参数。研究结果表明:灰缝强度降低是城墙变形失稳的主要原因;在土压力作用下,城墙破坏呈滑移-倾覆模式;城墙目前处于欠稳定状态,风化系数为0.45~0.48,灰缝强度粘聚力和内摩擦角分别为21 kPa和14°。在此基础上,提出了灰缝灌浆和外侧支撑两种加固方法并进行了比选,最终加固取得了良好的效果。研究结果可为石峁城墙的后续的加固保护提供借鉴和参考。

降雨作用下抗滑桩与三维土工网垫植草护坡坡体的稳定分析

针对抗滑桩与三维土工网垫植草护坡在降雨作用下的稳定性问题,采用有限元强度折减法,利用ABAQUS建立抗滑桩与三维土工网垫植草护坡坡体的三维有限元模型,以坡底水平位移突变情况作为边坡失稳的判断标准,分别比较了不同工况下护坡安全系数随降雨时长的变化规律,以及降雨作用下抗滑桩桩位、桩长对抗滑桩与三维土工网垫植草护坡坡体的稳定性影响,并与未考虑降雨时的影响规律进行对比。结果表明:降雨时长对三维土工网垫植草工况的边坡稳定性影响较为明显;抗滑桩桩长对边坡稳定性影响较大,桩长宜取8 m;无降雨作用下将桩位置于坡中时边坡整体获得最大安全系数,降雨作用下将抗滑桩置于相对位置(L 0.4=4.8 m)时能够起到更好的抗滑效果;抗滑桩与三维土工网垫植草在降雨作用时加固护坡的效果比无降雨时更好,且优于原边坡。

饱和岩土边坡的孔压增量强度折减极限分析方法

目前饱和边坡的强度折减法流固耦合分析是在总应力的静水压力差法基础上,通过调整浸润面位置、考虑材料浮力作用加以实现,未能解决强度折减过程孔隙水压力变化的情况。本文从岩土体固相介质强度参数(c、φ)与液相介质强度参数(孔隙水压力)相互关系出发,解释了固体骨架、自由水不同步的荷载传递过程,提出了有效应力的强度折减法、孔压增量近似确定方法,并在总应力静水压力差方法基础上给出了孔压增量强度折减方法的实现过程。研究表明:孔压增量强度折减方法计算的饱和边坡零孔隙水压力面升高0.34~0.44 m(4%~5%),与目前在涉水边坡流固耦合分析中按经验选取0.5 m的浸润面抬升值较为一致。

破碎岩体隧道洞口开挖诱导滑坡与古滑坡耦合分析

以大栗树高速公路隧道洞口施工为工程背景,研究了在考虑古滑坡因素下洞口工作面边坡失稳及其加固技术。利用钻孔测斜数据(BCD)和Midas GTS折减强度有限元分析模型,分别推测了最危险滑动面,得知两者滑动面位置相似。并采用不平衡推力传递法,基于BCD推断滑动面计算安全系数。以BCD和有限元法的滑动面为基础,将滑动面近似假设为对数螺旋线,考虑地形因素,建立考虑多台阶边坡上限分析模型,研究了不同加固措施对边坡稳定的影响。结果表明,3种方法计算出的边坡安全系数结果相近。