外文翻译--水平切片分析法

1、.英文原文Shahgholi, M., Fakher, A. & Jones, C. J. F. P. (2001). Geotechnique 51, No. 10, 881-885TECHNICAL NOTEHorizontal slice method of analysisM. SHAHGHOLI, ÃA. FAKHER Ãand C. J. F. P. JONES KEYWORDS: design; reinforced soils; theoretical analysis.INTRODUCTIONThere are numerous methods a

2、vailable for the stability analysisof slopes. Most of these may be categorised as limit equilibriummethods (Fang & Mikroudis, 1991). The general approach is toassume a failure surface and determine the factor of safety of asoil wedge against sliding using equilibrium equations. Thebasic assumpti

3、on is that Coulomb's failure criterion is satisfiedalong the assumed failure surface, and the factor of safety isoften defined as the ratio of available shear resistance to therequired shear resistance.Limit equilibrium methods can be divided into two maingroups. The first group considers the eq

4、uilibrium of the wholefailing mass, assuming a failure surface. These methods aresuitable for the analysis of homogeneous soils and specificfailure surfaces. Culmann's method is an example of this group(Taylor, 1984).In the second group, a sliding wedge or active' mass isdivided into a numbe

5、r of vertical slices, and the equilibrium of each individual slice is considered. This procedure, known asthe method of slices, has been adapted to any type of failuresurface and soil. Fig. 1 illustrates the method and the forcesthat act on a typical slice. A list of the governing equations andunkno

6、wn parameters inherent to the vertical slice method isshown in Table 1. It can be seen that the number of unknownparameters is greater than the number of equations, and accord- ingly it is necessary to make further simplifying assumptions to reduce the number of unknowns.Various authors have present

7、ed vertical slice methods of analysis. The procedures differ principally in the equilibrium requirements that they satisfy and the manner in which they handle interslice forces, which are normally dealt with in terms of vertical and horizontal components (Sharma, 1991). The characteristics and the a

8、ssumptions involved in some of these methods are illustrated in Table 2.In addition to conventional analysis, limit equilibrium meth- ods can be used for the pseudo-static analysis of slopes against seismic loads and for the analysis of reinforced soil. In the case of seismic slope analysis the Mono

9、nobe-Okabe method is often used (Mononobe, 1926; Okabe, 1926). The Mononobe-Okabe analysis be can also used as the basis for the seismic analysis of reinforced soil structures (Richardson & Lee, 1975; Bathurst & Cai, 1995). In these analytical methods a planar failure surface is assumed, and

10、 a dynamic earth pressure component is added to the static earth pressure forces to determine the required reinforcement force.In the analysis of the stability of reinforced soil slopes the tension forces in the reinforcing elements need to be considered. Owing to the method of construction and the

11、usual orientation of the reinforcement, these forces are usually assumed to act horizontally. The limiting force developed in any reinforcing element,tj, is the lesser of the rupture strength of the reinforce- ment and the pull-out resistance (Fig. 2). It can be seen from Fig. 2 that the orientation

12、 of the reinforcement has a direct influence on the interslice forces, and that the reinforcement tensions are additional unknowns in the vertical slice method of analysis. As a result the vertical slice method is not particularly suited to the analysis of reinforced soil slopes.The design of reinfo

13、rced slopes in seismic areas has beenconsidered by Bonaparte et al.(1986) using a psuedo-static limit equilibrium approach, in which the internal stability can be assessed using a two-part wedge mechanism (Jewellet al., 1984). The same procedures are used in Japan by the Japanese Railway Technical R

14、esearch Institute and the Public WorksManuscript received 30 July 2000; revised manuscript accepted 8August 2001.Discussion on this paper closes 1 May 2002, for further details seeinside back cover.Ã University of Tehran, Iran. University of Newcastle, UK.Research Institute for the design of re

15、inforced soil walls and slopes.A static equilibrium approach for the design of reinforced soil has also been adopted by Leshchinskyet al.(1995), and has been extended to cover the seismic case (Linget al., 1997). In the latter approach the seismic horizontal force is considered as pseudo-static, and

16、 is obtained through a seismic coefficient that is taken as a percentage of the dead load of the potential failure soil mass acting horizontally at the centre of gravity. The method assumes a log-spiral failure mechanism, and has been developed as a computer program, ReSlope (Leshchinsky, 1997).HORI

17、ZONTAL SLICE METHOD OF ANALYSISThe limitations of the vertical slice method for the analysis of reinforced soil can be resolved by the use of horizontal slices, known as the horizontal slice method (HSM). In this method a failure surface is assumed, and the failure wedge is divided into a number of

18、horizontal slices. The forces that act on each slice are shown in Fig. 3. From Fig. 3 it can be seen that no interslice forces are generated by the reinforcements.The following assumptions are made:(a) The vertical stress on an element in the soil mass is equal to the overburden pressure. Overburden

19、 pressure under seismic loads is equal to (1+Kv)rh.(b) The factor of safety (FS) is equal to the ratio of the available shear resistance to the required shear resistance along the failure surface.(c) The factor of safety for all slices is equal.(d ) The failure surface can have any arbitrary shape,

20、but it does not pass below the toe of the slope or wall.Thus if the failure wedge is divided intoNhorizontal slices there are 4 N unknowns, which can be determined by 4N equa- tions, and a complete formulation is possible, as detailed inTable 3. The solution of the general formulation of the horizon

21、- tal slice method with 4N unknowns is difficult, and needs extensive mathematical effort; it is the subject of further research. However, a simplified formulation is presented here to show the advantage of the horizontal slice method in compari- son with vertical slice methods in the analysis of re

22、inforced soil structures.SIMPLIFIED FORMULATIONThe complete formulation can be simplified if only vertical equilibrium is considered for individual slices together with overall horizontal equilibrium for the whole wedge, no account being taken of moment equilibrium. In this case, the number of equat

23、ions and unknowns is reduced to 2N+1 (Table 4).Therefore, from Fig. 3:andSiis derived from equation (2) and substituted into equation (1).Niis derived as a function of the FS as follows :As a result Sican be derived as a function of the FS using equation (2). Having determined Siand Ni, the value of

24、 FS can be determined using equation (3) when tj is known and vice versa. It can be seen from equation (3) that distribution of reinforcement forces has no effect ontj.If the calculated value ofNi from equation (4) is smaller than zero, thenNiequals zero andSi=cbi/FS is used in equation (1) to calcu

25、late Vi+1.Note that vertical interslice forces (Vi andVi+1) could be calculated by integration of overburden pressures on horizontalborders. As an example, for a wall with a horizontal soil surface Viis equal to (1Kv)ã hiliand has a constant distribution on an element. Overburden pressure incre

26、ases with increase ofhi (vertical distance between any point and the external border of soil mass). Therefore, in the case of a vertical wall with sloping soil surface, the distribution of vertical stress on a horizontal element is trapezoidal. This assumption may not be precisely true for points ne

27、ar to the borders of the soil mass. However, it is considered to be reasonable when applying the horizontal slice method, and has been accepted previously (Atkinson, 1993). Moment equilibrium is not considered in the simpli®ed formulation of the horizontal slice method, and this is a limitation

28、.COMPARISON OF THE HORIZONTAL SLICE METHOD WITH RESLOPEThe horizontal slice method has been used to analyse re- inforced soil structures, and results show close agreement with published data. In order to illustrate the use of the method, the analysis of a typical reinforced soil wall is presented an

29、d compared with the results produced by an established analytical computer program, ReSlope (Leshchinsky, 1997; Ling et al., 1997). Details of the wall are given in Table 5 and Fig. 4. In Fig. 4, reinforcement layers 1-mare extended beyond the failure plane de®ned in a tieback analysis, so that

30、 their allowable tensile strengths can be developed. If the pullout resistance of the reinforcement, based upon tj- allowable of all m layers, is greater than required, the length of the reinforcements can be truncated. If the pullout resistance is inadequate the length isincreased. A number of fail

31、ure planes,i, are considered to identify the critical condition.The values oftjmaxdetermined using the ReSlope program can be compared with the values oftjmaxdetermined using the horizontal slice method for different values of Khandö (Table 6).Note that in the ReSlope program the slip surface i

32、s assumed to be a spiral, and in the horizontal slice method it is assumed to be polylinear. The critical slip surface is not necessarily identical in both methods.CONCLUSIONThe horizontal slice method overcomes the difficulties inherent in adopting the vertical slice method of analysis for thedesig

33、n of reinforced soil structures. in particular:(a) There are no interslice forces developed by the action of the reinforcement.(b) Different seismic accelerations at different heights of the soil structures can be modelled.The results of a trial analysis of a reinforced soil structure subjected to s

34、eismic forces agree closely with the results produced using a log-spiral assumption of a failure plane.NOTATIONbilength of base of sliceccohesion of soilFS factor of safetyhvertical distance between any point in soil mass and external borders of soil massHihorizontal interslice forcehidepth of horiz

35、ontal border of slicesKhhorizontal seismic coef®cientKv vertical seismic coefficientlilength of horizontal border of slicesmnumber of reinforcement layersNnumber of slicesNinormal force upon base of sliceSi shear force upon base of slicetjtensile force of reinforcementW iweight of sliceaiangle

36、of base of sliceunit weight of soiliangle of friction of fillffailure shear stressrrequired shear stressREFERENCESAtkinson, J. (1993).An introduction to the mechanics ofsoils and foundations. London: McGraw-Hill.Bathurst, R. J. & Cai, Z. (1995). Psuedo-static seismic analysis of geosynthetic rei

37、nforced segmental retaining walls. Geosynthetics Int.2, No. 5, pp. 787±830.Bishop, A. W. (1955). The use of the slip circle in the stability analysis of earth slopes. GeÂotechnique5, No. 1, 7±17.Bonaparte, R., Schwertmann, G. R. and Williams, N. D., (1986). Seismic design of slopes re

38、inforced with grids and geotextiles. Proc. 3rd Int. Conf. Geotextiles, Vienna, Austria, 2, 273±278, Balkema.Fang, H.-Y. & Mikroudis, G. K. (1991). Stability of earth slopes. In Foundation engineering handbook, 2nd edn (ed. H.-Y. Fang), pp. 379±409. New York: Van Nostrand Reinhold.Felle

39、nius, W. (1936). Calculation of the stability of earth dams.Trans. 2nd Int. Cong. Large Dams, Washington 4, 445±459.Janbu, N. (1954). Application of composite slip surface for stability analysis. Proc. Eur. Conf. Stability of Earth Slopes, Stockholm.Janbu, N., Bjerrum, L. & Kjaernsli, B. (1

40、956). Soil mechanics applied to some engineering problems, Norwegian Geotech. Inst. Pub. No. 16, Chs 1 and 2.Jewell, R. A., Paine, N. & Woods, R. I. (1984). Design methods for steep reinforced embankments,Proceedings ofsymposium on poly- mer grid reinforcement in civil engineering, pp. 1±12

41、. London:Thomas Telford.Leshchinsky, D. (1997). ReSlope.Geotech. Fabric Rep.15, No. 1, 40±46.Leshchinsky, D., Ling, H. I. & Hanks, G. (1995). Uni®ed design approach to geosynthetic reinforced slopes and segmental walls. Geosynthetics Int. 2, No. 5, 845-881.Ling, H. I., Leshchinsky, D.

42、& Perry, E. B. (1997). Seismic design and performance of geosynthetic-reinforced soil structures.GeÂotechnique 47, No. 5, 933±952.Mononobe, N. (1926). An investigation on vertical earthquake acceleration and structural vibration.Proc. Japan Soc. Civ. Engrs10, No. 5, pp. 1063±1094

43、(in Japanese).Morgenstern, N. R. & Price, V. E. (1965). The analysis of the stability of generalised slip surfaces GeÂotechnique15, No. 1, 79±93.Okabe, S. (1926). General theory of earth pressures and seismic stability of retaining walls and dams.J. Japan. Soc. Civ. Engrs10, No. 6, 127

44、7±1288.Richardson, G. N. & Lee, K. L. (1975). Seismic design of reinforced earth walls.J. Geotech. Engng, ASCE 101, No. 2, 167±188.Sharma, H. D. (1991). Embankment dams, p. 359. New Delhi: IBH.Spencer, E. (1967). A method of analysis of the stability of embankments assuming parallel in

45、ter-slice forces.GeÂotechnique17, No. 1, 11-26.Taylor, D. W. (1984).Fun damentals ofsoil mechanics. New York: Wiley.英文译文水平切片分析法关键字：设计；加筋土；理论分析。引言斜井的稳定性分析有许多种方法。这许多种方法可以被归类为极限平衡法（Fang&Mikroudis,1991）。一般方法是假设一个破坏面，同时用平衡方程确定滑动土楔的稳定系数。一般我们假定先前假设的破坏面满足库仑破坏准则，而且该稳定系数通常被定义为可用抗剪系数与必需抗剪系数的比值。极限平衡法可以

46、被分为主要的两大类。第一类方法考虑整个破坏体的平衡，这一类方法适用于均质土壤和特定破坏面的分析。Culmann方法是这类方法的一个例子（Taylor,1984）。在第二类方法中，一个滑楔或者“活性”物质被分隔成许多纵向切片，同时考虑每一个独立切面的平衡性。这个以切片法命名的过程已经被运用于任何破坏面和土壤。图1显示了这一方法在一个特定切片上的应用。表格1显示了一系列纵向切面所固有的控制方程和未知参数。可见未知参数的数量要多于方程的数量，同时相应地进一步简化假设以减少未知参数的数量是必要的。许多作者都已经对纵向切片分析法作了介绍，这些介绍的主要不同点在于这些分析法所满足的平衡条件和对间力的处理方

47、法各有差异，而这一差异在纵向和横向组件问题的处理中是很正常的（Sharma,1991）。表格2显示了与这些不同方法相关联的特点和假设。优于的通常分析法，极限平衡法可以被用于地震荷载的伪静态分析，也可以被用于加筋土的分析中。Mononobe-Okabe分析法经常用于地震荷载的分析中（Mononobe，1926；Okabe，1926）。Mononobe-Okabe分析法也可以作为加筋土结构的地震荷载分析的基础（Richardson&Lee,1975；Bathurst&Cai,1995）。在加筋土斜坡的分析中，加强元素中的张力应该被考虑在内。由于施工方法和加固的一贯方向的原因，我们通

48、常假设这些张力是在水平方向起作用的。在任意加强元素中形成的限制力tj是加强中的断裂强度和拉电阻中较小的那一个值（图2）。可以从图2看出增援的方向对间力有直接的影响，我们也可以看出在纵向切片分析法中拉筋是额外的未知量。因此垂直切片方法不是特别适合用于加筋土斜坡的分析。Bbnaparte(1986)等人使用伪静态极限平衡法进行了地震地区的边坡加固的设计，在这一方法中用由两部分组成的楔形机制测定了内部稳定性。这一方法也被日本铁路技术和公共事务研究所使用，用于加筋土墙和加筋土斜坡的设计。加筋土的设计中的静平衡方法也已经被Leshchinsky (1995)等人采用，这一方法已经被扩展到地震事件的分析中

49、（Ling等，1997）。在后一种方法中，地震水平力被认为是伪静态的，这一水平力通过一个被认为是潜在的故障土体静载水平重心的百分比的地震系数获得。这一方法假定了一个对数螺旋破坏机制，这一方法已经被发展成一个名为ReSlope(Leshchinsky,1997)的电脑程序。水平切片分析法纵向切片分析法分析加筋土的局限性可以被简称为HSM的水平切片分析法解决。在这一方法中，我们假设了一个破坏面，同时破坏楔面被分割成了许多水平切面。图3显示了作用在每一个切片上的作用力。从图3中我们还可以看出，增援没有形成切片间的间力。以下是我们做出的一系列假设：(a) 作用在土体中元素上的立式压力和覆压等同。（在地

50、震负荷下的覆压等于(1+Kv)rh (b) 安全系数（FS）等于可用的剪切阻力比沿着破坏面所需的剪切阻力的比值。(c) 所有切片的安全系数都相等。(d) 破坏面可以有任意的形状，但是他不通过下面的斜坡或墙壁的底部。这样，如果破坏楔面被分割为N个水平切片，就有4N个由4N个方程确定的未知量，那么就如表格3所述，我们有可能得到一个完整的方程。解出有4N未知量的水平切割法的通式是困难的，这需要广泛的数学知识。这正是以后研究的主题。然而，我们在这里展示一个简化的方程，以便显示出在分析加紧土结构时水平切片法优于纵向切片法。简化的方程如果只考虑单个切片的垂直平衡和整个楔形的整体水平平衡，不考虑力矩平衡，完

51、整的方程可以被简化。在这个例子中，方程和未知数的数量被减少到2N+1个（表格4）。因此，从图3中，我们可以得到：Si由方程2得出，将其带入方程1。Ni由以下安全系数的性质得出：所以Si可以用方程2同时考虑安全系数的性质得出。既然已经确定了Si和Ni的值，那么当tj之和的值已知时，安全系数的值就可以由方程3得出，反之亦然。从方程3可以看出，增援力量的分布对tj之和的值没有影响。如果由方程4得出的Ni的值小于零，那么令Ni的值为零，同时在方程1中用Si=cbi计算Vi+1。我们注意到垂直间力（Vi和Vi+1）可以由在水平边界上对覆压积分得到。举个例子说，对于拥有水平土壤表层的墙面来说，Vi和(1+

52、KV)rhili是相等的，而且Vi有一个上常量元素分布。当hi（任一点和土壤块体间的垂直距离）增加时，覆压也随之增长。因此，在坡地土壤表面与垂直墙的例子中，横向元素上的垂直压力是梯形分布的。这个假设对于土壤体边界的点来说也许是不准确的，然而，当使用水平切割法时这一假设被认为是合理的，而且这一假设之前被采纳过（Atkinson,1993）。在这一水平切割法的简化方程中没有考虑力矩平衡 ，这是这一方法的一个有局限性的地方。水平切割法与Reslope的比较水平切割法被应用于加筋土结构的分析中，实验结果显示出了和已公布的数据的紧密的一致性。为了展示这一方法的应用，一个典型的加筋土壁的分析结果和由一个已

53、建立的分析性电脑程序Reslope(Leshchinsky，1997；Ling等人，1997)得出的结果进行了比较。土墙的详细信息由表格5和图4给出。在图4中，加固层1-m延展到到由回接分析定义的破坏面之外，以便于形成他们所允许的拉伸强度。如果基于所有m层允许的tj值之上的钢筋抗拔力必须要的值大，那么增援的长度可以被截断。如果抗拔力不足，增援的长度就会增长。破坏面数量的描绘量i被认为用来定义临界条件。在Kh取不同值的情况下，由ReSlope程序确定的tjmax之和可以和由水平切割法确定的tjmax之和进行比较（表格6）。我们注意到在ReSlope程序中滑动面被认为是螺旋的，而在水平切割法中滑动

54、面是轴承滚道。在这两种方法中，临界滑动面不必要是相同的。结论水平切割法克服了采用纵向切割分析法设计加紧土结构时的固有缺点。特别地：（a） 这里没有由于加固的作用引发的间力。（b） 在土壤结构的不同高度上不同的地震加速度可以用模型描述。受地震力的加筋土结构的实验分析结果和采用对数螺线假设的破坏面的研究结果十分一致。注释bi 基地切片的长度c 土壤凝聚力h 任一点和土壤块体外边界间的垂直距离Hi 横向间力hi 切片的水平边界深度Kh 水平地震系数Kv 垂直地震系数Li 切片的水平边界长度m 加固层的数量N 切片数量Ni 切片上基础力Si 剪切力Tj 加固力W 重量切应力ai 切角大小 重度i 摩擦

55、角角度f 负剪切应力r 正剪切应力参考文献Atkinson, J. (1993).An introduction to the mechanics ofsoils and foundations. London: McGraw-Hill.Bathurst, R. J. & Cai, Z. (1995). Psuedo-static seismic analysis of geosynthetic reinforced segmental retaining walls. Geosynthetics Int.2, No. 5, pp. 787±830.Bishop, A. W.

56、 (1955). The use of the slip circle in the stability analysis of earth slopes. GeÂotechnique5, No. 1, 7±17.Bonaparte, R., Schwertmann, G. R. and Williams, N. D., (1986). Seismic design of slopes reinforced with grids and geotextiles. Proc. 3rd Int. Conf. Geotextiles, Vienna, Austria, 2, 273±278, Balkema.Fang, H.-Y. & Mikroudis, G. K. (1991). Stability of earth slopes. In Foundation engineering handbook, 2nd edn (ed. H.-Y. Fang), pp. 379±409. New York: Van Nostrand Reinhold.Fellenius, W. (1936). Calculation