（中文翻譯附后）

A Combined Retaining Structure and Its Application
 in Deep Excavation

Yuwen Yang

Senior Geotechnical Engineer, Wuhan Geotechnical Engineering and Surveying Institute, Wan Song Yuan Road 209#, Hankou, Wuhan, 430022, China; wayneywyang@hotmail.com 

ABSTRACT: In a combined structure, soil-nailing wall retains the upper and shallow soil while propped piles at the toe of the wall augments the overall stability of ground in deep excavation. Although such a structure developed from soil nailing wall plus internally-braced pile has widely been employed, it is regarded as not an integral structure, but a separate one to analyze and calculate. This treatment is unreasonable. By the numerical experiments, the combined structure is explored about its space earth-retaining mechanism as the integrated system. Analytical results indicate that the actual earth pressure exerted to the structure is different with that determined by Rankine’s theory. The distribution of Rankine’s pressure is adjusted to accommodate the calculation results. A case study proves the validity of the adjustment.

INTRODUCTION

    The combined structure in this paper refers to the earth-retaining wall developed from soil nailing wall plus internally-strutted piles, where soil nailing wall is used to retain the upper soils while the internally propped piles provide overall stability to ground in deep excavation. Such a structure is usually applied to the geological conditions: (1) top soil is the high strength fill, underlying which, there is soft soil and (2) underground facilities or nearby buildings are in close to the excavation and necessary to protect.
For stability and deformation analysis of soil nailing wall, many scholars have developed a variety of methods (Bridle, 1989; Yang et al, 1998; Yuan et al 2003 ), among which, the limit equilibrium method is popular. Pile wall is a traditional earth-retaining type, and the elastic spring resistant approach is widely used to predict pile deformation and earth pressure. However, to the combined structure which will be discussed, its retaining mechanism is different with either pile wall or soil nailing wall. Due to the upper soil restrained by soil nailing wall, the pile can be designed to be shorter.  Correspondingly, pile wall adjacent to the toe of soil nailing wall improves the overall stability of ground. It is difficult to consider the influence of stability of soil nailing wall on the lower pile wall or effect of pile resistance at the wall toe to soil nailing wall above.  So the mechanism of the combined structure has still remained unknown. In this paper, use FLAC for numerical simulation to explore its features such as deformation, soil stress, and pressure during excavation.

NUMERICAL SIMULATION
Assumptions
In the combined structure, soil nails, facing, pile, binding beam, internal props constitute a spatial structure as a whole to bear earth pressure and restrain excessive deformation. In order to reduce the volume of calculations and highlight main factors, the reasonable simplification for the issue is necessary. The assumptions are made in the following.   (1) it is plane strain problem in homogeneous soil;   (2) pile top is directly connected with prop neglecting existence of binding beam;   (3)except soil, all the structural elements are assumed to be elastic. Soil adheres to Mohr - Coulomb yield criterion;   (4) neglect overload on the ground, and  (5) neglect groundwater.
The binding beam directly linked with the tops of the adjacent piles transmits axial force of prop to pile tops and almost does not play a role in retaining. In addition, in the following numerical simulation, there is only one pile to involve. The effect of neglecting the binding beam on the calculation is limited.
Element types
Table 1 illustrates the types of structural elements to represent the combined structure. Soil nails are slender, flexible, and can be simulated by cable. The 100mm-thick facing may be separate with soil in active zone if large displacement occurs in soil nailing wall.  There is the coupling effect, and so liner structural element is applied to represents the facing layer. Pile wall is directly in use of pile element. Pile and the surround soil can be separate or close and there is also the coupling effect. Use beam element to represent the prop. Soil body is discretized into a series of cubes of hexahedral elements to improve the calculation accuracy. These structural elements are of basic features: beam element, the two-node straight-line element, can withstand axial force, shear, bending moment; cable element, the two-node straight-line unit, only to bear axial force, is mobilized with the surrounding soil through the interaction of frictional resistance; pile element, the two-node straight-line unit, similar to beam element, can also interact with the surrounding soil in separation or closure; liner element, three-node plane element, interacts with the surrounding soil in normal and tangent directions to separate or slide according to Mohr-Coulomb yield criterion. The combined structure consists of soil, a pile, 4 rows of soil nails, facing and one prop.

In numerical simulation, construction steps can be taken account. For soil nailing wall, while excavating, soil nails are installed one row by one row simultaneously forming the shotcrete facing. When excavation proceeds to a given depth,   install a pile at the toe of the wall and then set a prop to link the top of the pile. At the sixth step of excavation, install the pile; at the seventh step, set up the internal prop.
Simulation extent
As shown in Figure 1, the combined structure of the soil nailing wall plus pile wall is employed in a 50m-wide rectangular excavation in homogeneous soil with the final excavation depth of 10m. There are total steps of 10 to excavate, 1m deep each step. The structure is assumed to be thickness of 2.0m as a plane strain problem. The area of simulation is 50m × 30m. The simulation boundary is extended to 20.0m under the base of pit at last step (see Figure 1).
The values of parameters
Figure 1 shows the geometry of the structure and some of parameters used in simulation. The values of the parameters are in line with the actual conditions. The remaining parameters are given as below.
(1) Soil nailing wall. In the extent of simulation, there are four 5m-long soil nails in spatial arrangement SV × SH = 2.0 × 1.5m2, made from Φ22 steel bars with elastic modulus E = 2 × 108kPa and yield strength fy = 1.86 × 107kPa. Soil nails are installed in inclination of 15 ° to the horizontal. Pre-drilled holes with diameter D = 0.12m to insert soil nails are filled with cement mortar in C20. Soil nails are mobilized with surrounding soil up to the ulltimate frictional force = 15kPa. 100mm-thick facing layer makes up of reinforced concrete in C20 with elastic modulus E = 2.55 × 107kPa and Poisson's ratio  = 0.25. The normal and tangential stiffness between facing and the surrounding soil are assumed to be 100kPa / m , respectively, and their cohesive strength 2kPa.  (2) Pile. There exists a single pile with diameter of 1000mm and the central spacing of 2.0m, made from reinforced concrete in C30. Pile interacts with surrounding soil in the tangential and normal stiffness of 100kPa / m, 10000kPa / m, cohesive strength 10kPa, friction angle 20 °, respectively.  (3) Prop. only one prop is assumed to support the extent of 20 piles. The prop is rectangular in cross-section of 500 × 700mm2, made from reinforced concrete in elastic modulus of 2.55 × 107kPa and Poisson's ratio of 0.25.

Computational results
Figure 2 illustrates settlement δV and horizontal displacement δH at depth H = 5m, 10m, respectively. At H = 5m, the maximum horizontal displacement is below the base of pit, δHmax = 25mm, and the largest settlement is at the boundary, δvmax = 15mm.  At H = 10m, δHmax is near the bottom (δHmax = 70mm), and the largest settlement δvmax = 35mm also locates in the boundary. With increase in the excavation depth, deformation of soil nailing wall increases, but the distribution shape is kept to be similar. Location in maximum horizontal displacement is not near ground surface, but close to the base of pit.  This is due to soft soil to cause bottom uplift. At the different depths of excavation, if deformation in pile wall increases, displacement for soil nailing wall also increases.

Figure 3 illustrates coefficient distribution of the earth-pressure at depth H = 5m, 10m, respectively, where K0 is coefficient of earth pressure at-rest, K0 = 0.7; Ka  indicates coefficient of active earth pressure , Ka = 0.49; Kp is coefficient of passive earth pressure, KP = 2.04; σH5 and σH10 represent horizontal stresses exerted to the retaining structure  at depths of H = 5m, 10m, respectively.   and  represent the self-weight stresses back and in front of the combined structure.   is calculated from ground surface and   from the base of pit.
Figure 3 shows that at depth of H = 5m, the earth pressure exerted to the facing of soil nailing wall is far less than the values of Rankine’s active earth pressure. At H = 10m, the distribution of σH10 is complicated and there are two turning points, locating around the prop and near the middle of passive zone, respectively.  Under the base of pit, the value of earth pressure from simulation is greater than that from the Rankine’s theory and close to the earth pressure at-rest. Close to pile base, σH10 does not increase and essentially remains unchanged. Accordingly, within the extent of 3m in the passive zone, σH10 is larger than that from Rankine’s theory. Comparing to the passive earth pressure in pile wall (Hashash et al, 2002 ), the value of  passive earth pressure in pile wall in the combined structure increases by about 20%. This is due to the existence of soil nailing wall above the pile. The curves in Figure 3 also illustrate that the values of earth pressure applied to the facing of soil nailing wall decreases with increase in excavation depth, but the maximum value decreases by almost 50%, compared with that from Rankine’s theory. This proves that the pile and the soil nailing wall interact to keep stability of ground  during excavating.

To braced excavation, Terzaghi and Peck proposed a semi-empirical formula to predict the load on retaining structures (Craig, 2002). This paper involves the combined structures, whose characters are more complicated than only pile in braced excavation. Due to the prop to restrain deformation of ground, the soil in the vicinity of the prop may not have entered the plastic state and so Rankine’s theory is not applicable to predict the earth pressure. Soil body near the base of pit is affected less by the prop and likely to enter the plastic state and the Rankine’s theory is  appropriate. Near the pile base, because of the embedding effect of soil in active zone, soil body is inadequate to move and it seems to not apply Rankine’s theory. Numerical simulation results show that (see Figure 3), at H = 5m, the facing in soil nailing wall is subjected to the earth pressure less than that determined by Rankine’s theory. With increase in excavation depth, due to the pile near its toe to limit displacement of soil around, the pressure acting on the facing decreases, as shown in Figure 3. at H = 10m, around the base of pit, the earth pressure is close to that conducted by the Rankine earth pressure theory, while near the prop and pile base,  the earth pressure is larger. Therefore, as shown in Figure 3, the pile along its depth in the active zone can be divided into three sections: ab, cd, ef, and in passive zone gh to amend coefficients of the earth pressure determined by Rankine theory as follows:

In equation (1), the signs ka, kp represent the average coefficient of active earth pressure and passive earth pressure coefficient from Rankine’s theory along excavation depth, respectively.

CASE STUDY

Overview
The Jianghua residential complex building was surrounded by Sanyang Road to the north, Zhongshan Road to the east, a tall building near Jinghan Road to the west. The project consisted of one 13-storey, one 15-storey, one 2-storey office buildings, as well as three 18-storey residential buildings, with two-storey basements to extend the total area. Layout of these six buildings was similar to the "courtyard", China’s traditional house type. The basement in perimeter of 516m is rectangular in shape occupying an area of about 14400m2 with depth of 9.4 m to10.6m. To the north and to the east, there existed underground pipes or cables very close to excavation boundaries. These nearby underground facilities are necessarily protected to avoid damage during excavation.
Take the section fa,  close to Sanyang Road, as an example to illustrate the geology on site. Strata  related to excavation from ground surface included (1) fill; (1-2) fill; (2-1) silt; (2-2) silty clay; (3) silt and fine sand; (4-1) fine sand; (4-2) fine sand . Groundwater involves the upper perched water and confined water, the former in fill and the latter in the fourth layer of fine sand. Deep well is designed to lower water head to 2m below the base of pit. Along boundaries of excavation, cement-soil mixing piles in 6m long were arranged to shutoff the perched water in fill layers. The internally-propped pile wall was selected in deep excavation.  In order to reduce the bending moment within piles, the 4m-deep upper fill was removed to form a 4m-wide platform, as shown in Figure 4. The cut slope was retained using soil nailing wall (Figure 4). The profile of excavation included two types of retaining structures: pile wall and soil nailing wall, namely, the combined structure. According to the geology and environment along excavation boundaries, earth-retaining plans are different slightly.  Design in the section fa is shown in Figure 4.
Some of monitoring results were illustrated in Figure 4 in the section fa on September 23, 2007 at final depth of 10.6m: the maximum bending moment of 390kN • m, maximum displacement of 26mm, both locating near the base of pit, the horizontal displacement of 39mm, 26mm at the top and toe of soil nailing wall, respectively, and settlement 18.1mm at the crest.
Numerical simulation
The profile in the section fa is selected to carry out numerical simulation. The assumptions are similar to that previously introduced in this paper except heterogeneous soil instead of homogeneous soil. Neglect the resistance of  cement-soil mixing  piles.
Excavation is proximately rectangular in shape with 185.8m long and 96.9m wide. The section fa is located in the middle of the long side. Take it as a plane strain problem with simulation thickness of 1.2m. Choose the simulation extent of 100m × 35m. The section fa  is the middle of 100m and 50m in and outside away from the excavation side, respectively.  From the final depth of excavation, the simulation boundary is extended 24.4m.  Set 11-step excavation, 1m deep each step for former 10 steps and 0.6m deep for the last one. The values of the soil parameters are shown in Table 2. In Figure 4, layer thickness, excavation geometry and retaining structure are depicted. The remaining parameters for structural elements are similar to that previously-stated in the case in homogenous soil.

Part of computational results is shown in Figure 5. At depth of H = 4.1m, maximum horizontal displacement in soil nailing wall reaches to 19.7mm. At H = 10.6m, horizontal displacements in crest and the toe are 32mm, 22mm, respectively. In crest,  settlement is equal to 22mm.The maximum horizontal displacement is 32mm near the base of pit.  It can be found out that the deformation computed in the combined structure has very close to the values of  monitoring results on September 23, 2007. Maximum bending moment in pile is calculated to be equal to 409.6kN.m, very close to values of the measured data, too.

CONCLUSIONS

The earth-retaining structure is subjected to the earth pressure, which is related to many factors such as soil elasto-plastic states, strength, stress-related path as well as structure own stiffness. Deformation and earth pressure in the combined structure are discussed in this paper to regard it as a whole. Within the combined structure, soil nailing wall and pile interact to bear earth pressure. For example, due to effect of the pile, the facing  in soil nailing wall is subjected to the earth pressure much reduced. On the contrary, due to the existence of soil nailing wall, the passive earth pressure to pile becomes larger.  In the combined structure, the distribution of earth pressure is inconsistent with that from Rankine theory. based on numerical simulation results, the depth of excavation in the active zone is found to divide into three sections. Coefficients of active earth pressure are adjusted to meet the results of simulation each section.   
REFERENCES
Bridle, R. J.(1989)  “Soil nailing—analysis and design”, Ground Engineering, Vol. 22(6): 52–56
Craig R.F. (2002)  Soil mechanics ( 6th edition), Spon press
Hashash, Y.M.A., and Whittle, A.J.(2002). “Mechanisms of load transfer and arching for braced excavations in clay”, J. Geotech. Eng., Vol. 128(3): 187-197
Yang, Y., Yuan, J. (1998) “Limit equilibrium method of soil nailing walls in deep excavation”, Geotechnical Investigation and Surveying, (6): 9-11
Yuan, J., Yang Y., Tham,L.G., Lee P.K.K. and Tsui Y. (2003), “A new approach of limit equilibrium and reliability analysis of soil nailed walls”, International Journal of Geomechanics, ASCE, Vol.3( 4): 145 -151

組合支護(hù)結(jié)構(gòu)和在基坑工程中的應(yīng)用

楊育文
（武漢市勘測設(shè)計(jì)研究院，漢口萬松園路209號，430022） 

    摘要：土釘墻維護(hù)淺層土穩(wěn)定，內(nèi)支撐樁排維護(hù)整體穩(wěn)定， 這種組合支護(hù)方式已在大型深基坑工程中廣泛采用，但是在計(jì)算分析中一般沒有將它們作為一個整體的空間結(jié)構(gòu)來分析，這與實(shí)際情況是不相符合的。為了探討這種組合支護(hù)方式的空間受力與擋土機(jī)理，采用數(shù)值模擬實(shí)驗(yàn)方法并結(jié)合實(shí)際工程進(jìn)行研究，提出了組合支護(hù)整體剛度系數(shù)的新概念。分析結(jié)果表明了組合支護(hù)受到的土壓力與Rankine土壓力不相同，文中提出了修改建議等。獲得的結(jié)論在一實(shí)例中得到了檢驗(yàn)。

    前言
    本文中組合支護(hù)方式指土釘墻加內(nèi)支撐：土釘墻維護(hù)淺層土穩(wěn)定，內(nèi)支撐樁排維護(hù)整體穩(wěn)定。這種組合支護(hù)的使用條件:淺部雜填土強(qiáng)度較高，基坑周邊建筑物或地下設(shè)施離開挖面相距較近，基坑頂部雜填土范圍內(nèi)土體用土釘墻維持穩(wěn)定，而下部較軟弱土層則采用內(nèi)支撐樁排支護(hù)，限制土體位移，防止過大位移引起相鄰構(gòu)筑物破壞。
    針對土釘墻穩(wěn)定和變形分析，國內(nèi)外學(xué)者已發(fā)展或應(yīng)用多種不同方法，其中， 極限平衡法應(yīng)用最廣泛。內(nèi)支撐樁排是一種傳統(tǒng)的支護(hù)方式，彈性抗力法在工程中應(yīng)用較普通。作為組合支護(hù)，它們一起發(fā)揮擋土作用，擋土機(jī)理是不同的。上部土釘墻擋土，下部樁排可以設(shè)計(jì)得短一些。同時(shí)，下部樁排維護(hù)了土釘墻的穩(wěn)定。本文采用FLAC軟件，對這一組合支護(hù)方式進(jìn)行數(shù)值模擬分析，探討基坑開挖過程中它的變形、土體中應(yīng)力、土壓力等大小及開挖過程中發(fā)生的變化，結(jié)合一基坑工程實(shí)例來分析其擋土機(jī)理等。

    數(shù)值模擬
    假設(shè)條件
    在土釘墻內(nèi)支撐樁排組合支護(hù)中，土釘、噴錨面層與樁排、鎖口梁、內(nèi)支撐組成的一個空間結(jié)構(gòu)，作為整體來承受土壓力和限制土體變形，是一個非常復(fù)雜的空間結(jié)構(gòu)問題。為了減少計(jì)算工程量，合理簡化問題，考慮主要影響因素，突出主要受力特點(diǎn)，在下面的模擬分析中，引入以下假設(shè)條件：
  （1）土釘墻內(nèi)支撐樁排組合支護(hù)作為均質(zhì)土中的平面應(yīng)變問題；
  （2）不考慮鎖口梁受力，內(nèi)支撐與樁頂直接相連；
  （3）除了土體按彈塑性考慮外，所有結(jié)構(gòu)單元假設(shè)為彈性體；
  （4）地面不存在超載;
    (5)不考慮地下水的影響。
    鎖口梁主要作用是將相鄰樁排連接在一起，整體受力，將內(nèi)支撐推力傳遞到各個樁頂，它幾乎不直接發(fā)揮擋土作用。另外，在下面數(shù)值模擬中模擬厚度內(nèi)只存在一根樁。因此，不考慮鎖口梁對計(jì)算結(jié)果影響不大。
    單元選擇
    表1給出了支護(hù)結(jié)構(gòu)組成與所選擇的單元類型。土釘細(xì)長，柔性大，可選擇桿單元模擬；土釘墻面層一般100mm厚，面積大，它與主動區(qū)土體在發(fā)生較大變形時(shí)可能會分離，存在耦合作用，用襯墊單元模擬較合適；鋼筋混凝土內(nèi)支撐與鎖口梁澆筑(鎖口梁和樁排澆筑)在一起，可用梁單元模擬；樁排與土體間存在相互耦合作用；土體采用幾乎是正方體的六面體單元，可以提高計(jì)算精度。各結(jié)構(gòu)單元基本情況：梁單元，兩結(jié)點(diǎn)直線單元，可承受軸力、剪力、彎距；桿單元，兩結(jié)點(diǎn)直線單元，只承受軸力，與周圍土體通過摩阻力相互作用；樁單元，兩結(jié)點(diǎn)直線單元，類似于梁單元，還可以與周圍土體發(fā)生法向、切向耦合作用，與周圍土體分離或閉合；襯墊單元，三結(jié)點(diǎn)平面單元，可與相鄰?fù)馏w發(fā)生切向、法向作用，與周圍土體彈性連續(xù)，根據(jù)Mohr-Coulomb屈服準(zhǔn)則，可與土體脫開或發(fā)生滑動。

    數(shù)值模擬中充分考慮具體施工步驟與方法。如頂部土釘墻，邊開挖、邊插入土釘、邊噴射混凝土形成面層; 基坑上部開挖到位后，設(shè)置下部樁排內(nèi)支撐。土層采用分層開挖模擬，第六步開挖前設(shè)置樁排，第七步開挖前設(shè)置內(nèi)支撐。
    模擬范圍
    圖1所示為寬度50m均質(zhì)土長方形基坑，最終開挖深度10m，采用土釘墻和樁排支護(hù)。分10層開挖，每次開挖1m深度。對上部傾斜45°坡角土釘墻，每步開挖完成后即設(shè)置該層土釘和噴射面層。假設(shè)為平面應(yīng)變問題，厚度取2.0m，模擬范圍50m×30m，最終開挖深度以下取20.0m(見圖1)。模擬范圍內(nèi)，包括一根樁、一排土釘、一個內(nèi)支撐。
    計(jì)算參數(shù)的選擇
    圖1表示出了土體幾何尺寸、部分計(jì)算參數(shù)值、土釘墻和內(nèi)支撐樁排相對位置。下面分別介紹計(jì)算過程中所采用的其它參數(shù)值，它們基本上和實(shí)際情況相符。
  （1）土釘墻。計(jì)算厚度內(nèi)一列土釘，長5m，土釘空間布置SV×SH= 2.0×1.5m2，材料為Φ22鋼筋，E=2×108kPa，屈服強(qiáng)度fy=1.86×107kPa。土釘與水平方向成15°傾角。灌漿孔徑D=0.12m，灌注水泥砂漿，強(qiáng)度C20，土釘與周圍土體間極限摩阻力 =15KPa。土釘墻面層由布置鋼筋網(wǎng)和C20噴射混凝土組成，為彈性體，E=2.55×107kPa，=0.25，厚100mm。面層與土體交界面上法向與切向剛度均為100KPa/m，粘結(jié)強(qiáng)度2kPa。
  （2）樁排。計(jì)算厚度內(nèi)存在單樁，直徑1000mm，樁中心距2.0m，C30混凝土，彈模和泊松比大小如圖1所示。它的土體之間切向和法向剛度分別為100KPa/m、10000KPa/m、粘結(jié)力10kPa、摩擦角20°。
  （3）內(nèi)支撐。計(jì)算范圍內(nèi)一個支撐，假定給20根樁提供支撐力。內(nèi)支撐矩形截面，尺寸500×700mm2，C20混凝土，彈模2.55×107kPa，泊松比0.25。

    計(jì)算結(jié)果
    圖2所示為開挖深度H=5m、10m時(shí)，基坑地表沉降δV，在開挖面處沿深度方向水平位移δH分布圖。當(dāng)H=5m時(shí)，最大水平位移位于坑底以下，δHmax=25mm，最大沉降δvmax位于邊界上，δvmax=15mm；當(dāng)H=10m時(shí)，δHmax在坑底附近，δHmax=70mm，最大沉降δvmax=35mm，同樣位于邊界上。隨著開挖深度的增加，土釘墻變形增加，但分布形狀類似。最大水平位移并沒有象預(yù)期的那樣發(fā)生在地表，而是出現(xiàn)在基坑底附近，這是由于土體強(qiáng)度較低，出現(xiàn)了坑底隆起現(xiàn)象。不同開挖深度，樁排與土釘墻兩者變形都存在協(xié)調(diào)性，樁排變形增加，土釘墻發(fā)生的位移也加大。

    圖3表示的是開挖深度H=5m，10m時(shí)，作用于土釘墻面層和樁排上的土壓力系數(shù)分布圖， K0-靜止土壓力系數(shù)，K0=0.7；Ka-主動土壓力系數(shù)，Ka=0.49；Kp-被動土壓力系數(shù)，KP=2.04；σH5、σH10分別表示H=5m、10m時(shí)開挖面水平方向的應(yīng)力； 、 分別表示支護(hù)結(jié)構(gòu)后面和前面土體自重應(yīng)力，其中 從基坑頂部地表算起， 從坑底H=10m處算起。

    對內(nèi)支撐樁排支護(hù)，Teriaghi和Peck提出了半經(jīng)驗(yàn)公式計(jì)算內(nèi)支撐上的荷載[13]。對本文介紹的組合支護(hù)，它的工作性狀要比一般的內(nèi)支撐復(fù)雜一些。由于樁頂處內(nèi)支撐約束了支護(hù)體系向坑內(nèi)的變形，附近土體可能沒有進(jìn)入塑性狀態(tài)，這時(shí)Rankine土壓力理論是不適用的；在靠近開挖面附近，受樁頂處內(nèi)撐影響較小，樁排向坑內(nèi)變形較大，該范圍主動區(qū)土體則有可能進(jìn)入塑性狀態(tài)，適合Rankine土壓力理論應(yīng)用條件；靠近樁下端附近，由于土體的嵌固效應(yīng)，限制了主動區(qū)土體變形，同樣Rankine土壓力不適用。數(shù)值模擬結(jié)果表明（如圖5所示），H=5m時(shí)，開挖面附近土釘墻面層上的土壓力接近Rankine主動土壓力，而上部則較小。隨著開挖深度的增加，由于下部的內(nèi)支撐樁排限制了主動區(qū)土體的位移，土釘墻面層受到的土壓力反而有所減少，如圖5所示。 當(dāng)H=10m時(shí)，開挖面附近土壓力系數(shù)接近Rankine主動土壓力系數(shù)，而支內(nèi)撐樁、樁下端附近則較大。因此，對于圖5所示的支護(hù)體系，可將主動區(qū)分成三段: ab、cd、ef，被動區(qū)以gh段表示，它們的土壓力系數(shù)分別修改如下:

    典型基坑工程實(shí)例分析
    基坑概況和實(shí)測數(shù)據(jù)
    江花辦公住宅綜合樓北臨三陽路、東臨中山大道、西臨京漢大道一高層建筑，總用地面積2.34公頃，由1棟13層、1棟15層、1棟2層辦公樓以及3棟18層住宅樓組成。6棟擬建建筑物在平面布局上組成類似于“四合院”型，擬設(shè)置2層滿鋪地下室，基礎(chǔ)埋置深度10.60m。地下室形狀呈長方形，基坑周長約516m，面積約14400m2，開挖深度9.4～10.6m。基坑北側(cè)、東側(cè)存在地下水管或光纜，距基坑邊線一倍開挖深度以內(nèi)，基坑周邊不允許有較大變形。以位于三陽路側(cè)fa段土層情況為例說明場址土層結(jié)構(gòu)。與支護(hù)相關(guān)的土層從上到下是（1）雜填土層，表層土; (1-2）素填土；（2-1）粉土夾粉質(zhì)粘土；（2-2）粉質(zhì)粘土；（3）粉土互層；（4-1）粉砂夾粉土；（4-2）粉砂，厚度d＞5m。場址存在上層滯水，賦存于表層填土層，地下承壓水存在于第四土層單元砂層中。施工中采用深井降水，將承壓水降低至開挖坑底面以下2m處，上層滯水采用封堵法，用6m長粉噴樁沿基坑四周布置?；硬捎脴杜偶觾?nèi)支撐支護(hù)方案，為了降低樁內(nèi)彎矩，將上面4.1m的高度土層進(jìn)行卸載成平臺，該范圍土坡用土釘墻加固，與內(nèi)支撐樁排支護(hù)結(jié)合在一起使用。由于基坑周邊土層分布存在差異，支護(hù)方案有一定變化，沿周邊分成六段，其中fa段設(shè)計(jì)剖面如圖6所示。

    江花基坑工程開挖深，地質(zhì)條件復(fù)雜，基坑周邊緊鄰重要構(gòu)筑物，開挖時(shí)恰逢雨季，是武漢地區(qū)特大型基坑工程。在開挖過程中，采用信息法施工。圖6中表示出了在2007年9月23號終止開挖深度10.6m時(shí)fa剖面附近E5號樁排實(shí)測彎矩圖以及該樁附近C7號測斜孔水平向位移圖：最大彎矩390kN•m，最大位移26mm，兩者都位于坑底附近，測得土釘墻頂部和墻趾水平位移分別為39mm、26mm，基坑頂部沉降18.1mm。
    計(jì)算分析
    將fa段基坑作為計(jì)算分析對象。計(jì)算中采用的假設(shè)條件除了將均質(zhì)土改變?yōu)槎鄬油烈酝?，其余與本文第1節(jié)中介紹的六個假設(shè)條件基本一致。計(jì)算中，不考慮用作擋水的沿基坑四周布置的粉噴樁的作用。
    基坑近似長方形，長185.8m，寬96.9m，fa段位于長邊靠中間位置上，分析中沿長邊取1.2m厚作為平面應(yīng)變問題考慮。模擬范圍100m×35m: 坑內(nèi)50m，坑內(nèi)50m，最終開挖面以下取24.4m。分11層開挖，前10次每次開挖1m深度，最后一次開挖0.6m。對上部土釘墻，每步開挖完成后即設(shè)置該層土釘和噴射混凝土面層，開挖第四步后設(shè)置樁排，第六步后加內(nèi)支撐。
    各土層計(jì)算參數(shù)值如表2中所示，圖6表示出了土層厚度、基坑幾何尺寸、土釘墻和內(nèi)支撐樁排相對位置，下面分別介紹計(jì)算過程中與土釘墻、樁排相關(guān)的參數(shù)值。

    計(jì)算部分結(jié)果如圖5所示。當(dāng)H=4.1m時(shí)，土釘墻水平方向最大位移19.7mm。 當(dāng)H=10.6m，土釘墻坡頂和墻趾水平方向位移分別是32mm、22mm，基坑頂部沉降22mm，沿樁身方向最大水平方向位移32mm，位于坑底附近，形狀如圖8所示。由此可以看出，組合支護(hù)變形計(jì)算值與2007年9月23號監(jiān)測結(jié)果比較接近。
    計(jì)算樁身最大彎矩409.6kN.m，形狀如圖8所示。與監(jiān)測數(shù)據(jù)比較可知，計(jì)算值與實(shí)測數(shù)據(jù)接近。

    結(jié) 論
    支護(hù)結(jié)構(gòu)受到的土壓力與附近土體的彈、塑性狀態(tài)、強(qiáng)度以及它本身的剛度、位移、應(yīng)力路徑等多因素相關(guān)。本文介紹的組合支護(hù)結(jié)構(gòu)數(shù)值模擬則能將它們作為一個整體考慮。由于樁排頂部一方面受內(nèi)支撐的約束，另一方面受上部土釘墻的影響，顯然不符合Rankine土壓力理論的適用條件。因此，這種組合支護(hù)變形特征、擋土機(jī)理等有待進(jìn)一步的探。通過以上討論，土釘墻內(nèi)支撐組合支護(hù)受到的土壓力沿深度方向變化復(fù)雜，與Rankine土壓力大小、分布都不一致。本文根據(jù)數(shù)值模擬結(jié)果，提出了沿深度方向?qū)⒅鲃訁^(qū)土壓力分成三段分別計(jì)算土壓力系數(shù)、對Rankine被動土壓力系數(shù)打折的建議，對實(shí)際工程有較好的參考價(jià)值。