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Numerical study of the soilstructure interaction within mining subsidence areasOlivier Deck *, Harlalka AnirudhLAEGO, Nancy-Universite, Ecole des Mines de Nancy, Parc de Saurupt, F-54042 Nancy, Francearticle infoArticle history：Received 24 September 2009Received in revised form 9 June 2010Accepted 3 July 2010Available online 24 July 2010AbstractStructures affected by mining subsidence are exposed to heavy damage potential in relation to the induced tensile or compressive horizontal ground strains. This study intends to specify and compare the mining subsidence effect in terms of building transmitted movements or induced stresses, given the soilstructure interaction phenomena produced at the interface between a “stiff” elastic structure and a “exible” elastoplastic soil. A series of models, developed using nite element software, has enabled a parametric study of the soilstructure interaction. Briey, the results of this study enabled visualisation and characterisation of various phenomena related to the soilstructure interaction as a function of the intensity of the free-eld horizontal ground strain caused by subsidence, the building length and stiffness, and the soil mechanical properties. It was thus possible to identify and assess the relations between free-eld horizontal ground movements and movements and stresses transmitted to the buildings. Differences between the traction and compression zones were investigated in order to identify the nonlinearity of the building loading. Finally, an analytical model of building loading assessment was tested and compared with the numerical results, with similar loading in the compression zone and discrepancies in the traction zone.2010 Elsevier Ltd. All rights reserved.Keywords：Mining subsidence; Soilstructure interaction; Horizontal ground strain; Buildings loading; Finite element method1. IntroductionMining subsidence refers to ground movements caused by the collapse of mines or underground quarries that are characterized by vertical and horizontal displacements and are the source of potentially severe damage to buildings located in subsidence areas (Fig. 1). Many countries are concerned by this hazard; the Lorraine region in France is an example. It contains a great number of iron, salt and coal deposits that were heavily mined until the beginning of the 1990s (salt continues to be mined). The presence of the former iron mines has raised many issues, including those of existing building vulnerability and building design.Many methods exist for evaluation of the free-eld ground movements of subsidence 1. The amplitude of the movement depends on the underground cavity geometry (e.g., opening, width, depth, and ore dip), the quarrying technique (e.g., caving, room and pillar methods) and the type of overburden (geological and geotechnical specications, presence of rock beds, material strength and stiffness). Mining subsidence is characterised by ground surface vertical that may reach a few meters in length and horizontal movements (Fig. 1a). Two main zones are identied： the compression zone and the traction zone. The former is located near the centre of the subsidence and is characterised by a sagging prole (vertical movements) and compressive horizontal ground strains (horizontal movements). The latter is located near the edge and is characterised by a hogging prole and tensile horizontal ground strains. In these two zones, the ground curvature typically lies between 500 m and 5000 m and the horizontal ground strain lies between 1 and 10 mm/m (Fig. 1b). Building damage (Fig. 1c) is mainly associated with the exion induced by the ground curvature and the horizontal load induced by the horizontal ground strain. However, the stiffness contrast between ground and buildings, possible building collapse and soil yield involve soilstructure interaction phenomena. The impact assessment of subsidence on buildings raises the following issues：(i) Comprehending associated soilstructure interaction phenomena and the behaviour of the ground in the vicinity of a building is necessary to improve existing damage assessment methods. Kratzsch addresses the effect of building stiffness as the underground displacement eld change and rupture shear planes appear in the soil with a direction that depends on the free-eld horizontal ground strain. In the compression zone, the shear planes are directed from the building edge outward the centre of the structure (Fig. 2a). In the traction zone, the shear planes are directed from the building edge toward the centre of the structure (Fig. 2b). The inuence of the ground mechanical properties and the building properties on these shear planes is not known.(ii) Free-eld displacements may not be fully transmitted to buildings when they are stiff and strong. In this case, the damage assessed by the free-eld groundmovements prole can be overestimated. The question of the relation between the free-eld and building displacements is Investigated with numerical modelling 39. The results show that the free-eld ground movements are not fully transmitted to the structure. The transmission ratio of the vertical and horizontal movements depends on the building strength and stiffness. Currently, the inuence of the ground mechanical properties, stiffness and strength, have not been investigated.(iii) The impact of subsidence can be investigated by assessing building-induced stresses or ground stress variations around the building 2,1012. Ground curvature induces variations in the vertical stresses under the foundations, and horizontal ground strain induces horizontal forces, including frictional forces beneath the structure foundations and horizontal ground pressure (active or passive forces) on the buried parts of the structure (Fig. 3). In compression zone, the horizontal force on the building is then bounded by shear sliding under the foundations and the passive Rankine state onthe horizontal walls under the ground surface (Fig. 3a). In traction zone, the horizontal force is bounded by shear sliding under the foundations and the active Rankine state(Fig. 3b). Currently, no experiments have been reported that may conrm this induced stress assessment model.Based on the Lorraine region as a test area, the aim of the present work is to investigate the inuence of the ground mechanical properties and building properties on the horizontal ground strain on buildings. In particular, this work focuses on understanding： (i) the associated soilstructure interaction phenomena; (ii) the transmission ratio of the free-eld horizontal ground strain to a building; and (iii) the associated horizontal building loading.For this purpose, a numerical model is developed. The results：(i) supplement the soilstructure interaction phenomena suggested by Kratzsch 2 in the traction and compression zones; (ii) indicate the transmission ratio of the free-eld groundmovements, which appear to be nonlinearly dependent on the free-eld ground movements; and (iii) validate the model of induced stresses in the compression area and invalidate the model in the traction area. 2. Modelling the behaviour of a structure under the inuence of subsidence2.1. Objectives of the numerical modelA numerical model is developed in order to investigate the inuence of the ground mechanical properties and the building tiffness on the building loading induced by mining subsidence stresses and transmitted displacements). A parametric study is arried out to extend the signicance of the results. The model is ot developed to predict or reproduce ground movements in a particular context. Consequently, the numerical model must satisfy the following equirements： (i) It must be able to reproduce a set of realistic free-eld ground displacements at the surface with a subsidence radius that is much greater than the building length, a maximal vertical displacement of some meters and associated horizontal ground strain that may reach 10 mm/m (Fig. 1). (ii) It must be able to model realistic soilstructure interaction phenomena that may occur around the building with soil yielding. Because these phenomena are expected to occur up to a depth close to the building half-length 13, the free-eld ground displacements must be realistic over a depth greater than the building half-length, and the soil must be modelled with elastoplastic properties. (iii) It must be able to assess stresses and transmitted displacements that a building must resist to in order to avoid significant damage. Consequently, the numerical model focuses on the building stiffness. Buildings are modelled with elastic properties, and the inuence of the potential building damage is not investigated. 2.2. Presentation of the modelThe numerical model is performed with nite element software (CESAR-LCPC) under the plane strain hypothesis. Real problem is 3D, but effect of mining subsidence is more effective in the direction of the subsidence radius than in the tangential direction. This study only addresses the effect of the major effect of subsidence, i.e. in the direction of the subsidence radius with a 2D nite element model. The model consists of two superimposed soil layers, each 50 m thick and 500 m long, with a building located in either the traction zone or in the compression zone (Fig. 4). The lower layer is assumed to be elastic, whereas the upper layer is modelled as elastoplastic with a MohrCoulomb criterion without strain hardening in order to investigate the ground yield (Table 1). The boundary conditions are： locked horizontal displacement on the right and left boundaries, locked vertical displacement over the left half of the lower boundary, and uniform vertical displacement imposed over the right half of the lower boundary to model the subsidence. The function of the lower layer is to prevent great strains and important ground yielding occurring in the vicinity of the lower boundary. If it happens, convergence of calculations and accuracy of the results in the vicinity of the buildings should be compromise. Combining the elastic lower layer and the boundary conditions (vertical displacements) is an innovativemethod that is used to apply boundary conditions on the upper layer that will consecutively induce realistic vertical and horizontal displacements in the upper soil layer (see next section for the description of these displacements and for model validation). Finally, the upper ground layer is the only one in which the stressstrain results will be interpreted.Seven values for the imposed vertical displacement are considered： 0.125 m, 0.25 m, 0.375 m, 0.5 m, 1 m, 1.5 mor 2 m. These values lead to equivalent maximal vertical displacement of the surface and to increasing values of the maximal horizontal ground strain, from 0.25 mm/m to 10 mm/m, which match the observed magnitude of this movement (Fig. 1).Many building typologies are concerned with mining subsidence： old masonry buildings without any reinforcement and wood oors, old masonry buildings without any reinforcement but with steel beams or concrete oors that may act as reinforcements 14, recent masonry buildings with concrete oors and slight reinforcements, and concrete buildings with extensive reinforcements. The numerical model is not designed to evaluate stresses and transmitted displacements for a particular building, but for a large sample of buildings in relation to their horizontal stiffness.Consequently, structures are modelled in two ways in order to investigate both stiff and exible buildings.(i) Use of the rst structure is intended to investigate the soilstructure interaction with a simple, rigid structure. The structure consists of a concrete raft that is 50 cm thick (Fig. 5a), with three possible lengths (L = 8 m, 16 m and 32 m), a Youngs modulus of Eraft = 20,000 MPa that is simply laid on the soil and loaded by a distributed 5 kN/ml force (representing a 15-cm concrete paving and its associated dead loads) and 100 kN point forces spaced every 4 m (representing a drop in load on load-bearing walls). In order to evaluate the horizontal stiffness of this structure Kraft”, the raft is assumed to be loaded by constant but opposite shear stresses s under each building half-length (Fig. 5a). Shear stresses lead to a global horizontal loading Fraft (Eq. (1) and a linear variation of horizontal strains over the raft that results into a displacement D of each edge of the raft (Eq. (2). Consequently, the average horizontal strain of the raft eraft,average is equal to 2D/L and shear stresses can be expressed with Eq. (7). Combining Eqs. (1)(3) gives the horizontal stiffness of the raft (Eq. (4). (1) 0xL/2 (2) (3)where A is the cross-section of the raft and is equal to 0.5 m for a unit width.=2=20000MN (4)Consequently, an old rubble stone masonry wall with a Youngs modulus of 3000 MPa, a width of 0.4 m and a height of 8 m or a recent concrete stone masonry wall with a Youngs modulus of 10,000 MPa, a width of 0.2 m and a height of 5 m would have the same horizontal stiffness. This structure is referred to as a “raft structure” or “rigid structure”.(ii) The second structure is intended to investigate the soilstructure interaction with a simple, “flexible” structure. It consists of a concrete frame structure, with a succession of concrete frames that are 4 m long and 2.5 m high, lying on shallow foundations (dimensions and mechanical properties are listed in Table 1 and Fig. 5b). Three different lengths are considered (L = 8 m, 16 m or 32 m) and the structure is loaded like the raft structure.In order to evaluate the horizontal stiffness of this structure“”, the frame is assumed to be loaded by two opposite horizontal loadings on the foundations (Fig. 5b). This results into a displacement of each foundation and an average horizontal strain of the frame equal to . The horizontal stiffness of this structure is then mainly dependent on the distance between the foundations and the first floor. It may be overestimated by assuming that each foundation is a cantilever beam (Eqs. (5) and (6). (5)where is the Youngs modulus of the columns, is the inertia of the cross-section (6.66) and H is the distance between the foundations and the first floor (H = 1 m). (6)For an 8-m long frame, is equal to 160 MN and it may be concluded that this structure is very flexible compare to the raft structure. The final results (Sections 4 and 5) validate the effectiveness of the assessed horizontal stiffness. This structure is referred to as a “frame structure” or “flexible structure”.Each modelled structure, considering length, is located either in the traction or compression zone of the subsidence. The experimental design technique is introduced to minimise the number of required studies. Ultimately, for a given structure (frame structure or raft structure, with a fixed length), a given location of the building in the subsidence (traction or compression zone) and a given imposed vertical displacement (0.125 m, 0.25 m, 0.375 m, 0.5 m, 1 m, 1.5 m or 2 m), five computations are performed, corresponding to a different mechanical set of Youngs modulus of the ground and friction angle E, (Table 1)： 50 MPa, 30, 350 MPa, 30, 200 MPa, 40, 50 MPa, 50 or 350 MPa, 50, which results in a total of 420 computations for the entire model. From a strictly numerical point of view, the mesh is composed of six-node quadratic elements and was refined adjacent to the structure, where the average mesh dimension is roughly 10 cm. Since computations are conducted in elastoplasticity, it was verified that an increase in the number of displacement increments (seven increments used to impose the 2 m subsidence) and a reduction in the convergence threshold values did not significantly change any of the results.2.3. Model validationThe numerical model is tested and validated by comparing the calculated displacements in the upper ground layer with monitored displacements and theoretical profiles of the ground displacements. The numerical model is not intended to predict vertical and horizontal displacements in a particular case, but to reproduce realistic displacements in order to further investigate the influence of the soilstructure interaction on building loading.The first step of the validation consists of comparing the vertical ground displacements with examples of monitored subsidence (Fig. 6). Three examples of mining subsidence are considered from different countries or a different mining basin： an iron mine in France that is about 150 m deep 15, a coal mine in France that is about 600 m deep 16 and a coal mine in South Africa that is about 100 m deep 1.在采矿塌陷区范围内的土壤结构相互作用的数值研究Olivier Deck , Harlalka Anirudh法国南锡大学南锡国立高等矿业学院，F-54042摘要采煤沉陷影响的建筑物存在很大的安全隐患，很有可能收到严重破坏，这与地面产生的拉伸与压缩应力有关。本研究鉴于土壤结构之间的相互作用在界面之间产生一个“硬的”弹性结构和一个“柔韧的”弹塑性土壤，旨在说明和比较采煤沉陷在建筑物传播移动或诱导应力方面的影响。通过有限元软件开发的一系列模型，使土壤结构相互作用参数化研究变得可行。简单的说，土壤结构的相互作用是由地面沉降，建筑物的长度和刚度以及土壤力学性质引起的，它可以通过水平地面的自由场强度函数来表示，本文的研究结果可以使土壤的相互作用变得可视化和特征化。这使得在确定和评估自由场水平地面移动和建筑物中的运动和应力传递之间的关系这种方案变得可行。为了确定建筑物荷载的非线性，进行了拉伸区与压缩区对比研究。最后，建立了建筑物荷载评估分心模型，并与数值模拟情况下相同荷载在拉伸区和压缩区的差异经行了比较。关键词：开采沉陷；土壤结构的相互作用；水平地面应变；建筑物荷载；有限元法1. 简介开采沉陷是指由采空区或地下采石场岩层垮落而引起地表移动，地表移动体现在地表的垂直和水平移动，并且对在塌陷区（图1）的建筑物有十分巨大的潜在威胁。很多国家已对此高度重视，法国洛林地区就是一个例子。该地区富含大量的铁、盐、煤炭资源，直到20世纪90年代才停止开采（盐仍在开采）。前面提到的铁矿的开采现如今产生了很多的隐患，包括现有建筑物的保护以及建筑物规划。对于地表移动变形的评价方法有多种。地表移动变形的剧烈程度取决于地下空洞的几何形状（例如开放式，采空区宽度和深度以及矿石富水性），采石技术（如全部垮落法，支护方法）和覆岩的类型（地质和岩土特性，岩床现状，岩石的强度和刚度）。开采沉陷的特点是地表在垂直和水平方向的移动可达数米（图1.a）。其中有两个主要区域：压缩区和拉伸区。前者位于沉降中心附近，这个区域的特点是呈凹形（垂直运动），水平方向受到压缩应力（水平运动）。后者靠近塌陷区边缘，这个区域的特点是呈现凸形且水平方向受拉。在这两个区域，地面曲率通常介于500m到5000m之间，地面水平变形介于1mm/m到10mm/m之间（图1.b）。图1.(a)主要地面沉降变形说明：垂直位移，水平应变和曲率(b)地面变形和沉降尺寸的代表值(c)塌陷区的受损坏建筑物建筑物的破坏（图1.c）主要与地表曲率大小和水平应力引起的水平变形有关。然而，通过地面与建筑物之间抗变形能力的对比研究，得出建筑物损坏和岩层移动变形中都包括土壤结构之间的相互作用现象。对建筑物沉降评估方面提出了一下建议：理解相关的土壤结构相互作用现象和建筑物附近地面的移动情况对于改善现有的建筑损坏评价方法是十分必要的。Kratzsch指出建筑物抗变形能力方面是随着地表移动变形量的大小和受地表水平变形影响而在剪切面同一方向断裂而变化的。在压缩区，断裂面由建筑物边界朝远离建筑中心的方向发展（图2.a）。在拉伸区，断裂面有建筑物边界向建筑物中心发展（图2.b）。地面的力学性能和建筑物性质对剪切面得影响目前尚不清楚。(1)地表移动变形可能无法完全传递到抗变形强的建筑物上。在这种情况下，地表移动变形剖面图的损害评估可能被高估。地表和建筑物之间移动变形关系问题已经在用数值模型的方法进行研究。研究结果表明，地表移动变形并没有完全传递给建筑物。垂直和水平变形的传动比决定于建筑物的强度和硬度。目前，地面力学性能，刚度和强度所产生的影响还没有进行研究。(2)我们可以通过建筑物荷载和其周围的地表应力变化来研究地表沉降所产生的影响。地面曲率引起的地基中的垂直应力以及水平应力引起的水平变形，包括地基中被埋藏的建筑部分的摩擦和水平压力（主动或被动）（图3）。在压缩区域，建筑物的水平应力受地基的剪切滑移和地基中的水平面的被动兰金指数的限制（图3.a）。在拉伸区域，水平应力受剪切滑移和地基中德积极兰金指数的限制（图3.b）。目前，还没有试验报告来证实这种应力评价模型。以洛林地区作为试验区的基础上，本工作的目的是研究地面机械性质和建筑物特性对建筑物水平方向应力的影响状况：1)相关的土壤结构相互作用现 2)地面水平应力到建筑物的传动比3)与水平建筑物荷载的关联性。为此目的，建立了数值模型。成果有：1) Kratzsch提出的在拉伸区域和压缩区域对土壤结构之间相互作用的现象的修复2)预计地表移动的传动比，这主要体现在地表的移动变形方面3)验证了在压缩区的应力模型否定了在拉伸区的模型。图2 Kratzsch指出的沉陷区域建筑物下的受力状况(a)压缩区(b)拉伸区2. 建立在采矿沉陷下的结构模型2.1 数值模式研究为了探讨地面力学性质和建筑物荷载的建筑特性由于开采沉陷（应力和移动传递）所产生的影响，建立了数值模型。为了体现该成果的重要性由提出了相关参数的研究模型。该模型没有发展到预测或重现在特定情况下的地表运动。因此，数值模型必须满足以下要求：1、它必须能够真实的再现随着沉陷半径地表所产生的移动变形，沉陷半径要比建筑物长度大得多，并且要有数米的最大垂直移动及地面水平变形要达到10mm/m（图1）。2、它必须能够模拟可能发生在建筑物周围受压缩土壤的真实的土壤结构之间的相互作用现象。因为这些现象可能发生在接近建筑物一半长度的深度范围。地表移动变形必须实现在地基深度超过建筑物长度一半的真实性，并且地基必须用弹塑性材料进行模拟。3、为了避免重大损失，该模型必须能够评估应力和建筑物能够承受的变形。因此，该数值模型的重点在于建筑物的刚度。用弹性模型模拟建筑物，对建筑物受到的潜在损坏的影响还没有进行研究。2.2 演示模型数值模型是在假设平面应力条件下用有限元软件（CESAR-LCPC）进行模拟的。现在的关键问题是3D技术，但采煤沉陷在沉陷半径方向的影响比在切线方向的影响要显著。本次研究仅涉及了主要沉降影响方面。例如沉陷半径方向的二维有限元分析模型。该