土工格栅加筋特性及其加筋结构计算方法研究
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摘要
土体作为天然的地质材料,具有良好的抗压特性,但其抗剪特性较差,抗拉性能几乎为零,因此在工程应用上受到很大程度的限制。为了提高土体承受侧向荷载的能力,在填方土体或地基内铺设适当的具有较好抗拉性能的土工合成材料。土工合成材料既能提高土体的抗剪强度、改善土体变形特性及透水特性,又能改善地基的动力特性。因此,在很多边坡、路堤、大坝及桥台等工程中均采用了土工合成材料进行加固处理,而其中以土工格栅作为加筋材料的工程处理效果尤其突出。然而,土工格栅在工作机理上不同于其它的土工合成材料,对于其特殊的受力条件、格栅与填土之间的复杂的相互作用机制、加筋地基的承载力计算方法等方面,目前尚缺乏广泛认可的理论体系和计算方法,还处于半经验半理论的不成熟阶段,设计理论远远落后于工程实践,因此需要开展深入及系统的理论分析与数值计算等方面的综合研究。为此,本文主要围绕土工格栅拉拔试验及其筋土之间的界面特性、加筋地基承载力计算方法以及土工格栅加筋结构的有限元模拟方法等方面进行了比较系统的探索,论文的主要研究内容及所取得的研究成果包括下列方面：
1.采用大尺寸土工格栅拉拔试验对土工格栅与填土之间的界面摩擦特性进行了研究。随着剪切位移的增大,格栅的拉拔阻力逐渐增大,摩擦应力沿着格栅表面逐渐向后传递,格栅任意位置处应变与时间的相互关系可以用S曲线函数进行描述。通过大量试验数据,针对格栅的变形与时间、纵向埋设位置之间的关系,建立了格栅应变的三维空间曲面,拟合出格栅应变函数ε(x,t),从而推得整段格栅随时间变化的拉拔力函数T(t),将预测的拉拔力函数与试验所得的拉拔力数据进行比较,最大误差不超过10%。在大型土工格栅加筋结构中,可以通过在格栅上分段预埋应变仪,用所得格栅应变数据推导出格栅全段的应变函数ε(x,t),采用上述方法可求得任意位置处的拉拔力T(t)函数,从而对加筋结构中格栅的拉拔力进行预判。
2.针对土工格栅在粉土填料中加筋效果并不理想的实际工程问题,将不同含量的工程碎石掺入粉土,在不同的法向荷载作用下进行若干组土工格栅拉拔试验,研究了碎石含量对土工格栅拉拔阻力及筋土界面摩擦系数的影响。试验发现,随着法向荷载的增加,土工格栅与填土之间的界面剪切作用逐渐增强,但是由于粉土与土工格栅的界面摩擦角较小,导致土工格栅在粉土中的加筋效果并不理想。在粉土中加入适量工程碎石,可使格栅横肋的被动阻抗作用得到了提高,但在法向荷载较小的情况下,碎石导致回填土产生了剪胀现象,格栅表面的法向应力大幅削弱,土工格栅的整体拉拔力反而降低。在竖向荷载较大的情况下,随着碎石含量的增加,土工格栅在粉土中的加筋效果显著增强。法向荷载在提高土工格栅表面的摩擦剪切阻力的同时,也抑制了填土所产生的剪胀现象,大幅增加了碎石对格栅横肋的被动阻抗作用。试验数据也表明在土工格栅加筋结构设计中,现有的界面摩擦角经验公式明显偏于保守。根据试验所得筋土之间界面摩擦系数随碎石含量x变化的数据,通过曲线拟合建议了两者之间的关系式。该试验结果对加筋结构设计与施工具有一定的参考价值。
3.开发并制作了小型独立拉拔装置,进行了一系列的室内土工格栅横、纵肋独立拉拔试验,研究了不同的法向荷载和拉拔速率对格栅加筋效果的影响,探讨了土工格栅横肋与纵肋的加筋机理及两者之间的相互影响,并将试验所得结果进行了比较系统地对比和分析。结果表明,格栅纵肋的摩擦阻力随着法向荷载的增大而增大,两者之间呈线性增长关系,但拉拔速率对纵肋的摩擦阻力影响并不明显。格栅横肋的被动阻力同样随着法向荷载的增大而增大,但变化速率与格栅纵肋比较相对较缓,格栅横肋的加筋作用需要一定的筋土相对位移才能充分发挥,建议在实际工程中对土工格栅采取相应的预应力拉拔措施；拉拔速率对格栅横肋的被动阻力影响较大,在法向荷载和拉拔速率较小的情况下,横肋所产生的被动阻力值接近于冲剪破坏模式下的计算值,而当法向荷载和拉拔速率逐渐增加时,试验结果则逐渐接近常规剪切破坏模式下的计算值,建议在加筋结构设计中应根据实际情况合理地选择格栅横肋的破坏模式进行计算。在剪切过程中,土工格栅横肋与纵肋之间存在着相互影响,两者的拉拔阻力并不能简单地叠加。格栅表面的法向应力变化导致纵肋的摩擦阻力逐渐减小,而横肋的被动阻力在剪切过程中进一步增加,占格栅整体拉拔阻力的66%左右,因此,在实际工程中应对格栅横肋的加筋效果予以足够的重视。该试验结果对土工格栅加筋结构设计提供了理论基础。
4.针对条形基础下加筋地基的极限承载力问题,根据塑性极限平衡原理,考虑各层筋材的拉力关系及拉力方向,在Mohr-Coulomb破坏准则的基础上,将加筋地基极限承载力问题等价为一个泛函极值问题。利用变分原理得到与平衡方程相等价的积分约束条件以及相应的欧拉方程与横截条件,在引入边界条件后,求得了加筋地基破坏时的滑裂面、滑裂面上法向应力及加筋地基极限承载力。与此同时,研究了土体内摩擦角、土工材料受拉方向、土工材料加筋层数及铺设层间距等因素对地基极限承载力的影响。计算结果表明,随着土体内摩擦角的增加,加筋地基的承载力逐渐增大,土体滑裂面发展主要以向外侧扩张为主,在深度方向上的变化并不明显；随着土工材料铺设层数的增加,加筋地基的承载力显著增强,但最终仍趋于一个稳定值,土体滑裂面发展主要以向下扩张为主,水平影响范围并不明显；对一些具有较高强度的土工材料,如土工格栅,设计中将其拉力假定为水平方向是不合理的,土工材料拉力方向应与该点的极半径垂直；计算中引用了论文第二章拉拔试验的界面摩擦系数,对极限状态下格栅的临界铺设长度进行了求解；在满足地基承载力需求的前提下,通过该方法可以确定出土工材料的最大铺设间距和最小层数,对加筋地基的工程设计具有一定的理论价值。
5.针对土工格栅与填土之间复杂的界面相互作用,本文提出了一个改进的格栅加筋结构有限元数值模拟方法。首先采用可变实体单元对土工格栅进行模拟,用球体对土工格栅横肋进行替换,球体高度通过土工格栅实际物理尺寸推导求得,从而实现对格栅横肋所产生的被动阻力的模拟过程。其次,针对土工加筋结构中土体的大位移大变形问题,在模型中采用欧拉单元对土体进行模拟,针对其节点不动,但材料在网格内部可自由流动的特点,成功解决了土工格栅加筋结构中土体局部大变形问题。通过大型通用有限元软件ABAQUS,采用CEL技术(欧拉单元与拉格朗日单元耦合分析),针对第二章土工格栅拉拔试验和室内小比尺加筋条形地基模型试验分别进行了有限元模拟分析,将计算结果与试验数据进行了对比分析,得出如下结论：拉拔试验有限元模拟结果能够准确地反映出土工格栅横肋在土中的真实加筋效果,模型中横肋产生的土体破坏形式与现有的理论破坏机制完全吻合,从而证明了该方法的合理性和有效性。将加筋地基的有限元计算结果与试验结果进行对比分析,两者所得到的沉降曲线趋势一致,数据吻合较好,从而证明了该有限元模拟方法的准确性和可靠性。该方法可以很好地用来模拟土工格栅与回填土体之间的相互作用,对土工格栅加筋结构的设计与施工具有一定参考价值。
As a natural geomaterial, soil has good bearing capacity, but it is of weaker tension or virtually no tension strength. So soil is not used directly in engineering sometimes and the field is almost limited. Geosynthetic reinforcement is a better option in many soil improvement methods because it has the advantages of enhancing shear strength, decreasing compressibility, improving the permeability and dynamic characteristics of foundation. Recently, this method is widely used in slope, embankment, dam and abutment etc. Especially geogrid-reinforced foundation is obviously better than other geosynthetics. However, because the working mechanism of the geogrid-reinforced method is different from that of traditional treatment to soft foundation, the special loading conditions, complex interaction mechanism between geogrids and soil and computational methods for the bearing capacity of reinforced foundation have not been well clarified. Thus, it will be theoretically important and practically significant to examine the working mechanism and work out effective methods for evaluating bearing capacity of reinforced foundation in soft ground under complex conditions. Therefore, this dissertation studies the interaction between geogrid and soil, the bearing capacity of reinforced foundation and numerical method. The main investigations and achievements in this PHD thesis are composed of following portions:
(1) A series of experiments to investigate the friction on the surface of geogrids were conducted in the laboratory under various level of normal load. By analyzing experimental data, some conclusions were made that the friction on the surface of geogrids gradually transfers backwards along it, which rapidly increases in early time of the pullout test and approaches to a stable value ultimately. The relationship between the strain of the geogrids and pulling time was simulated by the sigmoid curve. Based on the experimental data of the strain of the geogrids at different embedment, a three dimensional strain surface that represents a function of coordinate and time was obtained. The time function T(t) for pullout force of geogrids can be deduced through integration of friction along total length of geogrids. In geogrids-reinforced earth structure, some strain gauge can be set on the surface of geogrids, then the tension of geogrids at any position can be predicted by this method.
(2) Considering the reinforcement effects of geogrids in the silt not optimal, the pullout resistance behavior of geogrids in silt mixing gravel were conducted in the laboratory under different normal stress and gravel content. The effects of gravel content on the pullout resistance and friction coefficient of interface between geogrids and soil are investigated in various conditions. With the increasing of normal load on surface of samples, the pullout resistance of geogrids increases steadily, but the increasement is not large. This problem was mainly due to the smaller friction coefficient of interface between geogrids and soil. The passive resistance of transverse ribs can be enhanced by mixing some gravel in the silt. However, many cracks occurred on the surface of sample, and the whole resistance of geogrids decreased when the normal load was not enough to overcome the dilatation of soil. While the normal load and the gravel content increased at same time, the resistance of geogrids increased rapidly to a higher value. The normal load of sample can enhance not only the friction resistance of longitude ribs, but also the passive resistance of transverse ribs. The experiment data showed that the existing empirical formula in design about geogrids-reinforced earth structure is obviously conservative. Based on the relation of interface friction coefficient and gravel content, a fitting formula about them can be obtained. The experimental data is of referring value for design of geogrids-reinforced earth structure.
(3) A series of experiments to investigate the resistance mechanism of transverse and longitudinal ribs are performed with newly developed individual-rib pullout devices under various normal load and pullout velocity. Some conclusions were made by analyzing experimental data that the friction resistance of longitudinal ribs rapidly develops in early time of the pullout test, and it increases appropriately linearly with the increase of normal load but is almost not affected by pullout velocity. The passive resistance before transverse ribs increases slowly with the increase of normal load comparing with frictional resistance. And relative displacement is necessary to the development of pullout force. The failure mechanism of passive resistance transforms from the punching failure mechanism to the general shear failure mechanism with the increase of normal load and pullout velocity. The ultimate pullout resistance can not be interpreted as the sum of the passive and shear components. The changes of load upon the ribs make the interface shear resistance gradually decrease, but the passive resistance obviously increase to 66% of whole pullout resistance. It is suggested that more attentions on reinforcement effect of transverse ribs of geogrids should be paid.
(4) As for the ultimate bearing capacity of strip footings on homogeneous reinforced foundation, based on the limit equilibrium theory and the yielding criteria of Mohr-Coulomb, the equilibrium equation can be equivalently transformed to the format of functional extremum with undetermined boundary values by using the variational principle. The function of the sliding surface and the failure envelope of strip footings on homogeneous reinforced foundation are achieved when the boundary conditions are introduced. The effects of the angle of internal friction, tension angle of geosynthetics, layer numbers of geosynthetics and layer spacing of geosynthetics on the ultimate bearing capacity of strip footings on homogeneous foundation and the failure envelop are studied. With the increasing of the internal friction angle, the bearing capacity of reinforced foundation increases gradually. The sliding surface mainly develops along horizontal, rather than vertical direction. With the increasing of the layer numbers of geosynthetics, the bearing capacity of reinforced foundation increases obviously, but eventually tends to be a steady value. The sliding surface mainly develops along vertical, rather than horizontal direction. For some geosynthetics with higher strength, such as geogrids, it is not reasonable to assume the direction of its tension is always horizontal in design. In fact, the direction of tension is perpendicular to paler radius at the same point. The interfacial friction factors in chapter two were referenced in calculation to discuss the rational laying length of geogrids under the stripe footing. To meet the bearing capacity of foundation, the maximum spacing and minimum layers of geosynthetics can be obtained by this method. It is of referring value for design and construction of reinforced earth structure.
(5) The interaction between geogrids and soil is the fundamental and crucial factor on stability of geogrids-reinforced earth structure. An improved FEM method considering the interaction between them is proposed. In this method, geogrids were simulated with entity elements, and transverse ribs were replaced with some spheres that can produce passive resistance. And the Eulerian elements used to simulate soil can solve the non-linear distortion problem. With the CEL (Coupled Eulerian-Lagrangian) technology, the pullout test and geogrid-reinforced foundation test are modeled by the finite element software ABAQUS. The results of FE analysis about pullout test can reflect the actual stress and displacement in the reinforced structure, which has proven that this simulation method is effective and reasonable. And the results of FE analysis about geogrid-reinforced foundation compared well with the experimental results, which has proven that this simulation method has accuracy and reliability. It is of referring value for FE analysis of reinforced earth structure.
1.采用大尺寸土工格栅拉拔试验对土工格栅与填土之间的界面摩擦特性进行了研究。随着剪切位移的增大,格栅的拉拔阻力逐渐增大,摩擦应力沿着格栅表面逐渐向后传递,格栅任意位置处应变与时间的相互关系可以用S曲线函数进行描述。通过大量试验数据,针对格栅的变形与时间、纵向埋设位置之间的关系,建立了格栅应变的三维空间曲面,拟合出格栅应变函数ε(x,t),从而推得整段格栅随时间变化的拉拔力函数T(t),将预测的拉拔力函数与试验所得的拉拔力数据进行比较,最大误差不超过10%。在大型土工格栅加筋结构中,可以通过在格栅上分段预埋应变仪,用所得格栅应变数据推导出格栅全段的应变函数ε(x,t),采用上述方法可求得任意位置处的拉拔力T(t)函数,从而对加筋结构中格栅的拉拔力进行预判。
2.针对土工格栅在粉土填料中加筋效果并不理想的实际工程问题,将不同含量的工程碎石掺入粉土,在不同的法向荷载作用下进行若干组土工格栅拉拔试验,研究了碎石含量对土工格栅拉拔阻力及筋土界面摩擦系数的影响。试验发现,随着法向荷载的增加,土工格栅与填土之间的界面剪切作用逐渐增强,但是由于粉土与土工格栅的界面摩擦角较小,导致土工格栅在粉土中的加筋效果并不理想。在粉土中加入适量工程碎石,可使格栅横肋的被动阻抗作用得到了提高,但在法向荷载较小的情况下,碎石导致回填土产生了剪胀现象,格栅表面的法向应力大幅削弱,土工格栅的整体拉拔力反而降低。在竖向荷载较大的情况下,随着碎石含量的增加,土工格栅在粉土中的加筋效果显著增强。法向荷载在提高土工格栅表面的摩擦剪切阻力的同时,也抑制了填土所产生的剪胀现象,大幅增加了碎石对格栅横肋的被动阻抗作用。试验数据也表明在土工格栅加筋结构设计中,现有的界面摩擦角经验公式明显偏于保守。根据试验所得筋土之间界面摩擦系数随碎石含量x变化的数据,通过曲线拟合建议了两者之间的关系式。该试验结果对加筋结构设计与施工具有一定的参考价值。
3.开发并制作了小型独立拉拔装置,进行了一系列的室内土工格栅横、纵肋独立拉拔试验,研究了不同的法向荷载和拉拔速率对格栅加筋效果的影响,探讨了土工格栅横肋与纵肋的加筋机理及两者之间的相互影响,并将试验所得结果进行了比较系统地对比和分析。结果表明,格栅纵肋的摩擦阻力随着法向荷载的增大而增大,两者之间呈线性增长关系,但拉拔速率对纵肋的摩擦阻力影响并不明显。格栅横肋的被动阻力同样随着法向荷载的增大而增大,但变化速率与格栅纵肋比较相对较缓,格栅横肋的加筋作用需要一定的筋土相对位移才能充分发挥,建议在实际工程中对土工格栅采取相应的预应力拉拔措施；拉拔速率对格栅横肋的被动阻力影响较大,在法向荷载和拉拔速率较小的情况下,横肋所产生的被动阻力值接近于冲剪破坏模式下的计算值,而当法向荷载和拉拔速率逐渐增加时,试验结果则逐渐接近常规剪切破坏模式下的计算值,建议在加筋结构设计中应根据实际情况合理地选择格栅横肋的破坏模式进行计算。在剪切过程中,土工格栅横肋与纵肋之间存在着相互影响,两者的拉拔阻力并不能简单地叠加。格栅表面的法向应力变化导致纵肋的摩擦阻力逐渐减小,而横肋的被动阻力在剪切过程中进一步增加,占格栅整体拉拔阻力的66%左右,因此,在实际工程中应对格栅横肋的加筋效果予以足够的重视。该试验结果对土工格栅加筋结构设计提供了理论基础。
4.针对条形基础下加筋地基的极限承载力问题,根据塑性极限平衡原理,考虑各层筋材的拉力关系及拉力方向,在Mohr-Coulomb破坏准则的基础上,将加筋地基极限承载力问题等价为一个泛函极值问题。利用变分原理得到与平衡方程相等价的积分约束条件以及相应的欧拉方程与横截条件,在引入边界条件后,求得了加筋地基破坏时的滑裂面、滑裂面上法向应力及加筋地基极限承载力。与此同时,研究了土体内摩擦角、土工材料受拉方向、土工材料加筋层数及铺设层间距等因素对地基极限承载力的影响。计算结果表明,随着土体内摩擦角的增加,加筋地基的承载力逐渐增大,土体滑裂面发展主要以向外侧扩张为主,在深度方向上的变化并不明显；随着土工材料铺设层数的增加,加筋地基的承载力显著增强,但最终仍趋于一个稳定值,土体滑裂面发展主要以向下扩张为主,水平影响范围并不明显；对一些具有较高强度的土工材料,如土工格栅,设计中将其拉力假定为水平方向是不合理的,土工材料拉力方向应与该点的极半径垂直；计算中引用了论文第二章拉拔试验的界面摩擦系数,对极限状态下格栅的临界铺设长度进行了求解；在满足地基承载力需求的前提下,通过该方法可以确定出土工材料的最大铺设间距和最小层数,对加筋地基的工程设计具有一定的理论价值。
5.针对土工格栅与填土之间复杂的界面相互作用,本文提出了一个改进的格栅加筋结构有限元数值模拟方法。首先采用可变实体单元对土工格栅进行模拟,用球体对土工格栅横肋进行替换,球体高度通过土工格栅实际物理尺寸推导求得,从而实现对格栅横肋所产生的被动阻力的模拟过程。其次,针对土工加筋结构中土体的大位移大变形问题,在模型中采用欧拉单元对土体进行模拟,针对其节点不动,但材料在网格内部可自由流动的特点,成功解决了土工格栅加筋结构中土体局部大变形问题。通过大型通用有限元软件ABAQUS,采用CEL技术(欧拉单元与拉格朗日单元耦合分析),针对第二章土工格栅拉拔试验和室内小比尺加筋条形地基模型试验分别进行了有限元模拟分析,将计算结果与试验数据进行了对比分析,得出如下结论：拉拔试验有限元模拟结果能够准确地反映出土工格栅横肋在土中的真实加筋效果,模型中横肋产生的土体破坏形式与现有的理论破坏机制完全吻合,从而证明了该方法的合理性和有效性。将加筋地基的有限元计算结果与试验结果进行对比分析,两者所得到的沉降曲线趋势一致,数据吻合较好,从而证明了该有限元模拟方法的准确性和可靠性。该方法可以很好地用来模拟土工格栅与回填土体之间的相互作用,对土工格栅加筋结构的设计与施工具有一定参考价值。
As a natural geomaterial, soil has good bearing capacity, but it is of weaker tension or virtually no tension strength. So soil is not used directly in engineering sometimes and the field is almost limited. Geosynthetic reinforcement is a better option in many soil improvement methods because it has the advantages of enhancing shear strength, decreasing compressibility, improving the permeability and dynamic characteristics of foundation. Recently, this method is widely used in slope, embankment, dam and abutment etc. Especially geogrid-reinforced foundation is obviously better than other geosynthetics. However, because the working mechanism of the geogrid-reinforced method is different from that of traditional treatment to soft foundation, the special loading conditions, complex interaction mechanism between geogrids and soil and computational methods for the bearing capacity of reinforced foundation have not been well clarified. Thus, it will be theoretically important and practically significant to examine the working mechanism and work out effective methods for evaluating bearing capacity of reinforced foundation in soft ground under complex conditions. Therefore, this dissertation studies the interaction between geogrid and soil, the bearing capacity of reinforced foundation and numerical method. The main investigations and achievements in this PHD thesis are composed of following portions:
(1) A series of experiments to investigate the friction on the surface of geogrids were conducted in the laboratory under various level of normal load. By analyzing experimental data, some conclusions were made that the friction on the surface of geogrids gradually transfers backwards along it, which rapidly increases in early time of the pullout test and approaches to a stable value ultimately. The relationship between the strain of the geogrids and pulling time was simulated by the sigmoid curve. Based on the experimental data of the strain of the geogrids at different embedment, a three dimensional strain surface that represents a function of coordinate and time was obtained. The time function T(t) for pullout force of geogrids can be deduced through integration of friction along total length of geogrids. In geogrids-reinforced earth structure, some strain gauge can be set on the surface of geogrids, then the tension of geogrids at any position can be predicted by this method.
(2) Considering the reinforcement effects of geogrids in the silt not optimal, the pullout resistance behavior of geogrids in silt mixing gravel were conducted in the laboratory under different normal stress and gravel content. The effects of gravel content on the pullout resistance and friction coefficient of interface between geogrids and soil are investigated in various conditions. With the increasing of normal load on surface of samples, the pullout resistance of geogrids increases steadily, but the increasement is not large. This problem was mainly due to the smaller friction coefficient of interface between geogrids and soil. The passive resistance of transverse ribs can be enhanced by mixing some gravel in the silt. However, many cracks occurred on the surface of sample, and the whole resistance of geogrids decreased when the normal load was not enough to overcome the dilatation of soil. While the normal load and the gravel content increased at same time, the resistance of geogrids increased rapidly to a higher value. The normal load of sample can enhance not only the friction resistance of longitude ribs, but also the passive resistance of transverse ribs. The experiment data showed that the existing empirical formula in design about geogrids-reinforced earth structure is obviously conservative. Based on the relation of interface friction coefficient and gravel content, a fitting formula about them can be obtained. The experimental data is of referring value for design of geogrids-reinforced earth structure.
(3) A series of experiments to investigate the resistance mechanism of transverse and longitudinal ribs are performed with newly developed individual-rib pullout devices under various normal load and pullout velocity. Some conclusions were made by analyzing experimental data that the friction resistance of longitudinal ribs rapidly develops in early time of the pullout test, and it increases appropriately linearly with the increase of normal load but is almost not affected by pullout velocity. The passive resistance before transverse ribs increases slowly with the increase of normal load comparing with frictional resistance. And relative displacement is necessary to the development of pullout force. The failure mechanism of passive resistance transforms from the punching failure mechanism to the general shear failure mechanism with the increase of normal load and pullout velocity. The ultimate pullout resistance can not be interpreted as the sum of the passive and shear components. The changes of load upon the ribs make the interface shear resistance gradually decrease, but the passive resistance obviously increase to 66% of whole pullout resistance. It is suggested that more attentions on reinforcement effect of transverse ribs of geogrids should be paid.
(4) As for the ultimate bearing capacity of strip footings on homogeneous reinforced foundation, based on the limit equilibrium theory and the yielding criteria of Mohr-Coulomb, the equilibrium equation can be equivalently transformed to the format of functional extremum with undetermined boundary values by using the variational principle. The function of the sliding surface and the failure envelope of strip footings on homogeneous reinforced foundation are achieved when the boundary conditions are introduced. The effects of the angle of internal friction, tension angle of geosynthetics, layer numbers of geosynthetics and layer spacing of geosynthetics on the ultimate bearing capacity of strip footings on homogeneous foundation and the failure envelop are studied. With the increasing of the internal friction angle, the bearing capacity of reinforced foundation increases gradually. The sliding surface mainly develops along horizontal, rather than vertical direction. With the increasing of the layer numbers of geosynthetics, the bearing capacity of reinforced foundation increases obviously, but eventually tends to be a steady value. The sliding surface mainly develops along vertical, rather than horizontal direction. For some geosynthetics with higher strength, such as geogrids, it is not reasonable to assume the direction of its tension is always horizontal in design. In fact, the direction of tension is perpendicular to paler radius at the same point. The interfacial friction factors in chapter two were referenced in calculation to discuss the rational laying length of geogrids under the stripe footing. To meet the bearing capacity of foundation, the maximum spacing and minimum layers of geosynthetics can be obtained by this method. It is of referring value for design and construction of reinforced earth structure.
(5) The interaction between geogrids and soil is the fundamental and crucial factor on stability of geogrids-reinforced earth structure. An improved FEM method considering the interaction between them is proposed. In this method, geogrids were simulated with entity elements, and transverse ribs were replaced with some spheres that can produce passive resistance. And the Eulerian elements used to simulate soil can solve the non-linear distortion problem. With the CEL (Coupled Eulerian-Lagrangian) technology, the pullout test and geogrid-reinforced foundation test are modeled by the finite element software ABAQUS. The results of FE analysis about pullout test can reflect the actual stress and displacement in the reinforced structure, which has proven that this simulation method is effective and reasonable. And the results of FE analysis about geogrid-reinforced foundation compared well with the experimental results, which has proven that this simulation method has accuracy and reliability. It is of referring value for FE analysis of reinforced earth structure.
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