土工格室+碎石桩双向增强复合地基承载特性及沉降计算研究
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摘要
土工格室+碎石桩双向增强复合地基作为一种新型的软基处治方法,因其良好的工作性能获得了工程界的青睐,目前在公路软基处治、铁路路基加固、油罐地基加固等工程中得到了广泛应用,并取得了良好的加固效果,但是该处治方法的理论研究尚欠成熟。为此,本文结合国家高技术研究发展计划(863计划)项目“大面积不均匀公路软弱地基按沉降控制双向增强处治技术”(2006AA11Z104)、国家自然科学基金项目(51078138)及湖南大学博士学位论文选题资助项目,从土工格室+碎石桩双向增强复合地基的承载机理分析、固结分析、桩土应力比计算、沉降计算等方面出发,通过理论分析和室内模型试验并结合工程实际进行较深入系统的研究。
本文首先针对土工格室和碎石桩复合地基的作用机理进行探讨,在此基础上对两者组合而成的双向增强复合地基的作用机理进行分析；对土工格室加筋垫层和碎石桩复合地基承载力计算方法进行总结,考虑土工格室与碎石桩复合地基两者相互作用,并结合碎石桩的固结效应,探讨了土工格室+碎石桩双向增强复合地基承载力计算方法。同时基于轴对称空间问题的弹性理论,选取不同的桩土单元,推导出碎石桩复合地基桩土应力比计算公式,并在此基础上考虑碎石桩三维轴对称固结模式,基于桩体和土体的应力时效特征,推导考虑时效的复合地基桩土应力比计算公式,并通过算例验证该解答的合理性。
其次,针对土工格室+碎石桩双向增强复合地基变形特点,探讨了其变形机理并总结了已有的沉降计算方法；在此基础上,考虑碎石桩复合地基桩土刚度差异并不大,将其视为一复合土体,土工格室加筋垫层则视为置于Winkler地基上的弹性地基梁(称为土工格室梁),同时考虑土工格室加筋垫层与碎石桩复合地基之间的切向摩阻力,提出了土工格室+碎石桩双向增强复合地基沉降计算模型,推导出土工格室+碎石桩双向增强复合地基变形计算的控制方程,并结合微分算子级数法求得相应的解析解,由此导得了土工格室+碎石桩双向增强复合地基沉降计算公式。算例分析表明该解析解是正确合理的,进一步的参数分析表明,复合土体的法向和切向弹簧刚度对土工格室+碎石桩双向增强复合地基的变形有较大影响,土工格室加筋垫层的力学参数如弹性模量等及几何参数如高度等则影响较小。
再次,根据前述土工格室+碎石桩双向增强复合地基沉降计算的弹性地基梁模型,引入分步计算法概念,首先考虑各种竖向荷载下土工格室梁的挠度计算,推导并汇总了工程中常见竖向荷载下土工格室梁的挠度解答,然后考虑土工格室梁的实际变形曲线特征,建立切向相对位移与挠度之间的关系式,并推导出相应土工格室梁的切向相对位移的解答,最后将地基反力和切向摩阻力作为荷载作用于土工格室梁上,导出土工格室梁的最终变形并进一步导得土工格室+碎石桩双向增强复合地基沉降计算公式。算例分析验证了分步计算法计算结果与前述解析解的一致吻合性,表明分步计算法切实可行。
基于前述土工格室+碎石桩双向增强复合地基沉降计算的弹性地基梁模型,从能量角度出发,根据最小势能原理,建立考虑切向摩阻力的土工格室梁挠度方程,并引入合适的位移函数,导出考虑切向摩阻力作用时土工格室梁的挠度解答并进一步导得土工格室+碎石桩双向增强复合地基沉降计算公式。算例分析表明该解答计算结果与前述解析解一致,表明该能量法解答切实可行,亦进一步完善了土工格室+碎石桩双向增强复合地基沉降计算的方法体系。
最后,根据相似理论,设计并完成了单纯软土地基、袋装砂井地基、土工格室加筋复合地基、碎石桩复合地基、土工格栅+碎石桩复合地基和土工格室+碎石桩复合地基等六组室内模型试验,并对试验成果进行了分析,从静载试验、应力分布、桩土应力比和孔隙水压力分布规律等方面探讨了袋装砂井地基、碎石桩复合地基、土工格栅+碎石桩复合地基和土工格室+碎石桩复合地基等的承载变形机理以及排水固结特点,并利用模型试验数据对前述沉降计算理论进行了验证分析。结果表明,土工格室加筋垫层可有效扩散和均化上部荷载,减小地基的总沉降和不均匀沉降；碎石桩桩顶应力集中效应明显,可有效加速地基排水固结；土工格室+碎石桩复合地基可有效提高地基承载力,降低桩土应力比,同时能够加速软基排水固结,减小地基沉降和不均匀沉降。此外,基于前述土工格室+碎石桩双向增强复合地基沉降计算的理论方法所得结果与室内模型试验实测结果吻合较好,也进一步验证了本文理论成果的合理性和可行性。
As a new soft foundation treatment method, the composite foundation bidirectionally reinforced by stone columns and geocell is favored for civil engineers for its better service behavior and widely applied in engineering practice such as soft soil improvement in highway, subgrade strengthening in railway and oil tank engineering and so on, obtaining favorable reinforcing effect. However, the theory of the composite foundation remains immature. In this paper, the bearing characteristic, consolidation analysis, pile-soil stress ratio and settlement calculation of the stone columns and geocell reinforced composite foundation have been discussed based on several aspects of theoretical analysis, model experiment and engineering practice. This paper is supported by the High Technique Research and Development Program of China (863program)——"The treatment technique of bidirectionally reinforced foundation based on the settlement control for large area and non-uniform soft subgrade in highway construction"(2006AA11Z104), the Natural Science Foundation of China (51078138) and the financial support program of topic selection of thesis for the degree of doctor of engineering in hunan university.
Firstly, the working mechanism of the two-direction composite foundation is studied based on the analysis of working mechanism of geocell and stone columns. The calculation methods for the bearing capacity of the geocell reinforced mattress and stone columns reinforced composite foundation are respectively summarized. The calculation method for bearing capacity of the composite foundation bidirectionally reinforced by stone columns and geocell is investigated with consideration of their interaction on each other and the consolidation character of the stone columns. According to axisymmetric elastic theory, the formula for the pile-soil stress ratio of stone columns reinforced composite foundation is obtained by choosing different pile and soil elements. Then the formula for the pile-soil stress ratio considering time effect and three dimensional axisymmetric consolidation model of gravel pile is derived based on the analysis of the time effect of pile and soil stresses. The rationality of the solution of the pile-soil stress ratio is verified by an engineering example.
Secondly, in view of the deformation characteristics of the composite foundation bidirectionally reinforced by stone columns and geocell, the deformation mechanism is discussed and the existing settlement calculation methods are summarized. Regarding the difference of stiffness of gravel pile and soil is not obvious, the composite foundation can be regarded as a composite soil. The geocell reinforced cushion can be regarded as a beam resting on a Winkler foundation which can be called the geocell reinforced beam. Considering the tangential frictional resistance between the geocell reinforced cushion and gravel pile composite foundation, the settlement calculation model of the composite foundation bidirectionally reinforced by stone columns and geocell is established, the governing equation is deduced and its corresponding analytical solution is obtained based on the differentiator series method. Thus the settlement calculating formula of the composite foundation is derived. The example analysis shows that the analytical solution is right and the parameter analysis shows that the normal and tangential spring stiffness of the composite soil have quite great influence on deformation of composite foundation, mechanical and geometric parameters of geocell reinforced cushion such as elastic modulus and height are less affected.
Then, based on the elastic foundation beam model for the settlement calculation of composite foundation bidirectionally reinforced by stone columns and geocell, the separate-step calculation concept is introduced. Firstly the deflection of geocell reinforced beam subjected to all sorts of vertical loads is considered and the deflection solutions of geocell reinforced beam are derived and summarized. Then considering the actual deflection curve of geocell reinforced beam, the relationship between tangential relative displacement and the deflection is established. The solution of tangential relative displacement is acquired. The subgrade reaction and tangential frictional resistance are obtained and applied to the geocell reinforced beam as loads so that the final deformation of geocell reinforced beam is developed. Thus the settlement calculating formula of composite foundation bidirectionally reinforced by stone columns and geocell is derived. The results calculated by separate-step calculation method is proved to be consistent with previous analytical solution in an example, which indicates that the separate-step calculation method can be used in the engineering practice.
Based on the beam model for the settlement calculation of the two-direction composite foundation formed by geocell reinforced mattress and gravel piles and the principle of minimum potential energy, the governing energy equations for geocell reinforced beam considering tangential frictional resistance are obtained and solved by an appropriate displacement function. Then the formula for the settlement of the two-direction composite foundation is acquired. The analysis of examples indicates the results calculated by the energy method agree well with those by the analytical solution proposed above. The validity and rationality of the solution are verified and the methodological system of the settlement calculation for two-direction composite foundation gets improved further.
Lastly, according to the theory of similarity, a group of indoor model tests including the untreated soft soil, subgrade reinforced by sand bag wells, geocell reinforced subgrade, composite foundation reinforced by gravel piles, composite foundation reinforced by geogrid and gravel piles and composite foundation reinforced by geocell and gravel piles are designed and completed. The obtained data from model tests is analyzed. The bearing and consolidation characteristic and deformation mechanism of subgrade reinforced by sand bag wells, geocell reinforced subgrade, composite foundation reinforced by gravel piles, composite foundation reinforced by geogrid and gravel piles and composite foundation reinforced by geocell and gravel piles are discussed by the analysis of the loading test, stress distribution, pile-soil stress ratio and water pressure. The settlement calculation method proposed above is verified by the model test data. The test results shows that the geocell reinforced mattress can spread and homogenize the loads, reduce the settlement and the non-uniform settlement of subgrade, the gravel pile can effectively accelerate the consolidation of subgrade and the stress concentration effect is clear, and the composite foundation formed by geocell and gravel piles can greatly increase the bearing capacity of subgrade, reduce the pile-soil stress ratio, accelerate the consolidation of soft foundation and reduce the settlement and the non-uniform settlement. Moreover, the results calculated by the theory method proposed above agree well with those from the model tests, which means the theory in this paper are rational and feasible.
本文首先针对土工格室和碎石桩复合地基的作用机理进行探讨,在此基础上对两者组合而成的双向增强复合地基的作用机理进行分析；对土工格室加筋垫层和碎石桩复合地基承载力计算方法进行总结,考虑土工格室与碎石桩复合地基两者相互作用,并结合碎石桩的固结效应,探讨了土工格室+碎石桩双向增强复合地基承载力计算方法。同时基于轴对称空间问题的弹性理论,选取不同的桩土单元,推导出碎石桩复合地基桩土应力比计算公式,并在此基础上考虑碎石桩三维轴对称固结模式,基于桩体和土体的应力时效特征,推导考虑时效的复合地基桩土应力比计算公式,并通过算例验证该解答的合理性。
其次,针对土工格室+碎石桩双向增强复合地基变形特点,探讨了其变形机理并总结了已有的沉降计算方法；在此基础上,考虑碎石桩复合地基桩土刚度差异并不大,将其视为一复合土体,土工格室加筋垫层则视为置于Winkler地基上的弹性地基梁(称为土工格室梁),同时考虑土工格室加筋垫层与碎石桩复合地基之间的切向摩阻力,提出了土工格室+碎石桩双向增强复合地基沉降计算模型,推导出土工格室+碎石桩双向增强复合地基变形计算的控制方程,并结合微分算子级数法求得相应的解析解,由此导得了土工格室+碎石桩双向增强复合地基沉降计算公式。算例分析表明该解析解是正确合理的,进一步的参数分析表明,复合土体的法向和切向弹簧刚度对土工格室+碎石桩双向增强复合地基的变形有较大影响,土工格室加筋垫层的力学参数如弹性模量等及几何参数如高度等则影响较小。
再次,根据前述土工格室+碎石桩双向增强复合地基沉降计算的弹性地基梁模型,引入分步计算法概念,首先考虑各种竖向荷载下土工格室梁的挠度计算,推导并汇总了工程中常见竖向荷载下土工格室梁的挠度解答,然后考虑土工格室梁的实际变形曲线特征,建立切向相对位移与挠度之间的关系式,并推导出相应土工格室梁的切向相对位移的解答,最后将地基反力和切向摩阻力作为荷载作用于土工格室梁上,导出土工格室梁的最终变形并进一步导得土工格室+碎石桩双向增强复合地基沉降计算公式。算例分析验证了分步计算法计算结果与前述解析解的一致吻合性,表明分步计算法切实可行。
基于前述土工格室+碎石桩双向增强复合地基沉降计算的弹性地基梁模型,从能量角度出发,根据最小势能原理,建立考虑切向摩阻力的土工格室梁挠度方程,并引入合适的位移函数,导出考虑切向摩阻力作用时土工格室梁的挠度解答并进一步导得土工格室+碎石桩双向增强复合地基沉降计算公式。算例分析表明该解答计算结果与前述解析解一致,表明该能量法解答切实可行,亦进一步完善了土工格室+碎石桩双向增强复合地基沉降计算的方法体系。
最后,根据相似理论,设计并完成了单纯软土地基、袋装砂井地基、土工格室加筋复合地基、碎石桩复合地基、土工格栅+碎石桩复合地基和土工格室+碎石桩复合地基等六组室内模型试验,并对试验成果进行了分析,从静载试验、应力分布、桩土应力比和孔隙水压力分布规律等方面探讨了袋装砂井地基、碎石桩复合地基、土工格栅+碎石桩复合地基和土工格室+碎石桩复合地基等的承载变形机理以及排水固结特点,并利用模型试验数据对前述沉降计算理论进行了验证分析。结果表明,土工格室加筋垫层可有效扩散和均化上部荷载,减小地基的总沉降和不均匀沉降；碎石桩桩顶应力集中效应明显,可有效加速地基排水固结；土工格室+碎石桩复合地基可有效提高地基承载力,降低桩土应力比,同时能够加速软基排水固结,减小地基沉降和不均匀沉降。此外,基于前述土工格室+碎石桩双向增强复合地基沉降计算的理论方法所得结果与室内模型试验实测结果吻合较好,也进一步验证了本文理论成果的合理性和可行性。
As a new soft foundation treatment method, the composite foundation bidirectionally reinforced by stone columns and geocell is favored for civil engineers for its better service behavior and widely applied in engineering practice such as soft soil improvement in highway, subgrade strengthening in railway and oil tank engineering and so on, obtaining favorable reinforcing effect. However, the theory of the composite foundation remains immature. In this paper, the bearing characteristic, consolidation analysis, pile-soil stress ratio and settlement calculation of the stone columns and geocell reinforced composite foundation have been discussed based on several aspects of theoretical analysis, model experiment and engineering practice. This paper is supported by the High Technique Research and Development Program of China (863program)——"The treatment technique of bidirectionally reinforced foundation based on the settlement control for large area and non-uniform soft subgrade in highway construction"(2006AA11Z104), the Natural Science Foundation of China (51078138) and the financial support program of topic selection of thesis for the degree of doctor of engineering in hunan university.
Firstly, the working mechanism of the two-direction composite foundation is studied based on the analysis of working mechanism of geocell and stone columns. The calculation methods for the bearing capacity of the geocell reinforced mattress and stone columns reinforced composite foundation are respectively summarized. The calculation method for bearing capacity of the composite foundation bidirectionally reinforced by stone columns and geocell is investigated with consideration of their interaction on each other and the consolidation character of the stone columns. According to axisymmetric elastic theory, the formula for the pile-soil stress ratio of stone columns reinforced composite foundation is obtained by choosing different pile and soil elements. Then the formula for the pile-soil stress ratio considering time effect and three dimensional axisymmetric consolidation model of gravel pile is derived based on the analysis of the time effect of pile and soil stresses. The rationality of the solution of the pile-soil stress ratio is verified by an engineering example.
Secondly, in view of the deformation characteristics of the composite foundation bidirectionally reinforced by stone columns and geocell, the deformation mechanism is discussed and the existing settlement calculation methods are summarized. Regarding the difference of stiffness of gravel pile and soil is not obvious, the composite foundation can be regarded as a composite soil. The geocell reinforced cushion can be regarded as a beam resting on a Winkler foundation which can be called the geocell reinforced beam. Considering the tangential frictional resistance between the geocell reinforced cushion and gravel pile composite foundation, the settlement calculation model of the composite foundation bidirectionally reinforced by stone columns and geocell is established, the governing equation is deduced and its corresponding analytical solution is obtained based on the differentiator series method. Thus the settlement calculating formula of the composite foundation is derived. The example analysis shows that the analytical solution is right and the parameter analysis shows that the normal and tangential spring stiffness of the composite soil have quite great influence on deformation of composite foundation, mechanical and geometric parameters of geocell reinforced cushion such as elastic modulus and height are less affected.
Then, based on the elastic foundation beam model for the settlement calculation of composite foundation bidirectionally reinforced by stone columns and geocell, the separate-step calculation concept is introduced. Firstly the deflection of geocell reinforced beam subjected to all sorts of vertical loads is considered and the deflection solutions of geocell reinforced beam are derived and summarized. Then considering the actual deflection curve of geocell reinforced beam, the relationship between tangential relative displacement and the deflection is established. The solution of tangential relative displacement is acquired. The subgrade reaction and tangential frictional resistance are obtained and applied to the geocell reinforced beam as loads so that the final deformation of geocell reinforced beam is developed. Thus the settlement calculating formula of composite foundation bidirectionally reinforced by stone columns and geocell is derived. The results calculated by separate-step calculation method is proved to be consistent with previous analytical solution in an example, which indicates that the separate-step calculation method can be used in the engineering practice.
Based on the beam model for the settlement calculation of the two-direction composite foundation formed by geocell reinforced mattress and gravel piles and the principle of minimum potential energy, the governing energy equations for geocell reinforced beam considering tangential frictional resistance are obtained and solved by an appropriate displacement function. Then the formula for the settlement of the two-direction composite foundation is acquired. The analysis of examples indicates the results calculated by the energy method agree well with those by the analytical solution proposed above. The validity and rationality of the solution are verified and the methodological system of the settlement calculation for two-direction composite foundation gets improved further.
Lastly, according to the theory of similarity, a group of indoor model tests including the untreated soft soil, subgrade reinforced by sand bag wells, geocell reinforced subgrade, composite foundation reinforced by gravel piles, composite foundation reinforced by geogrid and gravel piles and composite foundation reinforced by geocell and gravel piles are designed and completed. The obtained data from model tests is analyzed. The bearing and consolidation characteristic and deformation mechanism of subgrade reinforced by sand bag wells, geocell reinforced subgrade, composite foundation reinforced by gravel piles, composite foundation reinforced by geogrid and gravel piles and composite foundation reinforced by geocell and gravel piles are discussed by the analysis of the loading test, stress distribution, pile-soil stress ratio and water pressure. The settlement calculation method proposed above is verified by the model test data. The test results shows that the geocell reinforced mattress can spread and homogenize the loads, reduce the settlement and the non-uniform settlement of subgrade, the gravel pile can effectively accelerate the consolidation of subgrade and the stress concentration effect is clear, and the composite foundation formed by geocell and gravel piles can greatly increase the bearing capacity of subgrade, reduce the pile-soil stress ratio, accelerate the consolidation of soft foundation and reduce the settlement and the non-uniform settlement. Moreover, the results calculated by the theory method proposed above agree well with those from the model tests, which means the theory in this paper are rational and feasible.
引文
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