大直径筒仓的侧压力分析与筒仓地基三维固结分析
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摘要
筒仓广泛应用于粮食、化工、电力、冶金、建材和煤炭等多个行业。随着生产规模的快速发展和存储大量物料的迫切需要,大容量和大直径的圆形筒仓已应运而生,且尺度越来越大,其力学行为也表现得极其复杂。然而目前对大直径圆形筒仓的研究还开展的很少,对筒仓在工作荷载下的力学行为、储料侧压力、地基变形破坏机制还知之甚少,实际设计中多参照现有一般筒仓的设计方法,缺乏可靠的理论依据；由此造成大直径筒仓设计上不合理,引起部分筒仓出现筒壁结构性问题和工程倾斜事故。基于这一现状,本文对大直径圆形筒仓的储料侧压力和地基固结问题展开了较为系统而深入的研究,具体研究工作包括以下三个部分。
第一部分,大直径圆形筒仓侧压力的极限分析上限方法研究。
1.针对大直径筒仓内散料特定的破裂面形态,基于极限分析上限定理,建立大直径圆形深仓和浅仓的侧压力解析表达式；通过三个典型算例,验证了解析方法的正确性。在此基础上,深入探讨了筒仓高度和半径对大直径筒仓储料侧压力的影响；结果表明：相同高度的筒仓,半径越大,侧压力合力越大,但二者间并非呈线性关系,而是随着筒仓半径的增大,筒仓侧压力合力增大的幅度逐渐减小。
2.利用极限分析上限方法,推导出大直径圆形深仓和浅仓的临界高径比计算公式；在此基础上,进一步探讨了散料内摩擦角、储料顶面倾角、仓壁与散料之间的摩擦角等因素对临界高径比的影响。结果表明：仓壁与散料之间的摩擦角δ越小,筒仓临界高径比ξ0越大；储料顶面倾角β越小,临界高径比ξ0越大；当储料顶面倾角为零,即筒仓中散料平堆时,筒仓临界高径比ξ0随着内摩擦角φ的增大先减小后增大,而当储料顶面倾角为自然休止角时,筒仓临界高径比ξ0随着内摩擦角φ的增大单调减小。
第二部分,大直径圆形筒仓侧压力的三维有限元分析。
利用有限元程序ADINA,建立考虑筒仓处于静止状态、装料和卸料过程的三维有限元模型,对三种状态下的筒仓侧压力进行了数值分析。结果表明：通过有限元方法得到的侧压力与实测值吻合的较好,证明了有限元方法研究筒仓侧压力的可行性；大直径筒仓装料结束时的侧压力不大于静止侧压力；卸料开始阶段,破裂面与仓壁相交处的侧压力突然增大,最大的卸料侧压力值出现在筒仓底部,卸料开始阶段侧压力比静止侧压力大很多,在破裂面处是静止侧压力的2-3倍,在筒仓设计中应该予以足够的重视。此外,通过变动参数对比分析了散料和筒仓参数对筒仓侧压力的影响。
第三部分,轴对称变荷载作用下横观各向同性饱和地基的Biot固结分析。
针对圆形筒仓对地基作用的两个特性—轴对称和变荷载,使用有效应力原理和Laplace—Hankel联合积分变换,对圆形和环形变荷载作用下横观各向同性饱和地基的Biot固结问题进行了分析,得到了Biot固结问题的解析表达式,并且通过算例验证了本文解的正确性。进一步地,将圆形筒仓对地基的加卸载作用简化为梯形循环荷载,计算了基础中心点处的地表沉降,结果表明筒仓加卸载由于周期较长,每一个荷载周期的最大沉降量相差不大,且与恒载作用下的沉降量相差不大。最后研究了土体各向异性对土体沉降的影响,结果发现土体的各向异性对土体沉降有很大的影响。
Silos are widely used in a variety of industries, such as coal, chemicals, electric power, metallurgy, building materials and food. With the development of production, the capacity and diameter of silos is becoming bigger and bigger, and the mechanical behavior of silos is becoming more complex. However, up to date, there is little research on the structural behavior, lateral wall pressure, ground deformation and failure mechanics for large-diameter silos. The current design is more referring to the present design standard for general silos, without reliable theory is built to design a large scale silo. In view of this situation, a series of studies on lateral wall pressure and ground consolidation of circular silos were carried out in this paper. This work includes three parts as below.
The first part is relevant to upper bound limit analysis method of lateral pressure of large-diameter silos.
1. According to the specific fracture surface of bulk materials in large-diameter silos, lateral wall pressure of deep and shallow silos was respectively analyzed used upper bound limit analysis method. Analytical expression of lateral wall pressure was obtained. The correctness of this formula was proved through numerical examples. On the basis of this, the influence of silo height and radius on the lateral wall pressure is systematically investigated. The result shows that the lateral wall pressure increases with the increase of silo radius. However, the lateral pressure doesn't increase linely with silo radius, but more and more slow increasing trend between the lateral pressure and silo radius can be shown.
2. The critical ratio of height to diameter between deep and shallow silo was studied based on the upper bound limit analysis approach. The formula was obtained, and the influence of internal friction angle of bulk solid, top-surface inclination angle of bulk solid and friction angle between bulk solid and silo wall on the critical ratio was comprehensively analyzed. The result shows that the critical ratio of height to diameter increases with the decreasing of the friction angle between bulk solid and silo wall. The critical ratio also increases with the decreases of top-surface inclination angle of bulk solid. When the top-surface inclination angle of bulk solid is zero, the critical ratio decreases firstly, and then increases with the increase of the internal friction angle. When the top-surface angle of bulk solid is the natural angle of repose, the critical ratio decreases monotonically with the increase of the internal friction angle.
The second part is three-dimensional finite element analysis of lateral wall pressure of silos.
Elasto-plastic finite element analysis was carried out by using a large commercial software ADINA. Three-dimensional finite element models are respectively built when bulk material in silos was assumed at rest, at filling process and at discharge process. Then the lateral wall pressure under three kinds of conditions was studied. The result shows that wall pressure obtained by FEM is in good agreement with the measured value. It is feasible to study on the lateral wall pressure of silos with FEM. Lateral wall pressure of large-diameter silo at the end of filling process is not larger than the static one. At the beginning of discharge process, the lateral wall pressure increases suddenly at the intersection of the rupture surface and the silo wall. The maximum pressure at the beginning of discharge is at the silo bottom. The lateral pressure at the beginning of discharge is much larger than static lateral pressure. At the intersection of the rupture surface and the silo wall, the lateral wall pressure of discharge is2-3times to static lateral pressure. Lateral pressure at the beginning of discharge should be paid sufficient attention in silo design. In addition, the influence of material parameters on lateral wall pressure is also analyzed.
The third part is three-dimensional Biot consolidation analysis of transversely isotropic saturated soil ground under axisymmetric variable loading.
In general, the loading of silos on foundation is an axially symmetric and variable problem. In view of this situation, three-dimensional Biot consolidation of transversely isotropic saturated soil under round and circular load is analyzed. In the analysis process, effective stress and joint Laplace-Hankel integral transformation were used. Analytical solution of Biot consolidation was obtained. The accuracy of this analytical solution was verified by two simple examples. Then, the loading of filling and discharge process of silos is simplied to trapezoidal cyclic loading, the surface subsidence at the center at the silo base is calculated. The result shows that there is little difference on the maximum settlement induced between simplified cyclic loading and constant loading. This is because the process of the loading cycle is very long. Based on the above analysis, the process of loading and unloading is not necessary to consider in the final settlement calculation in actual project. Lastly, the influence of soil anisotropy on foundation settlement was studid. The result shows that soil anisotropy has a great impact on foundation settlement.
第一部分,大直径圆形筒仓侧压力的极限分析上限方法研究。
1.针对大直径筒仓内散料特定的破裂面形态,基于极限分析上限定理,建立大直径圆形深仓和浅仓的侧压力解析表达式；通过三个典型算例,验证了解析方法的正确性。在此基础上,深入探讨了筒仓高度和半径对大直径筒仓储料侧压力的影响；结果表明：相同高度的筒仓,半径越大,侧压力合力越大,但二者间并非呈线性关系,而是随着筒仓半径的增大,筒仓侧压力合力增大的幅度逐渐减小。
2.利用极限分析上限方法,推导出大直径圆形深仓和浅仓的临界高径比计算公式；在此基础上,进一步探讨了散料内摩擦角、储料顶面倾角、仓壁与散料之间的摩擦角等因素对临界高径比的影响。结果表明：仓壁与散料之间的摩擦角δ越小,筒仓临界高径比ξ0越大；储料顶面倾角β越小,临界高径比ξ0越大；当储料顶面倾角为零,即筒仓中散料平堆时,筒仓临界高径比ξ0随着内摩擦角φ的增大先减小后增大,而当储料顶面倾角为自然休止角时,筒仓临界高径比ξ0随着内摩擦角φ的增大单调减小。
第二部分,大直径圆形筒仓侧压力的三维有限元分析。
利用有限元程序ADINA,建立考虑筒仓处于静止状态、装料和卸料过程的三维有限元模型,对三种状态下的筒仓侧压力进行了数值分析。结果表明：通过有限元方法得到的侧压力与实测值吻合的较好,证明了有限元方法研究筒仓侧压力的可行性；大直径筒仓装料结束时的侧压力不大于静止侧压力；卸料开始阶段,破裂面与仓壁相交处的侧压力突然增大,最大的卸料侧压力值出现在筒仓底部,卸料开始阶段侧压力比静止侧压力大很多,在破裂面处是静止侧压力的2-3倍,在筒仓设计中应该予以足够的重视。此外,通过变动参数对比分析了散料和筒仓参数对筒仓侧压力的影响。
第三部分,轴对称变荷载作用下横观各向同性饱和地基的Biot固结分析。
针对圆形筒仓对地基作用的两个特性—轴对称和变荷载,使用有效应力原理和Laplace—Hankel联合积分变换,对圆形和环形变荷载作用下横观各向同性饱和地基的Biot固结问题进行了分析,得到了Biot固结问题的解析表达式,并且通过算例验证了本文解的正确性。进一步地,将圆形筒仓对地基的加卸载作用简化为梯形循环荷载,计算了基础中心点处的地表沉降,结果表明筒仓加卸载由于周期较长,每一个荷载周期的最大沉降量相差不大,且与恒载作用下的沉降量相差不大。最后研究了土体各向异性对土体沉降的影响,结果发现土体的各向异性对土体沉降有很大的影响。
Silos are widely used in a variety of industries, such as coal, chemicals, electric power, metallurgy, building materials and food. With the development of production, the capacity and diameter of silos is becoming bigger and bigger, and the mechanical behavior of silos is becoming more complex. However, up to date, there is little research on the structural behavior, lateral wall pressure, ground deformation and failure mechanics for large-diameter silos. The current design is more referring to the present design standard for general silos, without reliable theory is built to design a large scale silo. In view of this situation, a series of studies on lateral wall pressure and ground consolidation of circular silos were carried out in this paper. This work includes three parts as below.
The first part is relevant to upper bound limit analysis method of lateral pressure of large-diameter silos.
1. According to the specific fracture surface of bulk materials in large-diameter silos, lateral wall pressure of deep and shallow silos was respectively analyzed used upper bound limit analysis method. Analytical expression of lateral wall pressure was obtained. The correctness of this formula was proved through numerical examples. On the basis of this, the influence of silo height and radius on the lateral wall pressure is systematically investigated. The result shows that the lateral wall pressure increases with the increase of silo radius. However, the lateral pressure doesn't increase linely with silo radius, but more and more slow increasing trend between the lateral pressure and silo radius can be shown.
2. The critical ratio of height to diameter between deep and shallow silo was studied based on the upper bound limit analysis approach. The formula was obtained, and the influence of internal friction angle of bulk solid, top-surface inclination angle of bulk solid and friction angle between bulk solid and silo wall on the critical ratio was comprehensively analyzed. The result shows that the critical ratio of height to diameter increases with the decreasing of the friction angle between bulk solid and silo wall. The critical ratio also increases with the decreases of top-surface inclination angle of bulk solid. When the top-surface inclination angle of bulk solid is zero, the critical ratio decreases firstly, and then increases with the increase of the internal friction angle. When the top-surface angle of bulk solid is the natural angle of repose, the critical ratio decreases monotonically with the increase of the internal friction angle.
The second part is three-dimensional finite element analysis of lateral wall pressure of silos.
Elasto-plastic finite element analysis was carried out by using a large commercial software ADINA. Three-dimensional finite element models are respectively built when bulk material in silos was assumed at rest, at filling process and at discharge process. Then the lateral wall pressure under three kinds of conditions was studied. The result shows that wall pressure obtained by FEM is in good agreement with the measured value. It is feasible to study on the lateral wall pressure of silos with FEM. Lateral wall pressure of large-diameter silo at the end of filling process is not larger than the static one. At the beginning of discharge process, the lateral wall pressure increases suddenly at the intersection of the rupture surface and the silo wall. The maximum pressure at the beginning of discharge is at the silo bottom. The lateral pressure at the beginning of discharge is much larger than static lateral pressure. At the intersection of the rupture surface and the silo wall, the lateral wall pressure of discharge is2-3times to static lateral pressure. Lateral pressure at the beginning of discharge should be paid sufficient attention in silo design. In addition, the influence of material parameters on lateral wall pressure is also analyzed.
The third part is three-dimensional Biot consolidation analysis of transversely isotropic saturated soil ground under axisymmetric variable loading.
In general, the loading of silos on foundation is an axially symmetric and variable problem. In view of this situation, three-dimensional Biot consolidation of transversely isotropic saturated soil under round and circular load is analyzed. In the analysis process, effective stress and joint Laplace-Hankel integral transformation were used. Analytical solution of Biot consolidation was obtained. The accuracy of this analytical solution was verified by two simple examples. Then, the loading of filling and discharge process of silos is simplied to trapezoidal cyclic loading, the surface subsidence at the center at the silo base is calculated. The result shows that there is little difference on the maximum settlement induced between simplified cyclic loading and constant loading. This is because the process of the loading cycle is very long. Based on the above analysis, the process of loading and unloading is not necessary to consider in the final settlement calculation in actual project. Lastly, the influence of soil anisotropy on foundation settlement was studid. The result shows that soil anisotropy has a great impact on foundation settlement.
引文
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