| Bridge pier, anti-sliding piles and retaining and protection of foundation excavations structure in geotechnical engineering are the most common three type structures. There are a lot of analysis and calculations in design to ensure the security and the stability of the structure under the load in common. When bridge substructures are subjected to horizontal loads, pile body damage occurs frequently. Thereby, the stability and the normal use of the bridge substructure are affected. While theory of flexible pier proposing, it provides the original rigid pier with certain flexibility, so that the pier could share the upper horizontal force. Anti-sliding piles pass force to stable formation and balance the landslide thrust by anchoring effect and passive resistance of stable formation with the interaction between piles and soils. Retaining and protection structures of foundation excavations mainly suffer earth pressures and water pressures, and then they passed it to supporting, it is a temporary retaining wall structure construction. With the factors are so many, it must choose the right forms according to the facts. Internal force of flexible piers is usually different because of the difference between top of piers and piles, and the horizontal force that the upper structure passes is also vary, due to the rigidity of pier. It is often calculated with integrate stiffness method, and steps are very tedious. Internal forces analysis of anti-slide piles under the horizontal force are often used circular arc method or method of landslide thrust to calculate, and the analysis process is complex, and human error are very common. Calculation of internal force of retaining structure of foundation excavations is mature, but calculation process is often very complicated if stratum conditions are complicated and excavation depth are deeper, it increases the risk of errors and inconvenient for design and construction.With the computer technology developing rapidly, all kinds of analysis software comes out continuously. Lizheng is widely used in internal force calculation of anti-slide piles and design of foundation excavations, and the finite element, Midas, and Dr bridge are widely used in bridge design. All these softwares are based on the theory of finite element, and partition the unit-structure of bridge pier, determine the constraints, and finally set up models of bridge pier on the computer. However, the finite element method in analyzing needs for meticulous division, and ensures constraints of nodes accurate, and the quality of elements division as well have great influence on accuracy of calculation results.The article takes the research on the internal force calculations of flexible piers, anti-slide piles and cantilever retaining structure that the common forms in geotechnical engineering under the horizontal forces act, with Maple algebra calculation software for platform and elastic foundation beam theory for based. It then discusses the applicability of Maple calculation software in internal force calculations of geotechnical engineering through actual cases. In the case, it compares calculation results by Maple with that obtained by other commonly used calculation methods, and summary of regularities between them, also proposes the correction for the actual test results by Maple, in order to provide reference and make calculation more accurate, convenient, and quick for internal force. In addition, the article also takes the research on internal force calculations of piers in the permafrost area under the frost heave force, and it analyzes the actual engineering for example. It provides data references for popularization and application of Maple in practical engineering. Through comparing results, it obtains the main achievement following:(1)Results of flexible piers, anti-slide piles and retaining and protection of foundation excavations by Maple are high accuracy, and the calculation process is convenient and program is easy to understand. As a new method of calculation, it can be used in practical engineering design.(2)Based on calculation principles of "m", it derives the support equation of the flexible piers, and establishes the boundary conditions of the whole bridge according to the influence of temperature, shrinkage and creep effect of concrete. Using Maple to calculate internal forces of structures without the tedious calculations, without a lot of looking up tables. By comparing the results calculated by Maple with that by integrate stiffness method and Midas finite element software, the regularities of internal force variation are basically the same, and it has a very high accuracy, even it can be used as a new method of internal force calculation of bridge pier to practical engineering calculations.(3)In anti-slide pile internal force calculation, it calculates both rigid short piles and long flexible piles according to the method of "m", and then it compares the results with that calculated by Lizheng. The variation tendencies of displacements, bending moments and shear force are basically the same. Viewing on numerical value, results calculated by Maple are slightly larger. By comparing displacement results with the actual monitoring data, correction coefficient of calculation results of rigid piles by Maple is 0.85, and flexible correction coefficient is 0.86. There is no need to distinguish whether rigid or flexible, and it only to correct the results that calculated by Maple, and the correction factor is 0.86. This calculation is accurate and reliable, and it can be used as a new method of anti-slide pile internal force calculation.(4)In the calculation of internal force of retaining structure of foundation excavations, it makes row-piles structure as an example, and compares the results by Maple with that calculated by Lizheng, Results of Maple are slightly larger, but the tendencies of displacement, bending moment and shear force are consistent. Comparing Maple calculation results with actual monitoring data, it calculates the correction factor of Maple is 0.85. Therefore, the Maple software can be applied to the calculation of internal forces of cantilever foundation excavation retaining structure, and the results are accurate and reliable.(5)According to characteristics of bridge pier in permafrost regions, it make an analog computation on pile-foundation. At the time of partition, it makes piles structure within frozen line as a single unit to consider, and takes into account of the horizontal load, lateral soil resistance and tangential frost heaving force at the same time. Pile of differential equations are derived mainly from the axial deformation and normal deformation. In the process, tangential frost-heave force is minimized by higher order, so that the whole process of tangential frost-heave force of impact can be considered negligible. In practice, tangential frost-heave force through construction techniques will remove it, basically equivalent to ignore tangential frost-heave force of impact. Therefore, Maple software also applies to internal force calculation analysis of bridge piers in permafrost regions.There are innovations of the article:(1)Based on elastic foundation beam theory, it derives the differential equations of support structure according to loading features of flexible pier structure under horizontal force, and it establishes the boundary conditions according to the influence of temperature, shrinkage and creep effect of concrete.(2)In anti-slide piles calculation, it doesn’t distinguish rigid and flexible, and calculates all in accordance with the analysis by method of "m", and compares the results of anti-sliding pile and piles which are belong to cantilever supporting structure with the actual monitoring data. It finally proposes the correction coefficient of Maple.(3)While calculating the internal force of bridge piers in permafrost regions, it simplifies the analysis process that the tangential frost-heave force can be calculated higher order minimum in differential equations by using Maple. Comparing the results with professional software, It verifies Maple calculation method in calculation of internal force of pile foundation at permafrost regions with a certain application. |
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