The formula of subgrade’s approaching plasticity load for rectangular footings
Received:June 25, 2021  Revised:August 10, 2021
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DOI:10.7511/jslx20210625002
KeyWord:approaching plasticity load  rectangular footing  strip footing  approximate calculation formula for square root  principal stress
           
AuthorInstitution
许年春 重庆科技学院 建筑工程学院, 重庆 ;能源工程力学与防灾减灾重庆市重点实验室, 重庆
郑瑞 重庆科技学院 建筑工程学院, 重庆
吴同情 重庆科技学院 建筑工程学院, 重庆 ;能源工程力学与防灾减灾重庆市重点实验室, 重庆
杨全虎 重庆科技学院 建筑工程学院, 重庆
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Abstract:
      At present,the formula of subgrade’s approaching plasticity load given in the textbook of soil mechanics is only applicable to strip footings.In practical engineering,rectangular footings under columns are more widely used than strip footings.The research on the formula of subgrade’s approaching plasticity load for rectangular foundation has not only theoretical significance for the development of soil mechanics,but also practical value for the design of rectangular footings.At first,the stress at the edge of the footing caused by the upward tensile stress in the left and right side regions of the rectangular footing is obtained by double integral;Then,the local rectangular coordinate system is established along the principal stress direction in the subgrade under the strip footing,and the stress expression at the edge of the rectangular footing is obtained by stress superposition.Then,an error analysis is carried out on the approximate calculation formula for square root with different values of coefficient n;Finally,the stress expression is substituted into the Coulomb strength criterion,and the formula of subgrade’s approaching plasticity load for rectangular footings is derived with the help of the square root approximation formula and the polar expansion of trigonometric function.The calculation examples of different types of subgrade soil show that the smaller the Poisson’s ratio is,the smaller the ratio of approaching plasticity load of rectangular footing to strip footing is.It is not safe to use the latter’s formula to calculate the former’s approaching plasticity load.