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张志贞. 条形均布荷载与最危滑动层的计算[J]. 岩土工程学报, 2011, 33(12): 1987-1987.
引用本文: 张志贞. 条形均布荷载与最危滑动层的计算[J]. 岩土工程学报, 2011, 33(12): 1987-1987.
ZHANG Zhi-zhen. Calculation of uniformly distributed strip load and the most dangerous sliding surface[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(12): 1987-1987.
Citation: ZHANG Zhi-zhen. Calculation of uniformly distributed strip load and the most dangerous sliding surface[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(12): 1987-1987.

条形均布荷载与最危滑动层的计算

Calculation of uniformly distributed strip load and the most dangerous sliding surface

  • 摘要: 为了探寻一个既经济又安全的条形均布荷载的计算方法,以沙湖年慈教授导出的土中任意受力点其最危截面上的稳固系数公式为基础,将地基主应力公式代入该式并求导, 从而解得了涵盖弹性、临塑、塑性及极限应力荷载的计算“通式”。还论证了在荷载作用下,沿荷载中线在( 0 °~ 90 °)之间存在最小稳固系数。在预设最小稳固系数的前提下,并可解得最危视角顶点定位在中线上的某点 N ,它随荷载的大小而沉浮。结合附加应力公式理论,可自基础两边过 N 点作出ANB弧,该弧即为最危滑动层的位置,在该层面上,稳固系数自上而下,由小到大,在 K 0 =1 处,恰为塑性区的最大深度。在施荷过程中,地基中各受力点的应力不断增加,稳固系数不断下降;故原来最小的稳固系数ANB 弧,上移到一个新的位置AMB弧处,如果对 弧上 M 点的 K 0min 值,进行相应的规范,那么,预设荷载在AMB弧上 M 点所产生的 K 0min 值,只要在规定范围之内,即可确定该荷载为设计荷载。

     

    Abstract: In order to search an economical and safe method for calculating the uniformly distributed strip load, based on the formula for stability factor proposed by Professor Sha Hunianci, the formula for the total stress of foundation is substituted and derived. Thus a “general formula” for the elasticity, plasticity, critical edge and extreme stress load is obtained. In addition, this study demonstrates that there exists the smallest stability factor along the load midline from 0 to 90 degrees under the action of load. The point N on the midline of dangerous view’s vertex can be obtained on the premise that the minimum stability factor is presupposed. It increases and decreases with the magnitude of the load. Based on the theory of additional stress formula, the arc ANB from the base to both sides can be drawn through the point N. The arc is the location of the most dangerous sliding surface. On the sliding surface, the stability factor is the smallest at the top and the largest at the bottom. It is exactly the maximum depth of plastic area when K0=1. During the process of applying load, the stress at each point in the foundation increases and the stability factor decreases. Therefore, the original minimum stability arc ANB moves up to a new place on the arc <>AMB. If we stipulate the minimum value K0 at point M on the arc AMB, then as long as the minimum value K0 produced by the preset load at point <>M on the arc <>AMB is within the specified scope, the load is defined to be the design load.

     

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