Abstract Passive bolting is used to stabilise unstable rock blocks in surface and underground structures due to the various advantages it offers. Despite its use, the design phase still presents aspects of considerable complexity because the fact that the load of the bolt and therefore, its static action depends on its interaction with the block and the stable rock. In the present work, a mathematical model was developed which is capable of directly calculating the stabilisation forces as a function of the characteristic parameters of the bolt and of its interaction with the rock. This discussion is based on a simplified hypothesis of bolt behaviour, which provides negligible errors, and on the observation that the critical point is positioned at the intersection of the bolt with one of the lateral surfaces that separate it from the portion of stable rock. The formulation of the stabilisation forces obtained made it possible to evaluate the static contribution of each single bolt to the stability of the rock block, by varying the diameter of the steel bar and then designing the bolting operation to achieve acceptable stability conditions for the rock block. The application of stabilising equations to a real case, for which the results of load tests on bolt tests were available, allowed us to outline steps to be taken in the bolt design process.

中文翻译：

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一种用于评估被动胶结锚杆施加到滑动岩块上的稳定力的简化数学方法

摘要 被动锚杆具有多种优点，可用于稳定地表和地下结构中不稳定的岩块。尽管使用了它，但设计阶段仍然呈现出相当复杂的方面，因为螺栓的载荷及其静态作用取决于它与块体和稳定岩石的相互作用。在目前的工作中，开发了一个数学模型，该模型能够直接计算作为锚杆特征参数及其与岩石相互作用的函数的稳定力。此讨论基于螺栓行为的简化假设，该假设提供的误差可忽略不计，根据观察，临界点位于锚杆与将锚杆与稳定岩石部分分开的侧表面之一的相交处。通过改变钢筋的直径，然后设计锚杆操作以达到岩块可接受的稳定性条件，所获得的稳定力的公式可以评估每个锚杆对岩块稳定性的静态贡献. 将稳定方程应用于实际案例，螺栓试验的载荷试验结果可用，使我们能够概述螺栓设计过程中要采取的步骤。通过改变钢筋的直径，然后设计锚杆操作，以达到岩块可接受的稳定性条件。将稳定方程应用于实际情况，螺栓试验的载荷试验结果可用，使我们能够概述螺栓设计过程中要采取的步骤。通过改变钢筋的直径，然后设计锚杆操作，以达到岩块可接受的稳定性条件。将稳定方程应用于实际情况，螺栓试验的载荷试验结果可用，使我们能够概述螺栓设计过程中要采取的步骤。