Limit Analysis & Soil Plasticity
Devoted to the theory and applications of limit analysis as applied to soil mechanics, this text also contains information on soil plasticity and rock-like material such as concrete.
TABLE OF CONTENTS Limit Analysis & Soil Plasticity
Chapter 3: Limit Analysis By the Upper-Bound Method
3.1 INTRODUCTION
The preceding chapter was concerned with basic assumptions and theorems used in limit analysis. In the following two chapters we shall discuss in more detail some of the basic techniques of applying these upper- and lower-bound theorems. Herein we shall illustrate the applications of these techniques by means of relatively simple examples; more complex applications will be taken up in later chapters.
The Upper-Bound Theorem
We shall begin by re-examining the rules of the upper-bound theorem. As stated in the upper-bound theorem, the imposed loads cannot be carried by the soil mass if for any assumed failure mechanism the rate of work done by the external forces exceeds the internal rate of dissipation. Equating of external to internal rate of work for any such valid mechanism thus gives an unsafe upper bound on the collapse or limit load. The equation formed in this way is called the work equation for a particular assumed mechanism. The conditions required to establish such an upper-bound solution are essentially as follows:
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A valid mechanism of collapse must be assumed which satisfies the mechanical boundary conditions.
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The expenditure of energy by the external loads (including soil weights) due to the small displacement defined by the assumed mechanism must be calculated.
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The internal dissipation of energy by the plastically deformed regions which is associated with the mechanism must be calculated.
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The most critical or least upper-bound solution corresponding to a particular layout of the assumed mechanism must be obtained via the work equation.
Any...
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