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# Deep Excavations - Limit Equilibrium Method

## Limit Equilibrium Analysis Method (LEM)

The Limit equilibrium method is the most common method for the analysis of retaining structures. Limit equilibrium is the method where limit state conditions are assumed. For excavations and earth retaining structures this usually means that earth pressures are assumed on both the retained and excavated sides. These pressures may represent a failure state such as active or passive lateral earth pressures, or an assumed redistribution such as diagrams by Peck or FHWA.

In Limit Equilibrium Analysis, the retaining wall is analyzed to provide moment and force equilibrium, when possible. Support reactions are also calculated, either by using the tributary area method, or by using a series of beam analysis methods for models with multiple support levels (Blum's Method, Simple Span Method, CALTRANS method and more).

### Concept of the LEM Analysis

In the Limit Equilibrium Analysis, we try to calculate the net pressures diagram, by taking into consideration:

1. The soil pressures on the driving and resisting side (active - passive - apparent)

2. The water pressures that are developed on the walls

3. The external loads that are applied on the walls (construction loads, buildings, traffic loads, cranes and more)

4. The seismic pressures that are applied on the walls (when we examine seismic long term conditions)

Fig. Concept of the Limit Equilibrium Analysis - DeepEX Software

DeepEX Software Implements all common Analysis Methods for the design of Deep Excavations

Limit Equilibrium Analysis - Non-Linear Analysis (Soil Springs) - Finite Element Analysis

### Advantages of the LEM Analysis

The advantages of limit equilibrium methods include:

a) They form a well known analysis method

b) They can provide quick answers

c) The assumed limit conditions are well understood

The disadvantages of limit-equilibrium methods include:

a) The analysis is valid only for simple conditions

b) Soil structure interaction is not properly captured

c) Calculated wall displacements are unrealistic for excavations with multiple bracing levels.

d) Computed wall bending moments are possibly uncoservative when more than one support levels are used.

e) Construction stage history is totally ignored.

Concluding, it always adds value to perform a limit-equilibrium analysis that can provide a backbone against which to compare a more rigorous non-linear elastoplastic solution.

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