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# At-Rest lateral Earth Pressures

## At-Rest Pressures in Deep Excavations

Soils in nature have an in-situ state of stress. This "in-situ" state of stress is commonly refered to as "At-rest" conditions. If a natural surface is level and all stratigraphy is also level, then the "At-rest" state of stress can be described by two main stresses:

a) The vertical stress (effective and total)

b) The horizontal stress

All effective horizontal stresses are typically defined as a ratio of the effective vertical stress times a coefficient of lateral pressure. For "At-rest" conditions, this coefficient is typically defined as:

Ko1 = [1-Sin(friction angle)]

However, as many researchers (Ladd et. al) have reported, the initial lateral state of stress is linked to the soil stress history. For example, soils that have experienced a greater vertical state of stress in the past tend to hold memory of their overloaded history. As a result, these types of soils tend to "lock-in" greater lateral stresses in "At-rest" conditions. These types of soils are typically referred to as overconsolidated. In such cases, the coeffiecient of at-rest lateral earth pressures can be defined from an equation relating to the Overconsolidation Ratio (OCR) such as:

Ko = Ko1 x (OCR )^n

Where OCR is the ratio of maximum past to current effective vertical stress. The exponent n can be defined by running a series of laboratory or insitu experiments.

When a sloped ground is included Eurocode 7 recommends multiplying the above coefficients by (1+ sin (Beta)) where Beta is the surface inclination angle.

Fig. At-Rest Pressures Diagram - DeepEX Software

DeepEX Software can Calculate all Soil Pressure Types for Deep Excavations

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### Do you have to include At-Rest Pressures for Your Design?

An important aspect of "At-Rest" lateral earth pressures is that they typically take place at zero lateral wall displacement. This means that a wall will experience full "At-Rest" lateral pressures only if it does not yield. Such a case could take place if a stiff gravity wall fully bears on bedrock, in such a condition a retaining wall will essentially feel the full "At-rest" driving soil pressures.

Given that "At-rest" pressures are considerably greater than active earth pressures, one might conclude that all braced excavations should be designed with at-rest pressures. Doing so, might actually do greater damage than good. While having a greater capacity might be beneficial, if a series of supports are prestressed to the "full" theoretical "at-rest" load then "in-practice" the wall might actually move back into the retained soil causing a series of unpredicted problems. The author is aware of a diaphragm wall designed this way that moved as much as 12inches (30 cm) back into the retained soil causing severe wall and pavement cracking in the process. Part of the reason for such observations is that engineers tend to be on the safe side when providing "at-rest" pressure coeffiecients and other geotechnical strength parameters. Thus, the actual "at-rest" coefficient might be smaller than originally predicted.