## Relationship for the Application of Drained and Undrained

**Description:
**

In the analysis of geosystems on or within fi ne-grained soils, we often consider two limit conditions— short-term and long-term conditions. Short-term condition (undrained condition) is assumed to simulate the stress state during and soon after construction. Long-term condition (drained condition) is assumed to simulate the stress state during the life of the structure or when the excess porewater pressure has dissipated.

We can now build a relationship between a soil at an initial stress state subjected to undrained loading and the same soil at the same initial stress state subjected to drained loading. We defi ne a ratio, aSL, to describe the ratio of the shear strength of a soil under undrained short-term condition (S in the subscript) to the shear strength under long-term condition (L in the subscript). From Equations and , we get

For the standard triaxial test condition, no 5 3 and Equation becomes

Substituting Equation and simplifying, we get

Two plots of Equation for L 5 0.8 and different values of Ro. The same data are plotted on both graphs for ease of use. When aSL is less than 1, the normalized shear strength under undrained condition at critical state is lower than that under drained condition. Therefore, undrained loading would be critical. On average, this occurs for soils with Ro less than about 3. The actual value of Ro for which undrained condition is critical depends on the critical state friction value. Higher critical state friction angles result in higher Ro at which undrained condition is critical. Drained condition is critical when aSL . 1 because the normalized undrained shear strength at critical state is greater than the normalized drained shear strength at critical state.

This relationship is of practical importance because it provides guidance on which one of these conditions would be critical. A soil with different Ro would have different critical (design) conditions. For example, if f9cs 5 308, Ro 5 1, and L5 0.8, then . Therefore, undrained loading would be critical. But if Ro 5 5 for the same soil, aySL 5 1.25 and drained loading would be critical. Equation applies only to critical state condition. If we were to consider peak (initial yield) stress state, then

Equation is plotted . If we were to compare Fig., we would notice that drained and undrained conditions are approximately reversed. For Ro , 2, drained loading is critical, but for Ro . 2, undrained loading is critical. Consider a tank foundation on an overconsolidated clay with OCR 5 10 and f'cs 5 288. Which of undrained or drained loading would be critical for soil yielding? From Figure , Ro 5 6.5 for OCR 5 10. From , and therefore yielding under undrained condition would be critical. However, if we were to consider failure (critical state), aSL 5 1.3 and drained loading would be critical.