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17 the phreatic surface is modeled at the lowest outlet elevation, and all soils that cannot drain as the reservoir is lowered are assigned undrained (total stress) shear strengths based on the effective stresses before drawdown, as calculated in the first stage. Coarser, free-draining soils having a permeability typically greater than 10-3 centimeters per second are assigned drained shear strengths based on the effective stress after drawdown [2]. In the third stage of the analysis, the rapid drawdown stability factor of safety is calculated using the lower of either the first-stage undrained or second-stage drained shear strength. Rapid drawdown is one of the more complex stability analyses and the analyst should consult relevant references such as [2], [3], and [4] for further details. The most common laboratory test used to measure shear strengths for the rapid drawdown loading condition is the CU’ triaxial test, because this test can measure both undrained (total stress) and drained (effective stress) shear strengths. Other laboratory tests used to measure drained shear strengths include the CD triaxial test and DS test. Other laboratory tests used to measure undrained shear strengths include the UC test, UU triaxial test, CU triaxial test, and DSS test. Shear Strength Characterization After the loading conditions for which an embankment dam should be analyzed are identified, appropriate shear strength parameters must be developed for the embankment and foundation soils under each applicable loading condition. Characterizing the shear strength of soils is dependent on both the type of soil and whether the soil behaves as undrained or drained under a particular loading condition. Provided below is a description of the shear strengths typically evaluated for coarse-grained, cohesionless soils (sands and gravels) and fine-grained, cohesive soils (clays and silts), including the corresponding laboratory and field testing to measure strengths and empirical correlations to estimate strengths. Coarse-Grained Soils (Sands and Gravels) Coarse-grained, or granular, soils (sands and gravels) are typically free-draining and defined by drained shear strengths, except for very rapid loading (e.g., seismic loading, which is not addressed in this article). These soils are similar in strength characterization since they have high permeabilities and sufficient drainage capacity to prevent pore water pressures from changing under most loadings. Characterizing the drained shear strength of coarse- grained soils involves evaluating or estimating the effective stress friction angle (φ’). The Mohr-Coulomb strength envelope for granular soils goes through the origin of stress, as illustrated in Figure 1, and thus the effective stress cohesion (c’) is zero. Coarse-grained soils are therefore also often referred to as cohesionless soils. Although the effective stress cohesion is zero, the strength envelope for denser soils is often curved, as illustrated in Figure 1. For mathematical simplicity, an analyst may approximate the strength envelope as linear over the normal stress range of interest for the analysis, which may result in an “apparent” effective stress cohesion, as illustrated in Figure 2. It is important to understand that this is a mathematical convenience, and not a true property of the soil. Figure 1: Mohr-Coulomb strength envelope for coarse-grained soils Effective stress – σ’ Sh e a r s tr e s s - τ φ’ c’ Linear Approximation of Shear Strength for stress range of interest Shear Failure Envelope (Curved) Figure 2: Curved shear strength envelope with linear interpretation and apparent cohesion, c’