Porous materials like soils have different design properties under drained and undrained conditions. As you all know in drained condition, the pore water can easily drain out from the soil matrix while in undrained condition the pore water is unable to drain out or the rate of loading is much quicker than the rate at which the pore water is able to drain out. The existence of either a drained or an undrained condition in a soil depends on (Ref. here):

• Soil type (e.g. sand, gravel, silt, clay)
• Geological formation (fissures, embedded sand layers in clay, etc.),
• Rate of loading.

Experiments have shown that the drained condition almost always exists for coarse-grained material such as gravels and sands under static/monotonic loading. This is because of the large permeability of the material so that the pore water can quickly drain out. Note that under seismic loading condition due to the quick rate of loading saturated loose sands can experience undrained loading condition resulting in liquefaction. On the other hand, due to the low material permeability, undrained condition almost always exist for clays and silts when subjected to quick static loads and earthquake loads.

In this article we want to clarify what type of parameters (drained or undrained) should be used in the typical geotechnical analyses listed below:

1. Slope stability analysis (short-term, long-term and pseudo-static)
2. Static settlement analysis (immediate and consolidation)
3. Seismic time-history analysis

Per the discussions above, it appears that drained parameters (E', \nu', \phi') must be always used for analysis of coarse-grained materials (i.e., gravels, sands). In case of liquefaction where unloading condition exists, the common approach is to either use residual strength parameters of liquefied soil per Idriss and Boulanger (2008) guidelines or adopt advanced constitutive models for which the input parameters are drained parameters.

Selection of drained/undrained parameters for saturated clays requires further discussion and elaboration. Let’s first review some characteristics of  saturated clays shear strength :

• Undrained shear strength of clays is represented by a single parameter denoted as S_u. This is illustrated in Figure 1 below and compared against the drained strength for better clarity. As noted in the figure, unlike the drained shear strength, the undrained shear strength (S_u) is stress-independent. This is because when undrained condition exists, the external load increment will be entirely carried by the pore water due to its much larger stiffness (K_{w,undrained} >> K_{soil}).

  

• Undrained shear strength is not a fundamental soil parameter. It generally varies over depth as a function of insitu confining stress at a given depth. Note that larger confining stress reduces void ratio over the historical time. By the decrease of void ratio, undrained shear strength increases. This is why there are several correlations available for determination of S_u from initial void ratio, water content/plasticity index, and historical effective confining pressure.
• For normally consolidated clays c'=0. For overconsolidated clays, c' is not very large and is typically within the range of 0 to 500 psf.
• By dissipation of pore water pressure, i.e., consolidation, effective stress (p' ) would increase and consequently soil shear strength  would increase following the drained strength envelop shown in Figure 1.
• Compared to drained strength (c', \phi'), undrained shear strength is often much easier and cheaper to measure. It can be derived from an unconfined compression test (UU triaxial), vane shear test  or simply using a pocket penetrometer. On the other hand, drained parameters are derived from more expensive consolidated drained (CD) or undrained (CU) triaxial tests. There are also some empirical correlations available in the literature for determination of drained strength in case conducting CD/CU tests is unfeasible in a certain project. Figure 2 presents one of the well-established correlations.

Now per the notes discussed above let’s see what parameters should be used for each of the analysis types listed above:

Slope stability analysis

Short-term condition: undrained parameters (E_u, \nu_u, S_u)*

Long-term condition: drained parameters (E', \nu', c', \phi')

       Pseudo-static condition: undrained parameters (E_u, \nu_u, S_u)*

*  If generation of pore water pressure is simulated in the analysis, drained stiffness parameter (E', \nu') must be used instead of E_u, \nu_u. This is because the analysis accounts for the pore water stiffness (K_w) in calculation of soil volume stiffness.

Static settlement analysis

Immediate settlement: undrained parameters (E_u, \nu_u, S_u)*

Consolidation settlement: drained parameters (E', \nu', c', \phi')

*  If generation of pore water pressure is simulated in the analysis, drained stiffness parameter (E', \nu') must be used instead of E_u, \nu_u. This is because the analysis accounts for the pore water stiffness (K_w) in calculation of soil volume stiffness.

Seismic time history analysis

Case #1 – the analysis is cable of simulating build-up and/or dissipation of pore water pressure over time:  drained parameters (E', \nu', c', \phi')

Case #2 – the analysis is formulated based on fully undrained conditions (in programs like PLAXIS): drained stiffness and undrained strength (E', \nu', S_u)
Note: The undrained analysis accounts for the pore water stiffness (K_w)  in calculation of soil volume stiffness.

Additional remarks:

• It is the common state of practice to use S_u as the soil shear strength even if drained condition exists. The reason is twofold: (a) conducting lab/field test for measurement of S_u is easier and cheaper; and (b) as shown in Figure 1 the S_u envelop generally lies below the drained strength envelop so using S_u would lead to a safer design. This is true only if the soil is subjected to an external loading. If the same soil is unloaded for example due to excavation, drained strength can be less than the undrained strength (see Figure 1).  Technically for overburden pressure (\sigma'_v) less than (S_u-c')/tan (\phi') drained strength would be less than undrained strength. So if the effective stresses are  estimated to be less than (S_u-c')/tan (\phi') it is better to use drained parameters in analyses if you do not 100% sure about existence of fully undrained condition.
• Undrained Young’s modulus (E_u) can be given by:

G_u=G', where G is shear modulus.

\frac{E_u}{2(1+\nu_u)}=\frac{E'}{2(1+\nu')}, where \nu_u=0.5.

E_u=\frac{3E'}{2(1+\nu')}