Suction Strength
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Introduction
The shear strength of an unsaturated soil comprises three components: cohesion, frictional strength,
and suction strength. Suction strength arises from the negative pore-water pressure acting on the
soil grains, which increases the effective stress. This component is often ignored is geotechnical
design, however, it can be important in certain classes of problems including rainfall-induced
instability or back analysis of overly steepened slopes. This example describes how to include
suction strength in a SLOPE/W analysis and the effect it has on the calculated factor of safety.
Background
There are a number of equations available in the literature to describe the shear strength of
unsaturated soils. Vanapalli et al. (1996) suggested a non-linear shear strength equation that
involved a normalization of the volumetric water content function given by:
𝜏 = 𝑐' + (𝜎𝑛 ‒ 𝑢𝑎)𝑡𝑎𝑛𝜙' + (𝑢𝑎 ‒ 𝑢𝑤)𝑆𝑒𝑡𝑎𝑛𝜑' Equation 1
where 𝜏 is the shear strength, 𝑐 the effective cohesion, (𝜎𝑛 ‒ 𝑢𝑎) the net normal stress on the failure
'
plane, 𝜎𝑛 the total normal stress; 𝑢𝑎 the air pore-air pressure; 𝑢𝑤 the pore-water pressure; (𝑢𝑎 ‒ 𝑢𝑤)
the matric suction; 𝜙 the friction angle; and, 𝑆𝑒 is the effective degree of saturation given by:
'
𝜃 ‒ 𝜃𝑟 Equation 2
𝑆𝑒 =
𝜃𝑠 ‒ 𝜃𝑟
where 𝜃 is the volumetric water content and the subscripts 𝑟 and 𝑠 indicate residul and saturation,
respectively. The suction strength is represented by the third term in Equation 1. The literature
clearly demonstrates that the unsaturated shear strength can be related to the volumetric water
content function. According to Equation 1, the shear strength of an unsaturated soil increases nearly
1
proportionally with matric suction until the air entry value is reached. At higher matric suctions, the
suction strength decreases non-linearly, and in accordance with the decrease in effective degree of
saturation, reaching zero once the volumetric water content is equal to the residual value (i.e. 𝜃 =
𝜃𝑟).
The relationship between suction strength and matric suction is soil type dependent via the
relationship between volumetric water content and matric suction. Figure 1 presents the volumetric
water content of a soil with a porosity of 0.5 and a residual water content of about 0.14. The
corresponding suction strength was calculated using the third term in Equation 1 assuming a friction
angle of 30. The suction strength does not begin to increase markedly until the air entry value is
exceeded.
Figure 1. Example of a volumetric water content function.
Numerical Simulation
The effect of the suction strength is illustrated for a simple 2:1 slope (Figure 2). The suction strength
is defined by selecting a volumetric water content on the Suction Strength tab. By default, SLOPE/W
does not include suction strength. GeoStudio includes sample VWC functions for a range of material
textures. Each of these sample functions are used to illustrate the effect on shear strength in six
slope stability analyses (Figure 3). The water table was defined using a piezometric line at the
elevation of 10 m.
2
Figure 2. Problem configuration.
Figure 3. Analysis Tree for the Project.
All of the analyses use a Mohr-Coulomb material model with a soil unit weight of 20 kN/m3, cohesion
of 5 kPa, and friction angle of 20°. The volumetric water content functions were estimated using
each of the sample types available in GeoStudio and a saturated volumetric water content of 0.5
(Figure 4).
0.5
Vol. Water Content (m³/m³)
0.4
clay
0.3 gravel
sand
0.2 silt
silty clay
0.1 silty sand
0
0.1 1 10 100 1000 10000
Matric Suction (kPa)
Figure 4. Volumetric water content functions used in each of the analyses.
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Results and Discussion
Figure 5 presents the pore-water pressure and suction strength values for each slice of the critical
slip surface for Analysis 2. The suction strength increases as the pore-water pressure becomes
negative, but then declines to zero as the pore-water pressure becomes large enough that the
residual water content is reached. Also, the suction strength is zero when the pore-water pressure is
positive.
20
-20 pwp : Slip 1
Undefined (kPa)
-40
-60
Suction : Slip 1
-80
-100
0 10 20 30
Slice #
Figure 5. Suction strength relative to the negative pore-water pressure (Analysis 2).
A plot of suction strength for all analyses is shown in Figure 6. Clay, being a fine grained soil, has a
relatively high air entry value and a relatively flat VWC function. Consequently, the strength suction is
a significant component of the overall shear strength. In contrast, sand has a relatively low air entry
value and a steeper VWC function. The suction contributes very little to the shear strength.
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Figure 6. Suction strengths for various materials.
The safety factors for the various soils are in presented in Table 1. The suction strength can have a
significant effect on stability. The factor of safety for the gravel slope represents the case in which
suction strength is excluded. For a clay slope, the factor of safety rises to 1.342.
Table 1. Safety factors for various soils.
Soil type Factor of safety
Clay 1.342
Silty-clay 1.226
Silt 1.183
Silty sand 1.171
Sand 1.167
Gravel 1.167
Summary and Conclusions
The shear strength that arises from negative pore-water pressures (i.e., matric suction), known as
suction strength, can be included in SLOPE/W. This strength component is often related to the
volumetric water content, producing a non-linear relationship. Although suction strength is
generally not included in engineering design, it can be essential to analyze and understand many
geotechnical problems such as rainfall-induced instability or unsupported vertical excavations that
remain stable. It can also be included in back-analyses to produce a more conservative value for the
friction angle.
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References
Vanapalli, S.K., Fredlund, D.G., Pufhal, D.E. and Clifton, A.W. 1996. Model for the prediction of shear
strength with respect to soil suction. Canadian Geotechnical Journal, Vol. 33 (3), 379 – 392.
