In Chapter 4, we discussed one-dimensional flow of water through soils. As water flows through soil it exerts a frictional drag on the soil particles resulting in head losses. The frictional drag is called seepage force in soil mechanics. It is often convenient to define seepage as the seepage force per unit volume (it has units similar to unit weight), which we will denote by js. If the head loss over a flow distance, L, is Dh, the seepage force is
js¼Dhgw
L ¼ igw (5.47)
If seepage occurs downward (Fig. 5.20a), then the seepage stresses are in the same direction as the gravitational effective stresses. From static equilibrium the resultant vertical effective stress is
s0z¼ g0zþ izgw¼ g0zþ jsz (5.48)
If seepage occurs upwards (Fig. 5.20b), then the seepage stresses are in the opposite direction to the gravitational effective stresses. From static equilibrium the resultant vertical effective stress is
s0z¼ g0z izgw¼ g0z jsz (5.49)
Seepage forces play a very important role in destabilizing geotechnical structures. For example, a cantilever retaining wall, shown in Fig. 5.21, depends on the depth of embedment for its stability. The retained soil (left side of wall) applies an outward lateral pressure to the wall, which is resisted by an inward lateral resistance from the soil on the right side of the wall. If a steady quantity of water is available on the left side of the wall, for example, from a busted water pipe, then water will flow from the left side to the right side of the wall. The path followed by a particle of water is depicted by AB in Fig. 5.21 and as water flows from A to B, head loss occurs. The seepage stresses on the left side of the wall are in the direction of the gravitational stresses. The effective stress increases and, consequently, an additional outward lateral force is applied on the left side of the wall. On the right side of the wall, the seepage stresses are upward and the effective stress decreases. The lateral resistance provided by
(a) Downward seepage z
(b) Upward seepage z
FIGURE 5.20 Seepage in soils.
5.9 TOTAL AND EFFECTIVE STRESSES 127
the embedment is reduced. Seepage stresses in this problem play a double role (increase the lateral disturbing force and reduce the lateral resistance) in reducing the stability of a geotechnical structure.
In Chapters 11 through 13, you will study the effects of seepage on the stability of several types of geotechnical structures.
The essential points are:
1. The effective stress represents the average stress carried by the soil solids and is the difference between the total stress and the porewater pressure.
2. The effective stress principle applies only to normal stresses and not to shear stresses.
3. Deformations of soils are due to effective not total stress.
4. Soils, especially silts and fine sands, can be affected by capillary action.
5. Capillary action results in negative porewater pressures and increases the effective stresses.
6. Downward seepage increases the resultant effective stress; upward seepage decreases the resultant effective stress.
EXAMPLE 5.5 Calculating Vertical Effective Stress
Calculate the effective stress for a soil element at depth 5 m in a uniform deposit of soil as shown in Fig. E5.5.
Strategy You need to get unit weights from the given data and you should note that the soil above the groundwater level is not saturated.
B Effective stresses
increase
Effective stresses decrease A
FIGURE 5.21 Effects of seepage on the effective stresses near a retaining wall.
Ground level S = 0.6
w = 30%
w = 40%
2 m
5 m
FIGURE E5.5
Solution 5.5
Step 1: Calculate unit weights.
Above groundwater level
g¼ Gsþ Se 1þ e
gw¼Gsð1 þ wÞ 1þ e gw Se¼ wGs; ;e ¼0:3 2:7
0:6 ¼ 1:35 g¼2:7ð1 þ 0:3Þ
1þ 1:35 9:8 ¼ 14:6 kN=m3 Below groundwater level
Soil is saturated; S ¼ 1
e¼ wGs¼ 0:4 2:7 ¼ 1:08 gsat¼ Gsþ e
1þ e
gw¼ 2:7 þ 1:08 1þ 1:08
9:8 ¼ 17:8 kN=m3
Step 2: Calculate the effective stress.
Total stress: sz¼ 2g þ 3gsat¼ 2 14:6 þ 3 17:8 ¼ 82:6 kPa Porewater pressure: u ¼ 3gw¼ 3 9:8 ¼ 29:4 kPa
Effective stress: s0z¼ sz u ¼ 82:6 29:4 ¼ 53:2 kPa Alternatively:
s0z¼ 2g þ 3ðgsat gwÞ ¼ 2g þ 3g0¼ 2 14:6 þ 3ð17:8 9:8Þ ¼ 53:2 kPa &
EXAMPLE 5.6 Calculating and Plotting Vertical Effective Stress Distribution
A borehole at a site reveals the soil profile shown in Fig. E5.6a. Plot the distribution of vertical total and effective stresses with depth.
Elevation (m)
20.6 5.4 3.0 2.0
0 Very fine wet sand with silt w = 5%, S = 40%
Fine sand saturated by capillary action Fine sand, w = 12%
Soft blue clay, w = 28%
FIGURE 5.6a
5.9 TOTAL AND EFFECTIVE STRESSES 129
Strategy From the data given, you will have to find the unit weight of each soil layer to calculate the stresses. You are given that the 1.0 m of fine sand above the groundwater level is saturated by capillary action. Therefore, the porewater pressure in this 1.0 m zone is negative.
Solution 5.6
Step 1: Calculate the unit weights.
0–2 m
Step 2: Calculate the stresses using a table or use a spreadsheet program.
Depth (m) Thickness (m) sz(kPa) u (kPa) s0z¼ s u (kPa)
Step 3: Plot the stresses versus depth—see Fig. E5.6b.
0
250 300 350 400 450
Total vertical stress
Porewater pressure
Effective vertical stress
FIGURE E5.6b &
EXAMPLE 5.7 Effects of Seepage on Effective Stress
Water is seeping downward through a soil layer as shown in Fig. E5.7. Two piezometers (A and B) located 2 m apart (vertically) showed a head loss of 0.2 m. Calculate the resultant vertical effective stress for a soil element at a depth of 6 m as shown in Fig. E5.7.
Strategy You have to calculate the seepage stress. But to obtain this you must know the hydraulic gradient, which you can find from the data given.
Solution 5.7
Step 1: Find the hydraulic gradient.
DH¼ 0:2 m; L ¼ 2 m; i ¼DH L ¼0:2
2 ¼ 0:1 Step 2: Determine the effective stress.
Assume the hydraulic gradient is the average for the soil mass; then
s0z¼ ðgsat gwÞz þ igwz¼ ð18:5 9:8Þ6 þ 0:1 9:8 6 ¼ 58:1 kPa &
What’s next. . . We have only considered vertical stresses. But an element of soil in the ground is also subjected to lateral stresses. Next, we will introduce an equation that relates the vertical and lateral effective stresses.