Base heave can occur, for example, at the bottom of a braced excavation for the installation of a service pipe, due to two factors:
• Reduction in vertical stress can produce sufficient shear stress, (σh− σv)/2, that the shear strength of the soil beneath the base of the exca-vation is exceeded. This condition can be a problem when excavating in soft clays.
• The uplift due to ground water, normally when trapped below an impermeable layer, is sufficient to overcome the weight of the soil.
An example of this second condition is shown in Figure 4.16. Assuming that
• The gravel/clay interface to be 3 m below the base of the excavation, and
• The groundwater table to be 4 m above the base of the excavation,
• The bulk unit weight of the sand and the clay to be 18 kN/m3, then
The uplift pore pressure
≈ (4 + 3) 10 = 70 kPa
Clay Sand
Gravel Total stress, σv
Pore pressure, u Shear stress
between wall and soil
Figure 4.16 Hydraulic uplift.
The downward vertical total stress under the clay, inside the excavation
= 3.18 = 54 kPa
Under these conditions uplift can only be prevented by the shear stresses (shown by the black downward arrows in Figure 4.16) acting between the walls and the soil below the base of the excavation. These are only likely to help in a narrow excavation.
4.3.3 Piping
Figure 4.17 shows an element of soil subjected to upward water flow. If side friction is ignored, there will be stability provided that the weight of the soil element is greater than the force resulting from the pore pressures on the upper and lower faces of the element. The weight of the element
W= γbulk.AB CA per unit length. .1 (4.10) The resultant force due to the difference in water pressure
U=(uAB−uCD).AB (4.11)
W D C
uAB uCD
hCD hAB
Flow
Figure 4.17 Instability due to piping, during upward seepage.
where
uAB = hAB.γw (4.12)
uCD=
(
hCD−AC)
.γ (4.13)w∴ U=(hAB−hCD).γw.AB+γw.AC.AB (4.14) For conditions of limiting stability, W = U, and therefore
AC(γbulk−γw) (= hAB−h )CDγw (4.15) or
(h h ) ( )
AC i
AB CD
crit bulk w
w
− = = γ −γ
γ (4.16)
Since γw = 9.81 kN/m3 and typically γbulk = 16–22 kN/m3, for piping to occur
icrit≈ 1 (4.17)
The condition of upward seepage with a hydraulic gradient greater than 1 can occur below the bottom of an excavation. An example of a possible situation is the seepage around sheet piling, as shown in Figure 4.18, where the soil inside the excavated area is at risk. The deeper the excavation in such a case, the greater the risk, because as the excavation is increased the flow length becomes smaller and the hydraulic head difference between the upstream and downstream boundaries becomes greater.
Experience shows that reductions in passive resistance and unstable con-ditions for equipment and labour may occur when the hydraulic gradient at the exit (i.e. at the base of the excavation) is of the order of 0.5–0.75.
Figure 4.19 shows the penetration of sheet piling required to prevent piping in an isotropic sand deposit, according to NAVFAC-DM7.
The computation of a factor of safety against piping at the base of an anchored sheet-pile wall can be carried out according to the method described by Terzaghi (1943). In this method, the equilibrium of a rectan-gular soil element, with a depth equal to the depth of embedment of the sheet piling and a width equal to one-half of that depth, is considered. The factor of safety is defined as the ratio between the head difference between the upstream and downstream boundaries required to cause instability
divided by the actual head difference. A factor of safety of 3–4 is suggested.
Example 4.4 carries out a calculation by this method.
Example calculation 4.4—Factor of safety against piping
Calculate the factor of safety against piping failure by the Terzaghi method, for the geometry in Figure 4.20, where
head difference, H = ai = 4 m Sheet-pile penetration, he = 4.8 m γbulk = 20.2 kN/m3
oe = 2.4 m
Calculate the buoyant weight of soil in element heop
Wbuoy= he eo− whe eo
= −
γ. . γ . . ( .20 2 10 0 4 8 2 4. ) . . .
≈≈118 kN//m run
Calculate the average head perpendicular to eo At e, he = 2.00 m
At b, hb = 1.50 m At c, hc = 1.38 m
D/2
D
Area at risk of piping
Fine sand Gravel
Sheet-pile wall
Impermeable
Figure 4.18 Example of soil vulnerable to piping.
At d, hd = 1.20 m At o, ho = 1.10 m
heo= 1 44. m
Proportion of total head loss
m h
Factor of safety against heave in loose sands and piping in dense sands
1.5 2.0
Ratio of penetration required to net head (D/Hw)Ratio of penetration required to net head (D/Hw) 2.0
Ratio of half width of excavation to net head (W/Hw) Ratio of half width of excavation to net head (W/Hw)
H1/Hw = 1
Figure 4.19 Penetration of sheet piling required to prevent piping in isotropic sand (NAVFAC-DM7 1982). Top—penetration required for sheeting in sands of infinite depth; Bottom—penetration required for sheeting in sands of limited depth.
Calculate the critical head at the base of element heop As shown above, the critical condition occurs when
hhp heo bulk w
w
− = −
4 8.
γ γ
γ
or
γw(hhp − heo) = 4.8(γbulk − γw)
∴eo.γw(hhp−heo)=Wbuoy
( ) .
. . . . hhp−heo = 117 5 ≈ m
10 0 2 4 4 9
h 4.9
crit= m = 4 9 0 36
. .
= 13.6 m
Impermeable a
i Sheet-pile wall H
e h
d p
o b c
Figure 4.20 Example calculation 4.4 - piping.
Calculate the factor of safety
In cases where it is not possible to achieve a satisfactory depth of Sheet-pile penetration, or where the required depth is clearly uneco-nomical, a number of other measures may be considered, such as
a. The use of well-points from original ground level, to lower the groundwater level in the area of the excavation (see Section 4.4).
This is suitable for relatively homogeneous soil conditions, or where permeability decreases with depth.
b. The use of pressure relief wells in the base of the excavation (see Section 4.4). This technique may be suitable where a thin rela-tively impermeable soil layer overlies permeable soil relarela-tively close to the base of the excavation.
c. The use of a filter layer in the base of the excavation. This method provides weight and prevents the upward movement of soil particles with the inflowing water (see Section 4.3.5).
If the groundwater level is higher than ground level on the upstream side of the wall, a clay carpet or bentonite slurry may be used to create a relatively impermeable barrier and reduce water inflow. The effectiveness of each option must be evaluated for the individual geometry of a particu-lar case on the basis of flownet sketching, or other seepage analysis.