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SAND DRAINS

The use of sand drains is another way to accelerate the consolidation settlement of soft, normally consolidated clay layers and achieve precompression before foundation construction. Sand drains are constructed by drilling holes through the clay layer(s) in the field at regular intervals. The holes are then backfilled with highly permeable sand (see Figure 12.24a). After backfilling the drill holes with sand, a surcharge is applied at the ground surface. This surcharge will increase the pore water pressure in the clay. The excess pore water pressure in the clay will be dissipated by drainage both vertically and radially to the sand drains—which accelerates settlement of the clay layer.
Note that the radius of the sand drains is γ (Figure 12.24a). Figure 12.24b shows the plan of the layout of the sand drains. The effective zone from which the radial drainage will be directed toward a given sand drain is approximately cylindrical, with a diameter of d .
To determine the surcharge that needs to be applied at the ground surface and the length of time that it has to be maintained, refer to Figure 12.18 and use the corresponding equation, Eq.(12.9):

U                   (12.11)

The notations   and   are the same as those in Eq.(12.9). However, unlike Eq.(12.9), the left-hand side of Eq. (12.11) is the average degree of consolidation instead of the degree of consolidation at midplane. Both radial and vertical drainage contribute to the average degree of consolidation. If U can be determined for any time t (see Figure 12.18b), the total surcharge  +  may be obtained easily from Figure 12.19. The procedure for determination of the average degree of consolidation (U ) is given in the following sections.
The successful use of sand drains has been described in detail by Johnson (1970b). As for precompression, constant field settlement observations many be necessary during the period of surcharge application.



Average Degree of Consolidation Due to Radial Drainage Only
The theory for equal-strain consolidation due to radial drainage only (with no smear) was developed by Barron (1948). It is based on the assumption that there is no drainage in the vertical direction. According to this theory,

U =1-exp(                                     (12.12)

Where U =average degree of consolidation due to radial drainage only

                m=                               (12.13)

n=                                               (12.14)

T =nondimensional time factor for radial drainage only
=                                              (12.15)
C =coefficient of consolidation for radial drainage
   =

Note that Eq.(12.16) is similar to Eq.(1.66), k was the coefficient of permeability in the vertical direction of the caly layer. In Eq.(12.16), k has to be replaced by k , the coefficient of permeability for flow in the horizontal direction. In some cases, k  may be assumed to equal k; however, for soils like varved clay, k >k.
Figure 12.25 shows the plot of U  against T  for various values of n.

Average Degree of Consolidation Due to Vertical Drainage Only

The average degree of consolidation due to vertical drainage only may be obtained from Eqs.(1.73)and (1.74)(or Figure 1.25):

T =        (for U =0-60%)                         (1.73)
and
           T =1.781-0.933 log(100-U %)      (for U >60%)              (1.74)
Where U =average degree of consolidation due to vertical drainage only
                  
T =                                                     (1.68)
C =coeffici of consolidation for vertical drainage





Average Degree of Consolidation Due to Vertical and Radial Drainage
For a given surcharge and duration t , the average degree of consolidation due to drainage in the vertical and radial directions is

U =1-(1-U )(1-U )

Wick Drains
The wick drain was recently developed as an alternative to the sand drain for inducing vertical drainage in saturated clay deposits. Wick drains appear to be better, faster, and cheaper. They essentially consist of paper or plastic strips that are held in a long tube. The tube is pushed into the soft clay deposit, then withdrawn, leaving behind the strips. These strips act as vertical drains and induce rapid consolidation. Wick drains can be placed at desired spacings like sand drains. The main advantage of wick drains over sand drains is that they do not require drilling, and thus installation is much faster.
Redo Example 12.2 with the addition of some sand drains. Assume that  .

Solution
Part a
The total primary consolidation settlement will be 167.7mm as before.

Part b
From Example 12.2, T =0.36. The value of U , from Figure 1.21, is sbout 67%. From Eq.(12.14),

        n=
Again,

        T
From Figure 12.25 for n=15 and T =0.36, the value of U  is about 77%. Hence
   U =1-(1-U )(1-U )=1-(1-0.67)(1-0.77)
      =0.924=92.4%
    Now,from Figure 12.19 for  =0.548 and U =92.4%, the value of  0.12. Hence
         (115)(0.12)=13.8KN/m