# Design of Sand Drains

The typical design parameters for the sand drains along with its permissible values are given as :

(i) Diameter of sand drains (ɸd) = 450 mm to 600 mm.

(ii) Spacing between two adjacent sand drains (S) = 1.8 m to 5 m cc (centre to centre).

(iii) Depth of sand drains (H) = 3 m to 35 m.

(iv) Thickness of sand blanket = 0.6 m to 1 m.

During designing, the values of diameter is rounded off to higher side and spacing is rounded off to lower side.

## Steps to Design Sand Drains

### Method 1

1. Total Settlement = mv.∆σ.h
2. Degree of consolidation, U = Settlement controlled * 100 / Total settlement
3. Tv = Cv.t / h²
4. Tv at U = 60% is 0.2827, So if Tv < 0.2827 i.e. U < 60% then Tv = Uv².∏/4 otherwise if Tv >0.2827 i.e. U > 60% then Tv = 1.781 -0.933 log (100 – U%)
5. After getting the Uv value from above equations, find Ur (required) value from the formula, (1-U) = (1-Uv)*(1-Ur)
6. Assume triangular or square pattern and spacing S; R = 0.525 S or R = 0.564 S
7. Tr = Ch.t/4R²
8. Assume Diameter (ɸd) or Radius (rd) of Sand Drains; then find n = R/rd
9. From the given graph find the value of Ur (calculated) corresponding to obtained n and Tr values.
10. If Ur (calculated) > Ur (required) then Design of Sand drains is OK otherwise assume another values from step 6 and keep on trying safe design values.

### Method 2

1. Total Settlement = mv.∆σ.h
2. Degree of consolidation, U = Settlement controlled * 100 / Total settlement
3. Tv = Cv.t / h²
4. Tv at U = 60% is 0.2827, So if Tv < 0.2827 i.e. U < 60% then Tv = Uv².∏/4 otherwise if Tv >0.2827 i.e. U > 60% then Tv = 1.781 -0.933 log (100 – U%)
5. After getting the Uv value from above equations, find Ur value from the formula, (1-U) = (1-Uv)*(1-Ur)
6. Assume n value; ranging from 5 to 40
7. From the given graph find the value of Tr corresponding to obtained Ur and assumed n value.
8. Tr = Ch.t/4R² ; get R value.
9. Find radius (rd) of Sand Drains, n = R/rd
10. Obtain Diameter of Sand Drains (ɸd) = 2(rd)
11. Let the pattern triangular or square pattern
12. Find spacing S from formula; R = 0.525 S or R = 0.564 S

Method 2 is more convenient than Method 1 as it does not require number of trails. The design obtained via Method 2 is all OK in first attempt. But if restricted values of few parameters are there then we should go for Method 1.

Representations used are :

• mv = co-efficient of volume compressibility
• ∆σ = change in stress
• h = Depth of clay layer (h = D/2 when two way drainage is there, h = D when one way drainage is there)
• ch or cvr = co-efficient of consolidation in horizontal / radial direction
• cv or cvz = co-efficient of consolidation in vertical direction
• R = Radius of zone of influence
• Tr = Time factor in radial direction
• Tv = Time factor in vertical direction
• U = Degree of total consolidation
• Ur = Degree of consolidation in radial direction
• Uv = Degree of consolidation in vertical direction