How to Design Vertical Sand Drains

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Introduction

A vertical sand drain is a boring through clay or silty soil that is filled with sand or gravel to facilitate drainage of a liquid from the soil. The use of sand drains is a necessity in construction work in places where drainage is poor due to very fine soils such as clay or silty soil. In most cases, they are used to pre-load the soil and hence pre-consolidate the soils before construction begins. The aim is to ensure that all settlement occurs before/during and not after construction.

Vertical sand drains are usually employed in the construction of highway and airport embankments over compressible or soft soils, construction of dams over soft grounds and foundations for buildings etc.

It should be noted that artificial sand drains are not suitable in expansive soils like montmorillonite and organic soils because major part of settlement is secondary settlement which is independent of pore pressure. This secondary settlement or compression cannot be controlled by vertical sand drains. Vertical sand drains are also dangerous in quick clays since one almost gets increased settlement and there is need to consider this in order to place sand drains in them before disturbance.

How to Design Vertical Sand Drains

The mechanism of consolidation in vertical sand drains is radial (see Figure 3). Hence, radial consolidation parameters are employed in the design. The basic target in the design is to choose a drainage spacing and diameter such that the specified percentage of consolidation (usually 80%) takes place in a specified period of time.

Geotechnical Parameters Required for the Design

• The thickness of the clay layer.
• The permeability of the materials underlying the clay layer.
• The coefficient of vertical consolidation, C_v values of the clay.

Assumptions for the Design of Vertical Sand Drains

• One dimensional consolidation (all vertical).
• No head loss in the well.
• Shear zone is neglected and load distribution is assumed constant over the whole area.

Steps in the Design of Vertical Sand Drains

1. Using a specified time, t and coefficient of consolidation, C_v, and the drainage path without sand drains, calculate the time factors, T_v; T_v = C_vt/H²

2. Use the theoretical time factor, T_v, to find the corresponding U_v. This gives the degree of consolidation that can be obtained without the use of radial drains.

3. If U_v is less than the required degree of consolidation, then calculate the required U_h; U_h = 1 – ((1-U_h)/(1-U_v)).

4. Choose a specific well-drain diameter, d_w and solve for the effective radial drainage, R, where, R = nr_w; n = constant and r_w = radius of well.

Patterns of Vertical Drains.

There are two patterns of vertical drains

Square pattern (see Figure 1)

Triangular pattern (see Figure 2)

Example

Determine the required spacing for a drain well 457 mm diameter to result in 80 % consolidation in 12 months. The clay layer is 6.1 m thick underlain by impervious rock

(Take C_v = 300 mm²/mm; K_H = K_V; C_r = C_v)

Solution

Tv = C_vt/H² = ((0.03 cm²/mm) (12 x 30 (days/month) x 24 (Hrs/day) x 60 (min/hr) min)) / (610 cm)2 = 15552 cm²min/mm/372100 cm² = 0.0418 min/mm.

From Table 1 below, for T_v = 0.0418, U = 22.7^o

Table 1; Variation of T_v with U

However, the value was gotten by interpolating between T_v/U values of 0.0415/23 and 0.0452/24.

U_r = 1 – ((1 – U_vr) / (1-U_v)) where U_vr = 80% and U_v = 22.7^o

U_r = 1 – (0.2/0.773) = 1 – 0.259 = 0.741 = 74.1^o

The well drain diameter, d_w = 45.7cm

Hence, well drain radius, r_w = d_w/2 = 45.7/2 = 22.85cm

Note: Solutions for R is made by successive approximations using at least 2 values of ‘n’ where n = R/r_w

and r_w = radius of well drain.

1^st Trial
Assume n = 5, hence R = 5(22.85) = 114.25cm

T_r = C_vt/4R² = ((0.03cm²/min) (12 x 30 x 24 x 60 min)) / (4 x (114.25cm)²) = 0.3

From Table 2 below, for T_r = 0.3, U_r = 91.9%

Table 2; Solution for Radial Drainage

Note: For the Table 2 captioned Solution for radial drainage, the values of U_r are determined for values of n and T_r. Where the exact value of T_r is not present which is the case most times, interpolation is done between the lower limit and upper limit nearest values of T_r and their corresponding values of U_r to determine the value of U_r that is being sought. Craig soil mechanics (7^th edition) provided this solution as a series of curves of n-values plotted between U_r and T_r values.

2^nd Trial
Assume n = 10, hence R = 10 (22.85) = 228.5 cm

T_r = C_vt/4R² = ((0.03cm²/min) (12 x 30 x 24 x 60 min)) / (4 x (228.5cm)²) = 0.0745

From Table 2, for T_r = 0.0745, U_r = 31.5^o

To determine the n-value corresponding to U_r value of 74.1^o, we do interpolation between the values presented in the table below

Ur	91.9o	31.5o	74.1o
n	5	10	nx

(n_x – 5) / (10 – 5) = (74.1 – 91.9) / (31.5 – 91.9)  

(n_x – 5) / 5 = 17.8 / 60.4

60.4 (n_x – 5) = 17.8 x 5

60.4 n_x – 302 = 89

60.4 n_x = 89 + 302

60.4 n_x = 391

n_x ≈ 6.5

Since ‘n’ for 74.1^o = 6.5, R = nr_w = 6.5 x 22.85 = 148.5 cm

Check for the Suitable Pattern of Spacing;

For square pattern, Spacing, S = R/0.564 = 148.5/0.564 = 263.3 cm = 2.63 m

For Triangular pattern, S = R/0.525 = 148.5/0.525 = 282.5 cm = 2.83 m

Craig stated that the expression for T_r confirms the fact that the closer the spacing of the drains, the quicker the consolidation process due to radial drainage proceeds. This could guide the choice of the spacing and spacing pattern to be adopted.

Construction of Sand Drains

Sand drains are constructed by drilling holes through the clay layer(s) in the field at regular intervals. The holes are backfilled with highly permeable sand or suitable grade of sand (see Figure 3). The sand must be capable of allowing the efficient flow of water while preventing fine soil particles from being washed in. Careful backfilling is also essential to avoid discontinuities which could give rise to ‘necking’ and which can render a drain ineffective.

After installing the drains, a surcharge load is applied. 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 (minor) and radially (major) to the sand drains which accelerates settlement of the clay layer.

Typical Practices in the Construction of Sand Drains

1. Drainage blanket should be between 0.6m and 2.4m thick.
2. Stage loading is essential during load application to avoid shearing of drains.
3. It is common for shallow depths but deep depths of 3m to 30m could be applicable.
4. Spacing of wells is often between 1.8m and 3m and the holes are usually between 30 cm and 60 cm in diameter.

Uses of Sand Drains

1. Used to hasten settlement and consolidation.
2. Used to increase rate of strength gain.
3. Mainly used in layered clays, silts and sand where K_horizontal (horizontal coefficient of permeability) is greater than K_vertical (vertical coefficient of permeability).

Credit for Note: Engr Prof C.M.O. Nwaiwu (Professor of Geotechnical and Geoenvironmental Engineering at Nnamdi Azikiwe University, Awka, Nigeria).

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