**4. Drainage systems**

The conventional drainage systems commonly adopted in road construction include open concrete drain and pipe drain. In the design of such a drain some factors which include hydraulic, structural, environmental, sociological and maintenance attributes are considered [4]. The weight attached to each of these factors is a function of engineering judgment and sustainability requirement.

#### **4.1 Open concrete drain**

Open drains can be provided on either or both sides of the road. It can be trapezoidal, rectangular or square in shape. The channel can be lined with mass concrete or reinforced concrete. For the drain to be effective the grade must be sufficient to mobilize minimum permissible velocity that will enhance self cleansing and gentle enough not to exceed the maximum permissible velocity that would initiate scouring of the lining. Open drain can easily be maintained in the face of high sediment load or rubbish load in an area. However it is unsightly and may be risky to road users in some cases. But when the invert slope is less than 2% as is the case with flat terrain, the drain can hardly function. In this situation a trenchless drainage system provides a good alternative.

#### **4.2 Pipe drain**

**P**ipe drain is often cylindrical or rectangular in shape, aligned and buried in the subsurface. Drainage through pipes simulates flow through conduits. Pipe drain is mainly suitable for high density and high value residential development. It provides a better appearance and safety than open drain but much more expensive to construct

and more challenging to maintain. To function effectively pipe drain must mobilize permissible flow velocities within the range of minimum and maximum. However when the drain invert or the slope of the terrain is less than 2% its conveyance becomes grossly inadequate. Then the alternative and effective choice is the trenchless drain system.

## **5. Trenchless drainage system**

The trenchless drainage system provides a solution for the evacuation of runoff from road pavement situated on flat terrain. It serves as a suitable alternative to open or pipe drains on such an environmental setting.

#### **5.1 Concept**

The concept behind trenchless drainage system is based on the application of engineered absorption field and grass cover to facilitate runoff infiltration into the subsurface [2]. This aligns with the concept of 'French drain' in a general term. The components of trenchless system is highlighted as follows.

**Absorption field**: An absorption field is an excavation or a trench, backfilled with relatively permeable material when compared with the native or in-situ soil. The excavation creates a wider surface area for the water to infiltrate and percolate in the underlying soil medium [5].

**Grasses:** The benefits of grasses as an aid to effective drainage of an area had been highlighted [6, 7]. The foliage intercepts raindrops that attempt to fall unto the ground to cause splash erosion. This, in consequence absorbs the terminal energy of the rain drop thereby reducing its erosivity. The foliage also provides an evapotranspiration medium for the system. The stem of the grass in conjunction with the leaves interrupt free flow of the runoff, thereby increasing the flow roughness. This provides suitable opportunity for infiltration to take place. The root system has numerous channels for water infiltration and as well acts as a transition channel for evapo-transpiration. Generally grasses bind soil particles into a matrix and provide numerous infiltration and evapo-transpiration pathways.

A combination of absorption field and grass in an engineered fashion provides a good infiltration sump for road wash. It also restricts migration of composite earth materials, such as silts and fine sand, in the runoff that could block infiltration channels.

#### **5.2 Preliminary studies**

The design of trenchless drain requires some fundamental parameters that must be studied and considered. These include rainfall intensity of the area receiving attention, the in-situ or native soil permeability/hydraulic conductivity, properties of the backfill material and the design road width [2].

**Rainfall Intensity**. The rainfall intensity of the area can be obtained from rainfall studies of the nearest metrological station. For optimal design the value may be determined from maximum daily rainfall data of 10 years return period. Rainfall intensity (I) can be calculated from the expression,

$$\mathbf{I} = \mathbf{D} \mathbf{r}./\mathbf{T} \tag{1}$$

where Dr. = depth of rainfall in cm, T = duration of rainfall in min.

**In-situ Soil Properties.** The permeability or hydraulic conductivity of the in-situ soil is required and this can be obtained through a number of simple field techniques. One of such techniques is the Auger Hole method [8], performed within a relatively shallow depth. A number of such a test is carried out along the length and breadth of the proposed road right- of- way. The soil permeability, K is estimated from the equation,

$$\mathbf{K} = \mathbf{C} \Delta \mathbf{H} / \Delta T \tag{2}$$

Where C = the geometry factor of the auger hole, ΔH = change in water level in the hole at time interval Δ*T:*

Ring infiltration method can also be used in estimating K [9]. It uses the principle of falling head permeameter. The evaluation follows the following equation:

$$\mathbf{K} = \mathbf{A}\_1 \,\mathrm{L}/\mathrm{A}\_2 \,\mathrm{(T\_2 - T\_1)} \text{ ln } \left(\mathrm{H}\_1/\mathrm{H}\_2\right) \tag{3}$$

Where A1 = cross sectional area of the observation tube, A2 = cross sectional area of the soil tube, L = length of the soil tube, H1 = head at the time T1, H2 = head at the time T2.

In addition to the estimation of soil permeability, other basic properties of the in-situ soil would be studied. These include the grain size distribution, the Atterberg limits, specific gravity, specific weight; etc. They can be used for classification of the soil.

**Backfill materials**. The materials that could be used to backfill the dug trench must have passed through a series or cycles of abrasion and then become stabilized after the erosive components of the material may have been dissolved and removed. This ensures that the likely cementing agents and organic matters had been washed away. Sands and gravels fall into this category. They can be sourced from alluvial deposits or processed to obtain the required properties.

The backfill must be relatively pervious compared to the in-situ soil. Its porosity can be obtained from laboratory measurements conducted on some samples of the backfill. Other laboratory studies that are required may include grain size distribution, specific gravity, and specific weight. Research has shown [10], that poor graded materials with relatively high values of diameter at 30% passing and relatively high values of uniformity coefficient are preferred as backfill.

**Road Width.** The width of the roadway is an input parameter in trenchless drainage design. It is a reference catchment area of the drain. The size may be obtained from preliminary design specifications or working drawing for the construction. Consideration would be given to the effective width of the road for drainage purposes. This may include areas outside the limit of asphalt coating. However the actual width to be used in the sizing of the drain will, principally, be dependent on the judgment of the drainage engineer.

## **6. Design of trenchless drainage system**

#### **6.1 Design philosophy**

The design of a trenchless drain assumes that only the road wash flows towards the sides of the road, and flow down the slope is restricted by the relatively flat nature of the terrain. That means in-flow from outside the road margins is not considered in the formulation of the enabling equation. By synthesizing inflow into the drain and outflow from the drain in the process of infiltration into the adjacent soil, the following equations were obtained [2, 11],

The volume of inflow, Q was given by

$$\mathbf{Q} = \mathbf{k\_1}\mathbf{1}\left(\mathbf{W\_r} + \mathbf{W\_t}\right) \tag{4}$$

While the volume of outflow, i.e. the infiltration capacity, F of the drain was given by

$$\mathbf{F} = \mathbf{k\_2} \,\, \mathbf{3} \,\, \mathbf{W\_t} \,\, \mathbf{K} \tag{5}$$

For optimal design, Q = F, and considering a square shaped drainage system, the equation becomes

$$\mathbf{k\_1}\mathbf{1}\left(\mathbf{W\_r} + \mathbf{W\_t}\right) = \mathbf{k\_2}\mathbf{3}\text{ W\_t K}$$

OR,

$$\mathbf{W\_{t} = k\_{1} \mathbf{1}} \; \mathbf{W\_{r}/(\mathbf{3} \; \mathbf{k\_{2}} \; \mathbf{K} \mathbf{T}^{n} \mathbf{-} \mathbf{k\_{1} \mathbf{1}})} \tag{6}$$

Where Wt = theoretical width of the square drain, 1 = rainfall intensity, Wr = design road width, k1, k2 = coefficients representing losses, generally <1, T = time factor, n = standing time of water pool, K = hydraulic conductivity of in-situ soil.

If the rate at which water flows into the drain is assumed to be the same as the rate it infiltrates into the adjacent soil (outflow from the drain), the water standing time, n will be zero i.e. n = 0, and T = 1. Hence Eq. (6) reduces to,

$$\mathbf{W\_{t} = k\_{1} \mathbf{1}} \,\mathrm{W\_{r}/(\mathbf{3 k\_{2}} \,\mathrm{K-k\_{1} \mathbf{1})} \tag{7}$$

However, the factors T, k1, k2 are site dependent and can be established empirically. Ideally, where there are no water losses through evaporation or evapotranspiration, k1 = k2 = 1

$$\mathbf{W\_t = 1 \ W\_r/(\Im \mathcal{K} - \mathbf{1})} \tag{8}$$

Wt is apparently the hypothetical width of the drain and is related to the effective design width, Wd by

$$\mathbf{W\_t = W\_d \ \eta} \tag{9}$$

Where η is effective area factor of the backfill and it is the same as its porosity [12]. By substituting Eq. (9) into Eq. (8)

$$\mathbf{W\_{d}} = \mathbf{1} \,\, \mathbf{W\_{r}}/(\boldsymbol{\eta} \,\, (\mathbf{3} \,\, \mathbf{K-1})) \tag{10}$$

#### **6.2 Design considerations**

In the design of the trenchless drainage system specific components are considered. They include the dimensions of the drain, backfill materials, grassing and gang way to user housing.

**Dimensioning.** The dimension of the drain is dependent upon a number of variables which include rainfall intensity, size and profile of the road, the porosity of the backfill and the hydraulic conductivity of subgrade soil [2, 10, 11]. Consequently for a square drain configuration,

$$\mathbf{W\_{d}} = \mathbf{1} \,\, \mathbf{W\_{r}}/(\boldsymbol{\eta} \,\, (\mathbf{3} \,\, \mathbf{K-1})) \tag{11}$$

Where Wd = design width/depth of the drain, cm, I = rainfall intensity, cm/sec, Wr = width of the road, η = porosity of the backfill, K = permeability/hydraulic conductivity of the in-situ soil.

For a square drain, in cross section, the **width (**Wd) is the same as the depth, and the infiltration surface can be taken to be 3Wd. The infiltration surface of the drain is its perimeter short of the upper width of the drain.

If a rectangular channel is to be considered the same infiltration surface determined by Eq. (10) will be used in its dimensioning. In such a case,

$$\mathbf{2d} + \mathbf{w} = \mathbf{3W\_d} \tag{12}$$

Where d is the depth of the rectangular channel and w is its width. For an example:


That means, the dimension of the rectangular drain, in cross section, will be 1.2 m x 1.65 m as against 1.5 m x 1.5 m for a square drain of the same infiltration capacity when fully mobilized.

The **rainfall intensity** to be used in the design shall represent a peak condition of at least 10 years return period. This creates room for an optimal design since rainfall is the subject of control in this scenario. Rainfall data from nearest, asymptotic and reliable meteorological station is appropriate.

The **width of the road surface (**Wr) is measured on site or taken from the construction drawing. If the road is cambered the road wash will flow unto both sides of the road from its centre line, supplying runoff to the drains on both sides. Thus, Wr that could be used in Eq. (10) will be half of the actual design width of the road to be drained.

The value of the **porosity** (η) of the backfill to be applied in the Eq. (10) could be obtained from laboratory analysis of representative samples using standard methods. Typical laboratory results from various soil types obtained in course of research [10, 11] are presented in **Table 1**.

The in-situ soil **permeability**, (K) can be obtained from the field using standardized methods [8, 9]. The measurement can be conducted on a number of locations on the right-of-way of the proposed road project. Measurements can also take place when the subgrade of the road pavement has been prepared. The choice is based on site conditions, construction philosophy and/or judgment of the drainage engineer. The in-situ soil properties could be determined to aid in the soil classification. Results obtained on a similar exercise are shown in **Table 1**.
