**7.2 Design method - Giroud et al.**

Giroud et al. [31, 32] presented a method for reinforced slopes using draining geogrid. Transmissivity and length of draining path are important for geogrids from the design point. Typical values of the parameters are: φ 'of 20° to 30°, drained cohesion, c' of 0–20 kPa, coefficient of consolidation, cv of 0.1–100 m<sup>2</sup> / year, and coefficient of compressibility, mv of 0.01–5 m2 /MN. Long term hydraulic transmissivity, θa, of draining geogrid is obtained by applying a set of reduction factors to the laboratory measured value. Reduction factors account for creep, particulate, chemical and biological clogging of drainage channels.

Geometry of reinforced fill is important from design point of view. A drain located at the back of reinforced zone (**Figure 13**) is generally used to prevent groundwater from flowing into the reinforced zone and to halve the drainage length

**27**

separately.

*7.2.1 Parametric study*

*Geoysynthetic Reinforced Embankment Slopes DOI: http://dx.doi.org/10.5772/intechopen.95106*

slope as in conventional practice.

H, overlying draining geogrid.

θ

θ

(T0 = 4Cv.t0/H2

90% in the fill.

and

channel is given by

calculated as under

in the draining geogrid. Design has two main components, viz., (i) determination of required transmissivity of draining geogrid and required time for rapid dissipation of porewater pressure and (ii) determination of stability and settlement of

The maximum porewater pressure in the drainage channel should not be too high nor too low. If the porewater pressure in the drainage channel is too high, vertical flow of water from the fill to the drainage channel will be slowed down, whereas, if the water pressure in the drainage channel is too low, flow of water will be too slow. Solution to this complex problem is presented by Giroud [58]. The rate of maximum vertical flow rate from fill to drainage channel depends on time factor

The following equations for the required transmissivity, θreq, are derived by Giroud [58], assuming that the maximum water pressure in the drainage channel, umax, is 10% of the overburden stress, consistent with a degree of consolidation of

00 0 req 10B k H 5B k if 1x10 6 1 *<sup>v</sup>*

The required transmissivity, θreq, must be less than the allowable transmissivity, θa. Parameter B in the above equation is dependent on length of draining geogrid. In case of draining boundary at the back of the reinforced zone (**Figure 13**) drainage path length is equal to half and in case of non-draining boundary it is equal to full length of reinforcement. The required transmissivity depends on hydraulic gradient in the drainage channel. An approximate value of hydraulic gradient in the drainage

=

where umax is maximum allowable water pressure in drainage channel and is generally taken as 10% of overburden stress. The time required for pore water pressure dissipation is estimated as time required to reach 90% consolidation and is

=

*t*

γ

2 90 <sup>90</sup> 4 *<sup>v</sup> T H*

*C*

where T90 is time factor for 90% consolidation. The parameter B is equal to the length of reinforcement and is obtained as part of stability analysis (Jewell [14]). Alternatively, the geogrid length is selected arbitrarily and stability is checked

Naughton et al. [32] conducted parametric studies to study time for pore pressure dissipation, and required transmissivity of the geogrid. From practical consideration, construction of one layer per day implies about 24 hours for porewater

avg max w i u /B (10)

(11)

2 2

2 2

) and occurs at the end of construction, t0, of fill layer of thickness,

= */ T / Ct* = −≤ ≤ *T* (8)

req = 10B k / HT0 5B k / 2C t if 1x10 6 1 = *<sup>v</sup>* <sup>0</sup> −≤ ≤ *T*<sup>0</sup> (9)

#### **Figure 13.**

*Geometry of reinforced slope with (a) and without drain (b) (after Naughton et al. [32]).*

*Geoysynthetic Reinforced Embankment Slopes DOI: http://dx.doi.org/10.5772/intechopen.95106*

in the draining geogrid. Design has two main components, viz., (i) determination of required transmissivity of draining geogrid and required time for rapid dissipation of porewater pressure and (ii) determination of stability and settlement of slope as in conventional practice.

The maximum porewater pressure in the drainage channel should not be too high nor too low. If the porewater pressure in the drainage channel is too high, vertical flow of water from the fill to the drainage channel will be slowed down, whereas, if the water pressure in the drainage channel is too low, flow of water will be too slow. Solution to this complex problem is presented by Giroud [58]. The rate of maximum vertical flow rate from fill to drainage channel depends on time factor (T0 = 4Cv.t0/H2 ) and occurs at the end of construction, t0, of fill layer of thickness, H, overlying draining geogrid.

The following equations for the required transmissivity, θreq, are derived by Giroud [58], assuming that the maximum water pressure in the drainage channel, umax, is 10% of the overburden stress, consistent with a degree of consolidation of 90% in the fill.

$$
\boldsymbol{\theta}\_{\text{req}} = \mathbf{1} \mathbf{O} \mathbf{B}^2 \mathbf{k} / \mathbf{H} \sqrt{T\_0} = \mathbf{5B}^2 \mathbf{k} / \sqrt{\mathbf{C}\_v t\_0} \text{ if } \mathbf{1x10} - \mathbf{6} \le T\_0 \le \mathbf{1} \tag{8}
$$

and

*Slope Engineering*

pressures.

adequate.

**7.2 Design method - Giroud et al.**

**7.1 Design methods**

draining backfill material is not readily available in close vicinity of the sites. Zornberg and Mitchell [55] and Mitchell and Zornberg [56] evaluated the use and performance of reinforced soil structures constructed with poorly draining and/or cohesive backfills. Permeable reinforcements are particularly appropriate for poorly draining backfills as they facilitate dissipation of excess porewater

Christopher et al. [29] provide design guidance for reinforced soil structures using poorly draining backfills, viz., total stress analysis ignoring the drainage contribution of geocomposite for short term and effective stress analysis considering drainage in the long term. Naughton et al. [30] improved the design method of Christopher et al. [29] and presented single stage effective stress analysis since excess pore pressure gets dissipated fully before construction of subsequent layers. Half meter thickness of each lift is proposed to control short term stability of the slope face. Giroud et al. [32] updated design method of Naughton et al. [30] for reinforced slopes using draining geogrid with focus on an improved determination of the required transmissivity of the same. The method is practical as it makes it possible to optimize the design by adjusting the parameters such as the construction time, time required for pore pressure dissipation, layer thickness and drainage length. Naughton et al. [57] present a parametric study of design parameters of low permeability fill and concluded that for typical compressibility and consolidation parameters vertical spacing of the reinforcement of 0.5 m was

Giroud et al. [31, 32] presented a method for reinforced slopes using draining geogrid. Transmissivity and length of draining path are important for geogrids

drained cohesion, c' of 0–20 kPa, coefficient of consolidation, cv of 0.1–100 m<sup>2</sup>

transmissivity, θa, of draining geogrid is obtained by applying a set of reduction factors to the laboratory measured value. Reduction factors account for creep,

Geometry of reinforced fill is important from design point of view. A drain located at the back of reinforced zone (**Figure 13**) is generally used to prevent groundwater from flowing into the reinforced zone and to halve the drainage length

φ

'of 20° to 30°,

/MN. Long term hydraulic

/

from the design point. Typical values of the parameters are:

particulate, chemical and biological clogging of drainage channels.

*Geometry of reinforced slope with (a) and without drain (b) (after Naughton et al. [32]).*

year, and coefficient of compressibility, mv of 0.01–5 m2

**26**

**Figure 13.**

$$
\boldsymbol{\theta}\_{\text{req}} = \mathbf{10B}^2 \mathbf{k} / \mathbf{H} \mathbf{T} \mathbf{O} = \mathbf{5B}^2 \mathbf{k} / 2 \mathbf{C}\_\flat \mathbf{t}\_0 \text{ if } \mathbf{1x} \mathbf{10} - \boldsymbol{\theta} \le T\_0 \le \mathbf{1} \tag{9}
$$

The required transmissivity, θreq, must be less than the allowable transmissivity, θa. Parameter B in the above equation is dependent on length of draining geogrid. In case of draining boundary at the back of the reinforced zone (**Figure 13**) drainage path length is equal to half and in case of non-draining boundary it is equal to full length of reinforcement. The required transmissivity depends on hydraulic gradient in the drainage channel. An approximate value of hydraulic gradient in the drainage channel is given by

$$\mathbf{i}\_{\text{avg}} = \mathbf{u}\_{\text{max}} \;/\; \mathcal{Y}\_{\text{w}} \mathbf{B} \tag{10}$$

where umax is maximum allowable water pressure in drainage channel and is generally taken as 10% of overburden stress. The time required for pore water pressure dissipation is estimated as time required to reach 90% consolidation and is calculated as under

$$t\_{\mathfrak{H}} = \frac{T\_{\mathfrak{H}}H^2}{4\mathcal{C}\_v} \tag{11}$$

where T90 is time factor for 90% consolidation. The parameter B is equal to the length of reinforcement and is obtained as part of stability analysis (Jewell [14]). Alternatively, the geogrid length is selected arbitrarily and stability is checked separately.

#### *7.2.1 Parametric study*

Naughton et al. [32] conducted parametric studies to study time for pore pressure dissipation, and required transmissivity of the geogrid. From practical consideration, construction of one layer per day implies about 24 hours for porewater pressure dissipation. Studies reveal that this is achievable unless cv is less than 30 m2 /year and vertical spacing is more than 0.5 m. For cv values greater than 50 m2 /year and thickness of fill not exceeding 0.5 m, the dissipation time required reduces to less than 12 hours (**Figure 14**).

For soils with cv up to 50 m2 /year, the unfactored required transmissivity in the draining geogrid is less than 1.2x10−6 m2 /s. As the drainage characteristic of the soil improves, i.e., cv > 75 m2 /year, the required transmissivity increases rapidly by orders of magnitude (**Figure 15**). The required transmissivity also depends on the vertical spacing of the draining geogrid.

Smaller vertical spacings and longer reinforcement lengths require larger transmissivity in the draining geogrid. Reinforcement spacing of 0.5 m optimizes the time for dissipation of pore pressures while, at the same time, requiring realistic and achievable transmissivity in the draining geogrid.

At this spacing a draining geogrid will dissipate pore pressures over the full range of likely values encountered in low permeability fills within 24 hours, with the further advantage that the required transmissivity is independent of reinforcement length. With above spacing, reinforced slope with poorly draining backfill can be analyzed as a normal slope for both internal and external stability for normal ranges of soil parameters.
