Depth of Significant Consolidation Pressure underlying Highway Embankment

The construction highway embankments may be needed on soft or very loose natural subsoil extended to a great depth. The assessment for bearing capacity and settlement of subsoil is subjected to the depth of stressed zone extended into the underlying poor subsoil. The significantly stressed depth of subsoil as a multiplication of embankment height was evaluated in [1] for 70% consolidation pressure. As extension of that research significantly stressed depth of subsoil as a multiplication of embankment height was evaluated through current study for full consolidation pressure. In this research, simplified ratios of embankment height to major influence depth or significant stressed zone are determined for different depths and crest widths of embankment.

Embankment Pressure at top of subsoil or at embankment bottom level is termed a_s q_e =γ eHe which is considered to be distributed as per Figure 1 [2].

Consolidation Pressure at Hs depth of subsoil below center of embankment [3],

where, Hs = Depth of Subsoil underlying embankment, γ_e = Bulk Unit weight of embankment fill, B_t = Width of embankment top.

And in equation (1)

the distance between stressed point and end of embankment top=B_t/2

Now, for Consolidation Pressure at H_s depth of subsoil below the end of embankment top (replacing B_t/2 by 0),

Considering the distance between stressed point and end of embankment top=0 in equation (2) –

Average Consolidation Pressure at Hs depth below the embankment,

where, 0 Δ_σ =Consolidation Pressure at H_s depth below center of embankment and 1 Δ_σ =Consolidation Pressure at H_s depth below edge of embankment top.

In Bangladesh the range of width carriage way is 3.0m to 22.0m [2]. The range of crest width including shoulder, verge and median is 5.0m to 30.0m. For 4 Lane and expressway the range of crest width may be 30m to 40m (Figure 1).

In this study the range of crest width (at top level of embankment) is kept between 5m and 50m. The range of embankment height 1.0m to 12.0m and side slope of embankment 1:2 are taken for analysis.

As recommended by [4] the depth of 20% of the foundation contact pressure is significant stressed zone for settlement analysis termed as the significant depth Ds. Terzaghi’s suggestion was based on his finding that direct stresses are regarded as negligible if they account for less than 20% of the applied stress.

Consolidation settling of the subsoil underlying the highway embankment will take place for embankment pressure or selfweight produced pressure. Consolidation Pressure (Δσ) is derived from only Embankment Pressure (qe). The transfer of embankment pressure is significant for assessment of consolidation settlement.

So that, significant stressed zones for Highway Embankment are analyzed accounting full Consolidation Pressure (Δσ) at Hs depth due self-weight induced pressure of embankment.

Now, Consolidation Pressure at Hs depth,

The values of the stress transfer ratio Δσ/q_e are calculated for different value of He, Be and Hs. Change of Δσ/q_e for different Depth Ratio H_s/H_e are presented in Chart-1 to Chart-5 for range of Bt =5m to 50m and range of H_e=1m to 12m.

Significant stressed zone for 20% Stress

Depth Ratio H_s/H_e at Δσ/q_e=0.20for width of Embankment Top, B_t =5m to 50m and height of embankment, He=1m to 12m is presented in Table 1 and in Chart-7.

Depth Ratio H_s/H_e at Δσ/q_e=0.20 at Δσ / qe = 0.20 for width of Embankment Top, Bt =5m to 50m and height of embankment, He=1m to 12m is presented alternately in Chart-6.

According to power trend line of Chart-6, Depth Ratio H_s/H_e for Δσ/q_e =0.2 is termed as (H_s/H_e)_0.2 may be expressed by equation (5) –

Significant stressed zone D_s for reduction of 100% consolidation pressure up to 20% is termed as,

Hence, the Significant stressed zone, D_s,cp may be expressed by equation (7) –

Values of coefficient a and b is given in Table 6.

Approximately simplified values of D_s,cp,20 is given in Table 2 (Table 2).

Table 1:Values of (H_s/H_e)_0.2 for width of B_t =5m to 50m and H_e =1m to 12m.

Table 2:Simplified values of Ds for reduction of consolidation pressure up to 20%.

Significant stressed zone for 30% Stress

The values of Ds for reduction of consolidation pressure up to 20% is too high. From this thought feasible value of Ds are obtained separately for reduction of consolidation pressure up to 30%. Depth Ratio H_s/H_e at / 0.20 e Δσ q = is termed as Δσ/q_e =0.2 for width of Embankment Top, B_t =5m to 50m and height of embankment, H_e=1m to 12m is presented in Table 3 and in Chart-8.

Table 3:Values of (H_s/H_e)_0.3 for width of Bt =5m to 50m and He =1m to 12m.

Depth Ratio H_s/H_e at Δσ / qe = 0.20 for width of Embankment Top, B_t =5m to 50m and height of embankment, H_e=1m to 12m is presented alternately in Chart-9.

According to power trend line of Chart-9, Depth Ratio s H_s/H_e fo rΔσ / qe = 0.20 is termed as (H_s/H_e)_0.3 may be expressed by equation (8) –

Significant stressed zone D_s for reduction of 100% consolidation pressure up to 20% is termed as,

Hence, the Significant stressed zone, D_s,cp may be expressed by equation (13.1) to (13.6) –

Values of coefficient a and b is given in Table 4.
Approximately simplified values of Ds is given in Table 5.

Table 4:Values of coefficient a and b..

Table 5:Simplified values of Ds for reduction of consolidation pressure up to 20%.

The depth of subsoil underlying a highway embankment is identified at which the consolidation pressure is reduced to 20%. This depth is significant stressed zone for Δσ / qe = 0.20 and termed as D_s,cp,20 . Values of D_s,cp,20 are found 4He to 9He for embankment top width 5-10m, 6He to 20He for embankment top width 20-30m and 8He to 30He for embankment top width 40-50m. These values are too high and indicates influence of highway embankment up to 70-80m for 30m wide embankment. Considering 70-80m of soft or very loose soil in design not to be feasible. Alternately, the depth is also identified at which the consolidation pressure is reduced to 30%. This depth is significant stressed zone for / Δσ qe =0.30 and termed as D_s,cp,30 . Values of D_s,cp,30 are found 2He to 4He for embankment top width 5-10m, 3He to 5.5He for embankment top width 20-30m and 6He to 4He for embankment top width 40-50m. . These values are not too high and indicates influence of highway embankment up to 20-35m for 30m wide embankment. Considering 20-35m of soft or very loose soil in design may be practically feasible.

The author acknowledged the support of the authority of Bangladesh Road Research Laboratory (BRRL), Mirpur, Dhaka, Bangladesh.

The author declares that they have no conflict of interest

1. Ahmed S (2022) The Influence Depth of a Highway Embankment. International Research Journal of Engineering and Technology (IRJET), 9(8).
2. Road Master Plan (2009) Roads and Highways Division (RHD), Bangladesh.
3. Das BM (2011) Foundation Engineering. Chapter-5, 7^th Edition, Global Engineering.
4. Geometric Design Standards Manual (2005) Roads and Highways Division (RHD), Bangladesh, P. 116.
5. Terzaghi K (1936) Opening Discussion on Settlement of Structure. First International Conference on Soil Mechanics and Foundation Engineering, Harvard University, USA.