Estimating Slope Stability Reduction due to Rain

Infiltration Mounding

BY

SUVADEEP DALAL

DEPARTMENT OF CIVIL ENGINEERING

IIT KHARAGPUR, KHARAGPUR

MARCH 2012

Mounding Problem

Fig.1: Schematic of the saturation mound

Mounding Problem

Heavy rainfall↓

Saturation of earth slope ↓

Reduction in stability (Mounding)

Purpose

To estimate the possible importance of mounding in reducing stability

Problem Variables

The size and geometry of the slope.The coefficient of permeability and its anisotropy.The rainfall intensity, duration, and sequencing.The location of the nearest horizontal

impermeable or permeable layer.The seepage effect of the mound and its negative

effect on downslope stability.

Phreatic Line Position Analysis

Considering the mounding problem as the reverse of the transient seepage sudden drawdown problem.

Extensive use of the approximate full and partial drawdown analysis presented by Newlin and Rossier.

Accumulation = Negative drainage.Relative mounding = M = 1-U, U = Relative drainage.Equivalent triangle approximation for drainage analysis &

trapezoidal approximation for stability analysis.Includes the effects of anisotropy.

1. k = (khkv)

2. f = (kh/kv)

Fig. 2: Trapezoidal approximation

Equivalent Triangle, TransientDrainage analysis method used by Newlin

and Rossier 3. U = (P – h)/P = {(P – hm)/P}2

4.

5.

Fig. 3: Newlin and Rossier (1967) transient drainage analysisMethod: Notation

Fig. 4: Newlin and Rossier (1967) transient drainage analysisMethod: Transient Drainage Specification

Caution against using Newlin and Rossier equations

U = 0.03 to 0.76, or M=0.97 to 0.24m = 2 to 3

Schmertmann assumed Eqs. 4 and 5 valid for all U and m.

6(a).

6(b). P = P’ + z

6(c). H = H’ + z

7.

Fig. 3: Newlin and Rossier (1967) transient drainage analysisMethod: Notation

Equilibrium rainfall infiltration rate(Re)

Solved for a reference slope withEquivalent isotropic permeability (kr) = 10−3 mm/ sTransformation factor (f) = 1slope m=1depths to the nearest horizontal impermeable layer,

D/H=0–0.8

Table. 1: Me versus Log of Re for Reference Slope

8.

9.

10.

11.

Rianfall Infiltration and Delay

Qmax = 1, Qmin = 0. Qavg = ½No swelling or shrinking of the slope.Rainfall infiltrates until reaching a max value

iv*kv.

12. Time delay =

Fig. 2: Trapezoidal approximation

Mound Seepage and Reduced Downslope Stability

Fig. 5: Using Morgenstern 1963 to estimate ΔF/Fo due to sudden drawdown and mounding: notations

Mound Seepage and Reduced Downslope Stability

Morgenstern produced a chart for F versus L/H for slopes (m) from 2 to 5, φ’=20–40°, and c /H=0.0125–0.050.

Schmertmann gave (− Δ F/F0) versus (L/H) results Using different combinations of L/H from 0 to 1, (c’ /ϒHtan φ) from 0.02 to 0.12, and m from 2 to 5.

Δ F = F - F0

13.

Fig. 5: Using Morgenstern (1963) to estimate ΔF/Fo due to sudden drawdown and mounding: fitting eqn 13 through results of author’s

parametric study of Morgenstern’s charts

Mound Seepage and Reduced Downslope Stability

Mound Seepage and Reduced Downslope Stability

14.

Separating the mounding effect from the combined steady

state plus mounding effects15. Uss+md = Uss * Umd

An Example:

Let Uss=0.60 and Umd=0.083

So, Uss+md = 0.60 * 0.083 = 0.05

M = 1 – 0.05 = 0.95

So, ΔF/F0=−0.30 (from graph or equation 13)

Fig. 2: Trapezoidal approximation

Fig. 5: Using Morgenstern (1963) to estimate ΔF/Fo due to sudden drawdown and mounding: estimating ΔF/Fo due to mounding

The effect of the location of the nearest horizontal impermeable or permeable layer.

Perfectly vertical drainage has no stability effect in a purely frictional soil and assumed for all soils.

ΔF/Fo is proportional to the percent of Re due to lateral flow.

If ΔF/Fo=−0.30 but lateral drainage equals only 50% of the total, then Δ F/F0 “drops” to −0.15.

Table. 2: Approximate Percent of Total Re due to Mound LateralDrainage with Permeable Horizontal Boundary Layer at all M

Fig. 2: location of the nearest horizontal impermeable or permeable layer and downslope stability

Steps for calculating ΔF/Fo

1. For a given slope select the values of P, ne, H, D, k, f, m, and QR versus time t.

2. Calculate Re from Eq. 8 after assuming an incremental M, starting from Mo=0. Then the average M over the first ΔM increment = (Mo + ΔM)/2. Obtain Re by linear interpolation in Table 1.

3. The ∑Δt values need to include the extra delay time δt whenever QR changes significantly. Use Eq. 12 for an estimate of each delay time.

Steps for calculating ΔF/Fo

4. Use Eq. 11 and the above Re’ to calculate a Δt time increment

5. Select another M and repeat Steps 2 and 3 to get the next increment of Δt to add to the current ∑Δt.

continue until QR changes, the ∑Δt reaches a desired value, or M approaches an asymptotic value Me.

6. Use Eqs. 13 and 14 or Fig. 5 with the applicable M values to make an estimate of the relative slope stability reduction due to mound formation.

Case History

In a recent publication, Blatz et al. 2004, details a case history.

Complete mounding (M = 1) & slope failure following an extreme rainfall event 30 years after construction.

Pre-failure F = 2.0–2.2 & post-failure F = 1.04According to Eqs. 13 and 14, or Fig.5 : Reduced

F=0.90–0.99 (simulate the case history).

Conclusions

1. Mounding can reduce stability 10% in some cases and 50% in special cases;

2. A permeable underlayer can greatly reduce the likelihood of significant mounding;

3. Soils within the effective permeability range of k=10−2–10−4 mm/ s can mound significantly. Above 10−2 they drain too quickly. Below 10−4 the mound may take too long to form;

4. Low mounds M(=0.4) have a negligible instability effect.

5. Higher mounds have a progressively greater effect with approximately 80% of the total effect occurring between M=0.75 and 1.0;

6. The details of rainfall rates, duration, and sequencing can have an important effect.

7. There exists a significant delay time between rainfall and resulting changes in the mound. It varies from hours to years;

8. Many variables affect mounding, making it difficult to evaluate by “engineering judgment.” Such judgment might improve with the application of the methods and findings presented in this paper.

ReferencesSchmertmann, J.H. 2006. “Estimating slope

stability reduction due to rain infiltration mounding”. Journal of Geotechnical and Geoenvironmental Engineering 132(9):1219–1228.

Newlin, C. W., and Rossier, S. C. 1967. “Embankment drainage after instantaneous drawdown.” J. Soil Mech. Found. Div., 936, 79–95.

Morgenstern, N. 1963. “Stability charts for earth slopes during rapid drawdown.” Geotechnique, 132, 121–131.

Blatz, J. A., Ferreira, N. J., and Graham, J. 2004. “Effects of near-surface environmental conditions on instability of an unsaturated soil slope.” Can. Geotech. J., 41, 1111–1126.