RE Wall Foundation – Geotechnical Assessment Report

Standalone Engineering Tool • Layered ground, bearing, stress distribution, settlement & SPT interpretation

RE Wall / Loading

Soil Profile

SPT / Sand Parameters

Actions

Key Results Summary

Stress Distribution

Stress Distribution Plot

Bearing Capacity Screening

Settlement Assessment

SPT / Strength Interpretation

Engineering Flags & Status

Important Limitations

This tool is a preliminary calculation aid and does not replace site-specific geotechnical investigations or certified supplier structural designs.

Theoretical Background & Formulations: RE Wall Foundation Assessment

This technical document details the engineering principles, mechanics, and empirical correlations implemented in the Reinforced Earth (RE) Wall Foundation Geotechnical Assessment Tool. The calculations cover foundation pressure distribution, bearing capacity evaluation, stress attenuation through soil layers, elastic settlement analysis, and Standard Penetration Test (SPT) data processing.

1. Reinforced Earth Wall Loading & Base Mechanics

Mechanically Stabilized Earth (MSE) / Reinforced Earth (RE) structures impose combined vertical gravity loads and overturning moments on the underlying foundation soil.

1.1 Total Vertical Force ($V_v$) & Average Pressure ($q_{\text{avg}}$)

If not directly overridden by structural analysis inputs, the total vertical force per meter run ($V_v$) is derived from the self-weight of the RE fill block plus external surcharge:

$$V_v = (H \cdot B \cdot \gamma) + (q_{\text{surcharge}} \cdot B)$$

The uniformly distributed average foundation pressure across the width ($B$) is:

$$q_{\text{avg}} = \frac{V_v}{B}$$

1.2 Foundation Eccentricity ($e$) & Contact Pressures

Overturning moments ($M$) acting about the center of the base shift the location of the vertical resultant. The eccentricity ($e$) is calculated as:

$$e = \frac{M}{V_v}$$

Assuming a rigid base and linear contact pressure distribution across the soil interface, maximum ($q_{\text{max}}$) and minimum ($q_{\text{min}}$) contact pressures are obtained via the standard elastic boundary equations:

$$q_{\text{max}} = q_{\text{avg}} \left( 1 + \frac{6|e|}{B} \right)$$
$$q_{\text{min}} = q_{\text{avg}} \left( 1 - \frac{6|e|}{B} \right)$$
The Middle-Third Rule: If $|e| > \frac{B}{6}$, $q_{\text{min}}$ becomes negative. Because soil cannot resist tension, loss of base contact occurs, triggering an engineering warning.

2. Bearing Capacity Analysis

Ultimate bearing capacity is determined using Terzaghi's classical bearing capacity theory formulated for continuous strip footings ($L \gg B$).

2.1 Terzaghi Bearing Capacity Equation

$$q_{\text{ult}} = c' N_c + \gamma_1 D_f N_q + 0.5 \gamma_1 B N_\gamma$$

Where the non-dimensional bearing capacity factors ($N_q, N_c, N_\gamma$) depend exclusively on the effective internal friction angle ($\phi'$) of the upper bearing layer:

$$N_q = e^{\pi \tan\phi'} \tan^2\left(\frac{\pi}{4} + \frac{\phi'}{2}\right)$$
$$N_c = \frac{N_q - 1}{\tan\phi'} \quad \text{(for } \phi' > 0\text{)}$$
$$N_\gamma = 2(N_q + 1)\tan\phi'$$

2.2 Allowable Bearing Pressure ($q_{\text{allow}}$) & Factor of Safety ($FS$)

Applying a global Factor of Safety of $3.0$ against ultimate failure:

$$q_{\text{allow}} = \frac{q_{\text{ult}}}{3.0}$$

The overall factor of safety against the maximum edge contact stress is evaluated as:

$$FS_{\text{bearing}} = \frac{q_{\text{ult}}}{q_{\text{max}}}$$

3. Stress Attenuation with Depth (2:1 Method)

Vertical stress dissipates as depth below the wall base increases. The tool utilizes the semi-empirical 2:1 (Vertical to Horizontal) Load Spreading Model to compute additional vertical stress ($\Delta\sigma_z$) at any depth $z$:

$$\Delta\sigma_z = q_{\text{avg}} \left( \frac{B}{B + 2z} \right)$$

For any soil layer bounded between top depth $z_{\text{top}}$ and bottom depth $z_{\text{bot}}$, the representative vertical stress increase ($\Delta\sigma_{\text{avg}}$) is taken as the numerical average of the boundary stresses:

$$\Delta\sigma_{\text{avg}} = \frac{\Delta\sigma(z_{\text{top}}) + \Delta\sigma(z_{\text{bot}})}{2}$$

4. Elastic Settlement Calculation

Subgrade settlement is evaluated for each soil layer using Hooke’s Law for 1D vertical deformation.

4.1 Layer Elastic Settlement ($S_i$)

$$S_i = \left( \frac{\Delta\sigma_{\text{avg}}}{E_i \cdot 1000} \right) \cdot t_i \cdot 1000 \quad \text{[mm]}$$

Where:

  • $\Delta\sigma_{\text{avg}}$ = Average incremental vertical stress in the layer ($\text{kPa}$)
  • $E_i$ = Elastic / Constrained Modulus of layer $i$ ($\text{MPa}$)
  • $t_i$ = Layer thickness ($\text{m}$)

4.2 Total Cumulative Settlement ($S_{\text{total}}$)

Summing settlements across all non-rock soil layers gives:

$$S_{\text{total}} = \sum_{i=1}^{N_{\text{layers}}} S_i \quad \text{(excluding competent rock strata)}$$

5. Standard Penetration Test (SPT) Corrections & Correlations

5.1 Energy-Corrected Blow Count ($N_{60}$)

Field SPT blow counts ($N_{\text{field}}$) are normalized to an $60\%$ energy efficiency ratio:

$$N_{60} = N_{\text{field}} \cdot C_E \cdot C_B \cdot C_S$$

5.2 Overburden-Corrected Blow Count ($N_{1(60)}$)

Corrected for effective overburden stress using the normalization factor $C_N$:

$$N_{1(60)} = N_{60} \cdot C_N$$

5.3 Empirical Friction Angle ($\phi'$) Correlation

For granular soil deposits, effective friction angle ($\phi'$) is estimated using a empirical relationship bounded between $26^\circ$ and $36^\circ$:

$$\phi' = \min\left(36^\circ, \, \max\left(26^\circ, \, 28^\circ + 0.28 \cdot \max(0, N_{1(60)} - 5)\right)\right)$$

6. Automated Engineering Screening Criteria

Engineering Check Trigger Logic / Condition Status Flag
Bearing Capacity Failure $q_{\text{max}} > q_{\text{allow}}$ ACTION REQUIRED
Low Bearing Margin $1.0 \le FS_{\text{bearing}} < 3.0$ CAUTION
Base Tension $|e| > \frac{B}{6}$ ACTION REQUIRED
Excess Settlement $S_{\text{total}} > S_{\text{permissible}}$ ACTION REQUIRED
Liquefaction Potential Saturated Sand stratum with $N_{1(60)} < 20$ CAUTION
Soft/Loose Subgrade $N_{1(60)} < 10$ ACTION REQUIRED