Bearing Pressure Assessment of Shallow Foundation on Coal Mine Overburden Dump with Spatial Variability Considerations

Abstract

This study presents a comprehensive approach to estimate allowable bearing pressure for overburden dump sites in open-cast coal mines by applying analytical and numerical methods, considering diverse data sources, and incorporating probabilistic analysis. In this regard, two dump sites from existing literature were chosen for analysis. Analytical assessment of allowable bearing pressure utilized various data sources, including Standard Penetration Test data, Multichannel Analysis of Surface Wave (MASW) data, plate load test results, and relevant laboratory findings. Additionally, deterministic finite element analysis, incorporating in situ material property profiles, and probabilistic analysis using random field theory and Monte Carlo simulations to model spatial variability in the dump soil matrix were performed.

The results indicate that plate load test data provided the highest allowable bearing pressure, while MASW data yielded conservative results. Deterministic numerical analysis outcomes aligned with analytical approaches, but probabilistic analysis resulted in greater bearing pressure values than deterministic numerical analysis. The generated failure patterns further support the study's objectives.

Appendix 1

a. Calculation of Bearing Pressure from SPT-N Number

From Fig. 2, for (S1B1), the SPT-N number at 4 m depth is taken as 8. Using Teng’s[16] equation, allowable bearing pressure can be calculated as follows:

$$q_{np} = 1.4\left( {N - 3} \right)\left[ {\frac{B + 0.3}{{2B}}} \right]^{2} W_{\gamma } R_{d} s$$

where N = SPT-N number, B = width of footing, s = the allowable settlement (25 mm) and W_γ= water table correction factor, R_d = the depth correction factor. Hence, for a 1m × 1m plate,

$$q_{np} = 1.4 \times \left( {8 - 3} \right) \times \left[ {\frac{1 + 0.3}{{2 \times 1}}} \right]^{2} \times 1 \times 25 = {\mathbf{73.93}} \,{\mathbf{ kPa}}$$

Similarly, for a 10m × 10m raft,

$$q_{np} = 1.4 \times \left( {8 - 3} \right) \times \left[ {\frac{10 + 0.3}{{2 \times 10}}} \right]^{2} \times 1 \times 25 = {\mathbf{46}}{\mathbf{.4}}\,{\mathbf{kPa}}$$

Allowable bearing pressure at each depth is calculated as above, and a mean value of 155.27 kPa and 110 kPa is obtained for the plate and raft, respectively.

b. Calculation of Allowable Bearing Pressure from MASW Data

Shear wave velocities within the zone of influence, i.e., 2B, are considered. For location 2 of Site 1(S1L2), for a 1m × 1m plate, averaged shear wave velocity up to 2 m is 148 m/s and unit weight, γ = 17.85 kN/m³. Tezcan’s[19] equation for allowable bearing pressure is given as follows:

$$q_{np} = 0.025\gamma V_{s} \beta$$

where V_s = Shear wave velocity (m/s), γ = Unit weight of soil, β = Correction factor for foundation width; β = 1 for 0.0 ≤ B ≤ 1.20 m, β = 0.83–0.01B for 3.0 ≤ B ≤ 12.0 m.

For a 1m × 1m plate,

$$q_{np} = 0.025 \times 17.85 \times 148 \times 1 = {\mathbf{66}}{\mathbf{.04}}\,{\mathbf{kPa}}$$

Similarly, for a 10m × 10m raft, averaged shear wave velocity up to 20m is 170 m/s. Hence,

$$q_{np} = 0.025 \times 17.85 \times 170 \times 0.73 = 55.38\,{\mathbf{kPa}}$$

c. Calculation of Net Safe Bearing Capacity from Laboratory Test Results

Laboratory tests on soil samples collected from Site 2 resulted in γ_d = 18.9 kN/m³, OMC = 11.2%, and ϕ = 35°. The bulk unit weight (γ), calculated from the above data is 21.02 kN/m³.

Meyerhof’s equation for ultimate bearing capacity is given as follows:

$$q_{u} = cN_{c} s_{c} d_{c} i_{c} + qN_{q} s_{q} d_{q} i_{q} + 0.5\gamma BN_{\gamma } s_{\gamma } d_{\gamma } i_{\gamma }$$

where s_c,s_q,s_γ are shape factors, d_c,d_q,d_γ are depth factors, and i_c,i_q,i_γ are inclination factors. For more information on the shape, depth, and inclination factors, refer to Meyerhof [20].

Since a surface footing is considered and cohesion is found to be negligible,

$$q_{u} = 0.5\gamma BN_{\gamma } s_{\gamma } d_{\gamma } i_{\gamma }$$

Meyerhof’s bearing capacity factor, N_γ = 37.75.

Shape factor, ${s}_{\gamma }=1+0.1{{\text{tan}}\left[45+\frac{\phi }{2}\right]}^{2}\frac{B}{L}=1.369$

Depth factor and inclination factors are taken as unity. Hence, the ultimate bearing capacity for a 1m × 1m plate, as per Meyerhof’s expression, is as follows:

$$q_{u} = 0.5 \times 21.02 \times 1 \times 37.75 \times 1.369 \times 1 \times 1 = 543.07\,{\text{kPa}}$$

Applying a factor of safety of 3;

$$q_{ns} = \frac{543.07}{3} = {\mathbf{181}}\,{\mathbf{kPa}}$$

Similarly, for a 10m × 10m raft,

$$q_{ns} = 1810\,{\mathbf{kPa}}$$