CELE Geotechnical Engineering — Stresses in Soil MassSummary

Effective stress is the stress transmitted directly through the soil skeleton (grain-to-grain contact) and is calculated as σ' = σ − u, where σ is total stress and u is pore water pressure. It is the effective stress that controls shear strength, compressibility, and all mechanical properties of soil. For example, in Example 1 of the reference, at 5 m depth with a water table at 3 m, the total stress is 94 kPa but pore pressure is 19.62 kPa, so effective stress is only 74.4 kPa. This distinction is crucial: two soil elements with the same total stress but different pore pressures have different strengths.

Total stress at depth z is the sum of the weight of all soil layers above that point: σ = Σ γᵢ zᵢ. Above the water table, use the moist (or dry) unit weight γ; below the water table, use the saturated unit weight γₛₐₜ. For a single layer: σ = γ·z. Example: a 3 m clay layer with γ = 18 kN/m³ and a 2 m saturated sand with γₛₐₜ = 20 kN/m³ above 5 m depth gives σ = 18(3) + 20(2) = 94 kPa. Total stress increases linearly with depth within a homogeneous layer but changes slope when layers change.

Pore water pressure is the pressure exerted by water filling the void spaces in soil. In static (hydrostatic) conditions, u = γ_w · z_w, where γ_w ≈ 9.81 kN/m³ (or 10 kN/m³ for approximation) and z_w is the depth below the water table. Example: at 2 m below a water table, u = 9.81 × 2 = 19.62 kPa ≈ 20 kPa. Above the water table, pore pressure is zero (or negative in unsaturated soil, but assume u = 0 for drained analysis). Under seepage conditions (upward or downward flow), add the seepage pressure to modify u.

For a concentrated load Q applied at the surface, the vertical stress increase Δσ at depth z and horizontal distance r from the load axis is: Δσ = [3Q / (2π z²)] · [1 / (1 + (r/z)²)^(5/2)]. Directly below the load (r = 0): Δσ = 3Q / (2π z²). The stress spreads with depth; at large r or large z, the increment becomes negligible. Example 3 in the reference: Q = 100 kN, z = 2 m, r = 0 gives Δσ = 3(100) / (2π·4) = 300 / 25.13 ≈ 11.9 kPa. This assumes an elastic, isotropic half-space.

A practical simplified method for rectangular footings: the load Q spreads outward at a 2 vertical : 1 horizontal slope, so the base area increases from B × L to (B + z) × (L + z) at depth z. The average stress increase is Δσ = Q / [(B + z)(L + z)]. Example 2: a 2 × 2 m footing with Q = 800 kN at z = 3 m gives Δσ = 800 / (5 × 5) = 32 kPa. This method is quicker than Boussinesq for footings and reasonably accurate (error ≈ 10%) for typical footing depths.

The location of the water table fundamentally changes the stress profile. Above the water table, all stress is effective (u = 0, so σ' = σ). Below the water table, u > 0 and σ' = σ − u is reduced. A rising or falling water table causes σ' to decrease or increase correspondingly. Building a profile requires: (1) identify layer depths and unit weights, (2) locate water table, (3) compute σ at each depth, (4) compute u below water table, (5) compute σ' = σ − u. Example 1 shows this step-by-step.

When water flows through soil (e.g., upward from an aquifer toward the surface), it exerts a drag force (seepage pressure, h_s) that adds to pore pressure: u_total = γ_w · z_w + seepage pressure. This reduces effective stress. At the critical condition where upward seepage pressure equals the submerged weight of overlying soil, effective stress becomes zero and the soil loses shear strength — entering the 'quick' or 'boiling' condition. This is dangerous in excavations near rivers or under dams with seepage. The seepage pressure gradient i = Δh / Δz (hydraulic gradient) quantifies the flow intensity.

For distributed loads (rectangular, circular, or strip areas), vertical stress increase at any point is computed using dimensionless influence factors (I values) from charts or formulas: Δσ = I · q, where q is the contact pressure (load / area). Newmark's chart is a classical method for combining rectangular zones. Influence factors depend on depth (z), position relative to the loaded area, and shape. Different factors apply for stress directly beneath the center, at the corner, or outside the loaded area.

Real sites rarely consist of a single soil layer. Stress calculations must account for changes in unit weight at layer boundaries. Total stress is computed cumulatively: σ_at_depth = σ_at_top_of_layer + Σ(γᵢ · thickness_i) for all layers above. Each layer uses its own unit weight (moist above water table; saturated below). Pore pressure is independent of layers — it depends only on depth below the water table. Example 1 demonstrates: 3 m of clay (γ = 18) plus 2 m of sand (γ_sat = 20) above the 5 m point.

Total stress at depth depends entirely on the cumulative weight of layers above. Changes in layer thickness or unit weight change σ. Doubling the thickness of a layer doubles its contribution to stress.

Pore pressure increases linearly below the water table (u = γ_w · z_w). Raising the water table increases u at any given elevation, reducing σ'. Lowering the table decreases u, increasing σ'.

Effective stress is the residual after pore pressure is subtracted from total stress: σ' = σ − u. If u increases (due to rising water table or seepage), σ' decreases; if u decreases, σ' increases. Both σ and u contribute.

Boussinesq and 2:1 methods show that Δσ decreases with depth (z) and horizontal distance (r). A deeper point or a farther point experiences less stress increase from the same surface load.

Quick condition occurs when seepage pressure (due to upward flow) equals the submerged weight of overlying soil, making σ' ≈ 0. High pore pressure from flow reduces effective stress to the point of instability.

The stress increase from a footing (computed via Boussinesq or 2:1 method) is superimposed on the in-situ effective stress. The total effective stress in the foundation soil determines bearing capacity and settlement. Accurate stress distribution is essential for safe foundation design per NSCP 2015.

Soil settlement is governed by changes in effective stress, not total stress. An increase in Δσ causes consolidation (if clay) or elastic compression (if sand). The magnitude and history of σ' determine compressibility.

An engineer designs a reinforced concrete footing (NSCP 2015) for a building column in Manila clay. The site investigation shows 2 m of soft clay (γ = 17 kN/m³), then 3 m of dense sand (γ_sat = 20 kN/m³), with the water table at 3 m depth. At the footing depth (say, 2 m), total stress is σ = 17(2) = 34 kPa, and pore pressure is zero (above water table), so σ' = 34 kPa. The applied footing pressure creates Δσ via the 2:1 method. The engineer checks that the effective stress beneath the footing does not exceed the bearing capacity (typically 100–200 kPa for Manila clay, depending on consolidation state). Settlement is computed from the stress increase and the clay's compression index, using effective stress change Δσ'.

A cutting is excavated in a slope. The slope's factor of safety against sliding depends on the effective stress within the slope: F = (c' + σ'·tan φ') / τ. If the water table rises during the rainy season, u increases and σ' decreases. This immediately lowers the shear strength, potentially reducing F below 1.0 and triggering failure. An engineer models the slope stability using a limit-equilibrium method, computing σ' profiles with and without the elevated water table, to determine the critical condition. Drainage (weeping tiles, berms) increases σ' and improves stability.

A bored pile (or driven pile) extends 30 m into a sand-clay sequence. At each depth, the bearing capacity of the pile soil contact depends on the effective stress in that layer. A Boussinesq point-load calculation (or similar) estimates the stress around the pile shaft, contributing to skin friction. Pore pressure in clay layers (especially after installation, if pore pressures are elevated) reduces effective stress and lowers skin friction. The engineer must account for both the tip bearing (in the bearing stratum) and shaft friction (distributed over depth), each governed by effective stress.

A basement excavation in Makati intersects the water table. If dewatering pumps lower the water table within the excavation, a steep hydraulic gradient develops across a sheet-pile wall or braced cut. Seepage toward the excavation raises pore pressure on the outside. If the seepage pressure exceeds the submerged weight of soil outside the wall (i.e., σ' → 0), piping can occur: soil flows, liquefies, and the wall fails. Engineers check the exit gradient (head loss / flow path length) and ensure it remains below a critical value (typically 0.5–1.0 for sand, varying by soil type). This is a direct application of effective stress and seepage mechanics.

During a geotechnical site investigation, a borehole encounters a loose sand layer with a rising water table. A field test (or calculation) indicates that the pore pressure (from hydrostatic + seepage) is high. At the quicksand limit, σ' ≈ 0 and the sand offers no strength. A drilled caisson or diaphragm wall in such a zone must be designed with special care: the slurry support pressure (in slurry trench construction) or the mud density must exceed the in-situ pore pressure to prevent 'blowout' of the sand. This scenario is common in deltaic environments like the Mekong Delta and Philippine floodplains.

An earth dam or tailings embankment is built on a saturated foundation. The weight of the embankment increases σ at depth, but immediately after construction, pore pressures may not have fully dissipated ('undrained' condition). The effective stress σ' is reduced due to high u, weakening the foundation and increasing the risk of failure. Over time, as water drains from the pores (consolidation), u decreases and σ' increases, restoring strength. Engineers use piezometers to monitor pore pressure during and after construction, and finite-element or infinite-slope stability analyses using effective stress parameters (c', φ') to assess safety factors.

An offshore platform in the Philippine Sea experiences wave loading and self-weight. The foundation consists of piles driven into soft marine clay and sand. Seawater pressure at depth is u_water = γ_w · depth_below_surface. The pore pressure in the soil is initially hydrostatic, equal to u_water at the mud line plus the weight of the water–soil column. When the platform loads the soil, the stress increase Δσ is superimposed, but pore pressures may lag behind, creating an 'excess' pore pressure. Over months (consolidation), excess pores dissipate. The effective stress history and consolidation behavior govern the foundation's stability and the long-term settlement.

Loose saturated sand near Manila Bay or Laguna de Bay is susceptible to liquefaction during earthquakes. Under strong shaking, pore pressures spike due to cyclic loading, and effective stress can approach zero. The sand loses all shear strength and behaves like a fluid. Structures founded on such deposits may sink or tilt. Mitigation includes densification (stone columns, vibroflotation) to increase effective stress at depth, or installing drains to dissipate excess pore pressures rapidly. Site characterization (CPT profiles, pore-pressure measurements) and seismic effective-stress analysis per modern standards (e.g., ASCE 41) are essential.