Soil Strength, Permeability, and Compressibility

Soil Strength, Permeability, and Compressibility

Choose the time model: The same saturated soil can behave undrained during rapid loading and drained after pore pressures dissipate. Strength and settlement parameters must match that drainage condition.

Total Stress, Pore Pressure, and Effective Stress

For saturated soil, Terzaghi effective stress is

σ' = σ - u,

where σ is total normal stress and u is pore-water pressure. Total stress comes from total unit weight and external loads. Hydrostatic pore pressure is u = γ_w h_w below the water surface. Effective stress is carried by the soil skeleton and governs many drained strength and compressibility relationships.

A useful check below a static water table is that the effective overburden increment equals submerged unit weight times depth. Do not calculate total stress using γ' and then subtract water pressure again; that removes buoyancy twice.

Worked effective stress and drained strength

A 20-ft saturated soil layer begins at the water table. Let γ_sat = 120 pcf, γ_w = 62.4 pcf, and use problem-given drained parameters c' = 0, φ' = 30°. At the base:

σ_v = 120(20) = 2,400 psf,

u = 62.4(20) = 1,248 psf,

and

σ'_v = 2,400 - 1,248 = 1,152 psf.

This also equals (120 - 62.4)(20) = 1,152 psf. The Mohr–Coulomb drained shear-strength expression is

τ_f = c' + σ'_n tanφ'.

Using the vertical effective stress as the stated normal stress for this illustrative plane,

τ_f = 0 + 1,152 tan30° = 665 psf.

This is a drained effective-stress calculation. It cannot be converted into a rapid undrained clay calculation merely by replacing one coefficient.

Drainage and Time

These are reasoning guides, not automatic labels. Compare loading duration with drainage time, permeability, and drainage path. Never combine total normal stress with c',φ', or effective normal stress with an undrained s_u, unless a specified formulation explicitly defines that combination. For a 2026 exam, use the current PE Civil handbook and AASHTO LRFD 8th edition with its May 2018 errata.

Permeability and Seepage

Darcy's law for one-dimensional laminar flow is

Q = kiA,

where k is hydraulic conductivity, i = Δh/L is hydraulic gradient, and A is cross-sectional area normal to flow. If k = 2.0 × 10⁻⁴ ft/min, i = 0.50, and A = 30 ft², then

Q = 2.0 × 10⁻⁴(0.50)(30) = 0.0030 ft³/min.

This Q/A is Darcy discharge velocity, not necessarily the average velocity through pore space. Flow through a smaller void area is faster. Hydraulic conductivity depends on soil fabric, void ratio, fluid properties, and saturation. Layering also makes horizontal and vertical equivalent conductivities different.

Seepage direction matters. Downward seepage increases effective stress relative to a hydrostatic profile; upward seepage reduces it. Near an excavation or hydraulic exit, sufficient upward gradient can cause boiling or piping. Draw total head and flow direction rather than assigning pore pressure from depth alone when conditions are nonhydrostatic.

Compressibility and Consolidation

Immediate settlement occurs with prompt soil deformation and is often important in granular soils. Primary consolidation in saturated fine-grained soil occurs as excess pore pressure dissipates and effective stress rises. Secondary compression continues after primary consolidation under sustained effective stress due to soil-structure rearrangement.

For a normally consolidated layer under a stated one-dimensional model, a problem may give

S_c = [C_c H/(1 + e_0)] log10(σ'_f/σ'_0).

Let H = 10 ft, e_0 = 0.80, C_c = 0.25, initial effective stress σ'_0 = 1,000 psf, and final effective stress σ'_f = 1,500 psf. Then

S_c = [0.25(10)/(1.80)]log10(1,500/1,000)

S_c = 0.2446 ft = 2.93 in.

Do not use layer-top stress when the method calls for a representative layer stress, and do not use total stress in the logarithmic effective-stress ratio. For overconsolidated soil, stress history and preconsolidation stress may require recompression and virgin-compression segments rather than one C_c expression.

Consolidation Rate

Settlement magnitude and settlement time are separate questions. The rate depends on coefficient of consolidation and drainage length. A layer draining from both faces has a shorter maximum drainage path than the same thickness draining from one face and therefore reaches a given degree of consolidation sooner, all else equal. Apply the handbook's time-factor relationship with the correct drainage boundary.

Integrated Workflow

1. Draw layers, loads, water levels, and drainage boundaries.
2. Compute total stress and pore pressure independently; subtract once for effective stress.
3. Decide drained, undrained, or time-dependent behavior from permeability, path, and loading duration.
4. Use strength parameters that belong to that stress framework.
5. For seepage, determine head loss, gradient, flow area, and direction.
6. Separate settlement magnitude into immediate, primary, and secondary components as required.
7. Check units and whether the requested answer describes short-term safety, long-term safety, settlement amount, or settlement rate.