Soil mechanics studies how soil behaves as a three-phase material made of solids, water, and air under engineering loads. Bearing capacity applies these ideas to foundation design by estimating how much load soil can safely support. This cheat sheet helps students connect index properties, seepage, stresses, strength, settlement, and shallow foundation formulas.
It is useful for quick review before solving geotechnical engineering problems.
Key Facts
- Void ratio is e = Vv / Vs, where Vv is volume of voids and Vs is volume of soil solids.
- Porosity is n = Vv / V, and it relates to void ratio by n = e / (1 + e).
- Degree of saturation is S = Vw / Vv, where S = 1 means all voids are filled with water.
- Total vertical stress is sigma_v = sum(gamma_i z_i), using the unit weight and thickness of each soil layer.
- Effective stress is sigma' = sigma - u, where sigma is total stress and u is pore water pressure.
- For saturated soil below the water table, buoyant unit weight is gamma' = gamma_sat - gamma_w.
- Mohr-Coulomb shear strength is tau_f = c' + sigma' tan(phi'), where c' is effective cohesion and phi' is effective friction angle.
- Terzaghi ultimate bearing capacity for a strip footing is q_ult = c' N_c + q N_q + 0.5 gamma B N_gamma.
Vocabulary
- Void Ratio
- Void ratio is the volume of void space divided by the volume of soil solids.
- Effective Stress
- Effective stress is the stress carried by the soil skeleton and controls strength and compression.
- Pore Water Pressure
- Pore water pressure is the pressure of water within the voids of a saturated or partially saturated soil.
- Shear Strength
- Shear strength is the maximum shear stress a soil can resist before failure along a surface.
- Consolidation
- Consolidation is the time-dependent settlement of saturated soil caused by drainage of pore water under load.
- Bearing Capacity
- Bearing capacity is the maximum foundation pressure that soil can support before shear failure or excessive deformation.
Common Mistakes to Avoid
- Using total stress instead of effective stress in shear strength calculations is wrong because soil strength is governed by sigma', not sigma.
- Forgetting pore water pressure below the water table gives an incorrect effective stress because u = gamma_w z reduces the stress carried by soil grains.
- Mixing void ratio and porosity is wrong because e = Vv / Vs while n = Vv / V, and they are not the same value.
- Applying Terzaghi bearing capacity factors without matching the soil friction angle is wrong because N_c, N_q, and N_gamma depend on phi'.
- Ignoring the factor of safety is unsafe because allowable bearing pressure is usually q_allow = q_ult / FS or net q_allow = q_net ult / FS.
Practice Questions
- 1 A soil sample has Vv = 0.36 m3 and Vs = 0.60 m3. Find the void ratio and porosity.
- 2 A saturated clay layer has total vertical stress sigma = 150 kPa and pore water pressure u = 65 kPa. Find the effective stress.
- 3 For a strip footing with c' = 0, q = 40 kPa, gamma = 18 kN/m3, B = 2 m, N_q = 18, and N_gamma = 15, calculate q_ult using q_ult = q N_q + 0.5 gamma B N_gamma.
- 4 Explain why a rise in groundwater level can reduce the bearing capacity of a shallow foundation even if the total soil thickness stays the same.