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.
Understanding Soil Mechanics & Bearing Capacity
Soil calculations begin with careful bookkeeping of volume and mass. A soil sample may look uniform, yet its grains form a skeleton with spaces between them. Those spaces can contain water, air, or a mixture of both.
Engineers use phase diagrams to keep each part separate before calculating unit weight, water content, or density. The most common errors come from mixing dry, moist, saturated, and submerged unit weights. Units deserve equal care.
A unit weight in kilonewtons per cubic metre must match the stress units used later. A small error in water content can change estimates of volume change, strength, and settlement.
Water in the pores has an especially important job. It carries part of the load, but it does not lock soil grains together in the same way that grain contact does. Effective stress describes the load transferred through the grain skeleton.
When pore water pressure rises, effective stress falls if total stress stays the same. This is why soil can lose strength during heavy rainfall, rapid loading, or an earthquake.
A lowering water table can have the opposite effect by increasing effective stress, though it may cause settlement in some deposits. Students should draw the water table clearly on every stress diagram and calculate pore pressure from the vertical distance below that level.
Shear strength controls whether soil slips, spreads, or remains stable. Friction develops when grains press against one another and resist sliding. Effective cohesion represents bonding or apparent sticking between particles.
In a shear strength calculation, the friction part depends on effective normal stress, while cohesion contributes a fixed amount within the model. The formula states that failure shear stress equals effective cohesion plus effective normal stress times the tangent of the effective friction angle. Clay and sand behave differently because drainage takes time.
Sand often drains quickly under normal field loading. Saturated clay may carry excess pore pressure for months or years. A drained test and an undrained test can therefore give very different strength values for the same soil.
A foundation does not fail only by sudden punching into the ground. It can fail through general shear, local shear, or punching shear, depending on soil density, strength, and footing shape. Bearing capacity equations estimate the pressure at which shear failure becomes likely.
The design load must still include a factor of safety and must be checked against settlement. Settlement is often the controlling issue for buildings on soft clay, even when shear failure is unlikely. Immediate settlement occurs as soil deforms under load.
Consolidation settlement occurs as water slowly leaves low permeability soil. Good solutions state the footing width, depth, groundwater condition, drainage assumption, and soil parameters before substituting numbers. Those details determine whether a result is physically believable.