Soil mechanics basics

Why it matters

Every structure ends in the ground. Foundations, retaining walls, embankments, pavements and pipelines all depend on how soil carries load, settles and drains. Soil is not a manufactured material with a data sheet: it varies from one borehole to the next, so geotechnical engineers combine site investigation, lab tests and conservative judgement. This lesson covers the three basics: describing a soil sample, classifying it, and estimating how much load a footing can carry.

Phase relations

A soil sample has three phases: solid grains, water and air. A few ratios describe it:

water content    w = mass of water / mass of solids
void ratio       e = volume of voids / volume of solids
porosity         n = e / (1 + e)
degree of sat.   S = volume of water / volume of voids
specific gravity Gs (of the solids, typically 2.65 to 2.75)

Two relations solve most problems:

S * e = w * Gs
gamma_d = Gs * gamma_w / (1 + e)     (dry unit weight; gamma_w = 9.81 kN/m^3)

Worked example. A saturated clay (S = 1) has w = 20% and Gs = 2.70. Then e = 0.20 × 2.70 = 0.54, n = 0.54 / 1.54 = 0.35, and gamma_d = 2.70 × 9.81 / 1.54 = 17.2 kN/m^3. Compaction specifications on earthworks are written in terms of dry unit weight (or dry density) and water contentThe mass of water divided by the mass of solids in a soil sample, used as a decimal in formulas..

Classification: the USCS

The Unified Soil Classification SystemThe ASTM D2487 system that gives each soil a two-letter symbol, such as SW, from its grain size and plasticity. (ASTM D2487) gives each soil a two-letter symbol from grain size and plasticity. The main steps for coarse soils:

1. Coarse or fine? If 50% or more passes the No. 200 sieve (0.075 mm), the soil is fine-grained (silt or clay) and is classified by its Atterberg limitsLab measures of a fine soil's plasticity, the liquid limit and plasticity index, used to classify silts and clays. (liquid limit and plasticity index) on the plasticity chart.
2. Gravel or sand? For coarse soils, compare the gravel fraction (retained on the No. 4 sieve, 4.75 mm) with the sand fraction. The larger gives the first letter: G or S.
3. Graded well or poorly? For clean soils (under 5% fines), use the gradation coefficients from the grain-size curve:

Cu = D60 / D10            Cc = D30^2 / (D10 * D60)
well graded (W): Cu >= 4 for gravel (>= 6 for sand) AND 1 <= Cc <= 3
otherwise poorly graded (P)

Soils with 5 to 12% fines get dual symbols (such as SP-SM), and those with more than 12% fines are silty or clayey (GM, GC, SM, SC), which needs Atterberg limits. The full procedure is in ASTM D2487.

Example. 85% passes the No. 4 sieve and 3% passes the No. 200 sieve, with Cu = 7.5 and Cc = 1.4. Gravel = 15%, sand = 82%, so it is a sand; clean; Cu >= 6 and Cc within 1 to 3: SW, well-graded sand.

Bearing capacity of a shallow footing

A footing fails in bearing when a wedge of soil shears out beneath it. Terzaghi's classic analysis, extended by later researchers, gives the ultimate bearing capacityThe pressure under a footing at which the soil fails in shear; designers divide it by a factor of safety. of a strip footing:

q_ult = c * Nc + gamma * Df * Nq + 0.5 * gamma * B * Ngamma

c is cohesion, gamma unit weight, Df embedment depth, B footing width. The bearing capacity factors depend on the friction angle phi. One widely used set (Prandtl, Reissner and Vesic) is:

Nq = e^(pi tan phi) * tan^2(45 + phi/2)
Nc = (Nq - 1) * cot phi      (5.14 when phi = 0)
Ngamma = 2 (Nq + 1) tan phi

For phi = 30°: Nq = 18.4, Nc = 30.1, Ngamma = 22.4. Other references give somewhat different Ngamma values, so state which set you used.

Illustrative example. A 1.5 m wide strip footing sits 1.0 m deep in sand with c = 0, phi = 30° and gamma = 18 kN/m^3:

q_ult = 0 + 18 × 1.0 × 18.4 + 0.5 × 18 × 1.5 × 22.4 = 331 + 302 = 634 kPa

With a factor of safety of 3 (a common choice for allowable stress design), the allowable bearing pressure is about 211 kPa. In practice, settlement often governs before bearing failure, groundwater reduces the effective unit weight, and shape, depth and inclination factors modify the equation. Codes and geotechnical reports also use resistance factors in LRFD.

Common mistakes

• Mixing up e and n, or using w as a percentage in a decimal formula.
• Classifying from grain size alone when the soil has more than 12% fines.
• Ignoring groundwater, which can roughly halve the gamma terms below the water table.
• Using lab-perfect parameters without considering site variability.

Professional responsibility

Foundation design must be based on a site-specific geotechnical investigation and report prepared by a qualified geotechnical engineer. These examples are for learning. Real designs need review and sealing by a licensed professional engineer (PE) under the codes your jurisdiction adopts. Field drilling and sampling also need site-safety training.

Recap

• Phase relations: S e = w Gs; gamma_d = Gs gamma_w / (1 + e).
• USCS: coarse vs fine at 50% passing No. 200; gravel vs sand; well or poorly graded from Cu and Cc.
• q_ult = c Nc + gamma Df Nq + 0.5 gamma B Ngamma; divide by a factor of safety and check settlement.

Try it

Open the Do tab to code phase relations, bearing factors and a simplified USCS classifier.