Soil Mechanics Guide: Shear Strength, Consolidation, and Site Characterization
Soil is the most variable and least predictable material that civil engineers work with. Unlike manufactured materials such as steel or concrete, soil is a natural material formed by the weathering of rock over thousands or millions of years. Its properties vary dramatically over both horizontal distance and depth.
Soil mechanics is the science that describes and predicts the behavior of soil under loading. The field was transformed in the 1920s by Karl Terzaghi, considered the father of soil mechanics, who published the theory of consolidation and established the principle of effective stress. His work made it possible to predict settlement and design foundations with confidence.
The Principle of Effective Stress
The effective stress principle is the most important concept in soil mechanics. It states that the stress carried by the soil skeleton — the effective stress — equals the total stress minus the pore water pressure:
σ’ = σ - u
where σ’ is effective stress, σ is total stress, and u is pore water pressure.
Effective stress controls all important aspects of soil behavior: shear strength, volume change, and compressibility. An increase in effective stress causes soil to gain strength and compress. A decrease in effective stress, such as from rising groundwater, reduces strength and can cause instability.
Total Stress and Pore Pressure
Total stress at a point in the ground is the weight of all material above that point divided by the area. For a 10-meter depth below the water table, the total vertical stress is approximately 200 kPa (assuming a saturated unit weight of 20 kN/m³). The pore water pressure at that depth is approximately 100 kPa (hydrostatic pressure). The effective stress is therefore 100 kPa.
If the water table rises to the surface, the pore water pressure becomes 200 kPa at 10 meters depth, and the effective stress drops to zero. This is why excavations can collapse when groundwater is not controlled — the loss of effective stress removes the soil’s strength.
Shear Strength of Soils
Shear strength determines the stability of slopes, the bearing capacity of foundations, and the earth pressure on retaining walls.
Mohr-Coulomb Failure Criterion
The Mohr-Coulomb criterion defines the shear strength as:
τf = c’ + σ’ × tan(φ')
where τf is shear stress at failure, c’ is effective cohesion, σ’ is effective normal stress on the failure plane, and φ’ is the effective friction angle.
For sands and gravels, cohesion is essentially zero — the shear strength comes entirely from friction. The friction angle ranges from 28° to 45° depending on particle shape, gradation, and density. Well-graded angular sands at high density can have friction angles over 40°.
For clays, effective cohesion may range from 0 to 50 kPa or more. The friction angle for clay ranges from about 18° for high-plasticity clays to 34° for low-plasticity clays.
Drained and Undrained Conditions
The key distinction in shear strength testing is whether drainage is allowed during loading. In drained conditions, pore water pressures dissipate as the soil is loaded. The soil volume changes and the shear strength is governed by effective stress.
In undrained conditions, water cannot escape from the soil pores during rapid loading. The volume cannot change, so pore water pressure increases (or decreases) in response to the applied load. The undrained shear strength Su is the shear strength under these conditions.
For normally consolidated clays, the undrained shear strength increases with depth approximately as Su/σ’v0 = 0.2 to 0.3. This relationship is used to estimate undrained strength from effective stress calculations.
Triaxial Compression Test
The triaxial test is the standard for measuring shear strength. A cylindrical soil specimen is enclosed in a rubber membrane, placed in a pressurized cell, and loaded axially to failure.
Consolidated drained (CD) tests allow full drainage during both consolidation and shearing. The test is slow — a clay specimen may take days or weeks to shear at rates that maintain zero excess pore pressure.
Consolidated undrained (CU) tests allow drainage during consolidation but prevent drainage during shearing. Pore pressure measurements during shearing allow calculation of effective stress strength parameters.
Unconsolidated undrained (UU) tests measure the undrained shear strength directly. No drainage is permitted at any stage. UU tests are used for rapid construction scenarios.
Consolidation
When a load is applied to saturated clay, the water in the pores initially carries the added stress, creating excess pore water pressure. Over time, water drains from the soil pores, the load transfers to the soil skeleton, and the soil compresses. This time-dependent process is consolidation.
One-Dimensional Consolidation Theory
Terzaghi’s consolidation theory describes the process with the differential equation:
∂u/∂t = Cv × ∂²u/∂z²
where Cv is the coefficient of consolidation, u is excess pore pressure, t is time, and z is depth. The solution gives the degree of consolidation as a function of time factor Tv = Cv × t / H², where H is the drainage path length.
For a clay layer with Cv of 5 m²/year, H of 2.5 meters (single drainage), the time for 50 percent consolidation is approximately 9 months. For 90 percent consolidation, the time is approximately 3.5 years.
Consolidation Parameters
The compression index Cc, determined from the oedometer test, governs the magnitude of consolidation settlement. Typical Cc values range from 0.2 for low-plasticity clays to 0.5 or more for high-plasticity clays.
The coefficient of consolidation Cv governs the rate of settlement. Cv decreases with increasing plasticity index. A CL clay might have Cv of 5 to 10 m²/year. A CH clay might have Cv of 0.5 to 2 m²/year.
Overconsolidation ratio (OCR) describes whether a clay has been loaded beyond its current stress in the past. Overconsolidated clays are stiffer and have higher undrained shear strength than normally consolidated clays at the same depth.
Compaction
Compaction is the mechanical densification of soil by removing air voids. It increases shear strength, reduces compressibility, and decreases permeability.
Proctor Test
The Standard Proctor test determines the relationship between water content and dry density for a given compaction energy. The optimum water content produces the maximum dry density.
For most soils, the compaction curve is a parabola. Too little water prevents dense packing. Too much water fills the voids and prevents further densification. The optimum water content for a silty sand is typically 11 to 14 percent with maximum dry density of 1.8 to 2.0 g/cm³.
Field Compaction
Compaction in the field is achieved by rollers — smooth drum, sheepsfoot, pneumatic tired, or vibratory. Soil is placed in lifts of 150 to 300 mm thickness. Each lift receives a specified number of passes (typically 4 to 8) at the specified water content.
Field density is measured using the sand cone test, nuclear density gauge, or rubber balloon test. The relative compaction is the ratio of field dry density to maximum dry density from the Proctor test, expressed as a percentage. Specifications typically require 95 to 100 percent relative compaction.
Soil Permeability
Permeability is the ease with which water flows through soil. The coefficient of permeability k is defined by Darcy’s law: v = k × i, where v is discharge velocity and i is hydraulic gradient.
Sands have permeability in the range of 10⁻² to 10⁻⁵ m/s. Clays have permeability of 10⁻⁸ to 10⁻¹² m/s — orders of magnitude lower. This enormous range explains why sand drains water readily while clay consolidates slowly.
Soil Classification and Engineering Behavior
Soil classification systems provide the first indication of engineering behavior. Beyond the USCS classification described earlier, the AASHTO soil classification system is widely used for pavement design. AASHTO classifies soils into seven groups (A-1 through A-7) based on grain size and plasticity, with a group index that quantifies the expected pavement performance.
The engineering behavior of a soil is not fully captured by classification alone. Two soils with the same USCS classification can have very different shear strengths and compressibility depending on their density, fabric, and stress history. This is why classification is only the first step — laboratory testing of undisturbed samples is essential for design.
Sensitive clays deserve special attention. Sensitivity is the ratio of undisturbed strength to remolded strength. Quick clays have sensitivity exceeding 30 — the remolded strength is less than 3 percent of the undisturbed strength. A quick clay slope can be stable for decades but fail catastrophically when disturbed by excavation or seismic shaking. The 1978 Rissa landslide in Norway, triggered by excavation, destroyed seven farms and moved 6 million cubic meters of clay.
Frequently Asked Questions
What is quick clay? Quick clay is a sensitive clay that undergoes a dramatic loss of strength when disturbed. The soil structure collapses upon remolding, and the clay flows like a liquid. Quick clay landslides have caused fatalities in Scandinavia and Canada.
How is soil compaction verified in the field? Field density is tested using a nuclear density gauge, sand cone test, or rubber balloon. The density is compared to the maximum dry density from the Proctor test to calculate relative compaction.
What causes soil to be expansive? Expansive soils contain clay minerals, particularly montmorillonite, that absorb water and swell. The swelling pressure can exceed 200 kPa, enough to lift foundations and crack pavements. Expansive soils cause more property damage annually than earthquakes and floods combined.
How deep do soil samples need to be taken for foundation design? A general rule is to explore to depths where the stress increase from the foundation is less than 10 percent of the existing overburden stress. For a large building, this may require borings to depths of 30 to 50 meters.
Geotechnical Engineering — Foundation Engineering — Construction Materials Guide