liminfoSoil Mechanics Reference
Free reference guide: Soil Mechanics Reference
About Soil Mechanics Reference
The Soil Mechanics Reference is a searchable guide to geotechnical engineering formulas, parameters, and design criteria used in foundation engineering, slope stability, and ground improvement. It covers soil classification systems (USCS and AASHTO), grain size analysis with uniformity and curvature coefficients, Atterberg limits for plasticity characterization, and field testing methods including SPT N-value interpretation for relative density and consistency, CPT cone penetration test result analysis using the Robertson classification chart.
The reference provides complete bearing capacity formulas including Terzaghi (strip, square, and circular footings with Nc, Nq, Ngamma factors), Meyerhof general formula with shape, depth, and inclination correction factors, and pile bearing capacity using static methods with tip resistance and skin friction calculations. Settlement analysis covers immediate (elastic) settlement using Boussinesq and Schmertmann methods, primary consolidation settlement for normally and overconsolidated clays using Cc and Cs compression indices, and consolidation time calculations using the Terzaghi Tv factor.
For lateral earth pressure and stability analysis, the reference covers Rankine active/passive earth pressure coefficients (Ka and Kp), Coulomb earth pressure theory with wall friction, retaining wall stability checks for overturning, sliding, and bearing capacity, Mohr-Coulomb shear strength parameters from UU/CU/CD tests, and Bishop simplified method for slope stability with safety factor criteria for normal, seismic, and rainfall conditions. It also includes seepage analysis using Darcy law and flow nets, compaction control, site investigation planning, and soft ground treatment methods including PBD, deep mixing, and geosynthetic reinforcement.
Key Features
- Terzaghi and Meyerhof bearing capacity formulas with shape, depth, and inclination factors for shallow foundations
- Pile bearing capacity calculations using static formulas for tip resistance and skin friction (alpha and K-tan-delta methods)
- Primary consolidation settlement for normally and overconsolidated clays with Cc, Cs indices and time factor calculations
- Rankine and Coulomb earth pressure theories with active/passive coefficients and retaining wall stability checks
- Mohr-Coulomb failure criterion with UU, CU, and CD shear test parameter interpretation
- Bishop simplified method for slope stability analysis with safety factor criteria for multiple loading conditions
- Seepage analysis using Darcy law, flow net construction, and piping safety factor calculations
- Ground improvement method reference covering PBD, vacuum consolidation, deep mixing, grouting, and geosynthetics
Frequently Asked Questions
What is the Terzaghi bearing capacity formula for a strip footing?
The Terzaghi ultimate bearing capacity for a strip footing is qu = c*Nc + q*Nq + 0.5*gamma*B*Ngamma, where c is cohesion, q is overburden pressure at foundation depth, gamma is soil unit weight, B is footing width, and Nc, Nq, Ngamma are bearing capacity factors dependent on the friction angle phi. For phi = 30 degrees, Nc = 37.2, Nq = 22.5, Ngamma = 19.7. The safety factor should be at least 3.0: qa = qu/FS.
How do I calculate consolidation settlement for clay?
For normally consolidated clay: Sc = Cc*H/(1+e0) * log((sigma_v0 + delta_sigma)/sigma_v0), where Cc is the compression index, H is the clay layer thickness, e0 is the initial void ratio, sigma_v0 is the initial effective stress, and delta_sigma is the applied stress increase. For overconsolidated clay where the final stress stays below the preconsolidation pressure Pc, use the swelling index Cs instead of Cc.
What is the difference between Rankine and Coulomb earth pressure theories?
Rankine theory assumes a smooth (frictionless) wall and derives earth pressure from stress states: Ka = tan^2(45 - phi/2) for active and Kp = tan^2(45 + phi/2) for passive. Coulomb theory accounts for wall friction (delta, typically 2/3 of phi) and sloping backfill, resulting in more realistic but complex expressions. Coulomb is generally preferred for retaining wall design as it gives more economical (slightly lower active) pressures.
How do I check retaining wall stability?
Three checks are required: overturning (FS = resisting moment / overturning moment >= 2.0), sliding (FS = (V*tan(delta_b) + c_b*B) / Pa_h >= 1.5), and bearing capacity (q_max <= allowable bearing pressure). The eccentricity e = B/2 - (sum of resisting moments - sum of overturning moments)/V should be within B/6 to avoid tension at the base. Maximum base pressure q_max = V/B * (1 + 6*e/B).
What are the safety factor requirements for slope stability?
Using the Bishop simplified method or similar limit equilibrium analysis, the minimum required safety factors are: FS >= 1.5 for normal (static) conditions, FS >= 1.1 for seismic conditions, and FS >= 1.3 for rainfall conditions. The Bishop formula iteratively calculates FS = sum[c'*b + (W-u*b)*tan(phi')/m_alpha] / sum[W*sin(alpha)], where m_alpha depends on FS itself, requiring convergence.
How do I estimate permeability from soil type?
Typical permeability ranges are: clean gravel 10^0 to 10^1 cm/s, coarse sand 10^-1 to 10^0 cm/s, fine sand 10^-2 to 10^-4 cm/s, silt 10^-4 to 10^-6 cm/s, and clay 10^-6 to 10^-9 cm/s. For laboratory testing, use the constant head method for coarse soils (k > 10^-3 cm/s) and the falling head method for fine soils (k < 10^-3 cm/s). Field tests include pumping tests and slug tests.
What is the flow net method for seepage analysis?
A flow net consists of flow lines and equipotential lines forming a pattern of approximate squares. Seepage quantity Q = k*H*(Nf/Nd), where k is permeability, H is the total head, Nf is the number of flow channels, and Nd is the number of equipotential drops. The piping safety factor FS = ic/i_exit should be at least 2.0-3.0, where the critical hydraulic gradient ic = (Gs-1)/(1+e), approximately 1.0.
What are the main soft ground improvement methods?
Methods include: replacement (excavate and fill with good soil), consolidation acceleration using prefabricated vertical drains (PBD) with surcharge loading or vacuum consolidation, solidification through deep cement mixing (DCM/CDM) or chemical grouting (SGR, LW), and reinforcement using sand compaction piles (SCP) or geosynthetics (geotextiles and geogrids). The choice depends on soil conditions, project requirements, construction time, and budget constraints.