Geotechnical Formulas

Overview

Welcome! In this session, we’ll break down the foundational concepts and formulas underpinning geotechnical engineering calculations. From how soils behave under stress to the crucial ratios and coefficients used in design, you’ll gain a practical understanding of the terms, relationships, and methods that professionals apply daily. By the end, you’ll be equipped to recognize, use, and reason through core geotechnical formulas and definitions with confidence.

Concept-by-Concept Deep Dive

Soil Structure and Phases

Understanding soils begins with recognizing that soil is a three-phase system: solids (minerals), water, and air. The way these phases are arranged and interact greatly influences soil behavior.

Particle Arrangement (Compaction)

• Soil compaction is the process of rearranging soil particles to reduce the volume of air between them, increasing density and strength.
• The arrangement after compaction determines key properties like porosity and permeability.

Volume Relationships

• Total Volume (V): Includes solids, water, and air.
• Void Volume (Vv): Space taken by water and air.
• Solid Volume (Vs): Occupied by soil particles.
• Void Ratio (e): Ratio of void volume to solid volume.
• Porosity (n): Ratio of void volume to total volume.

Recipe: To analyze a soil’s structure, identify the mass and volume of each phase. Use these to compute ratios such as void ratio and degree of saturation.

Misconception: Confusing void ratio (voids/solids) with porosity (voids/total volume). Always double-check which base volume is used in each ratio.

Soil Properties: Strength, Compressibility, and Deformability

Soil mechanics hinges on how soils respond to loading.

Bearing Capacity

• The maximum pressure soil can support without failing.
• Calculated using empirical or theoretical equations, often factoring in cohesion, internal friction angle, and unit weight.

Shear Strength and Modulus

• Shear Strength: Resistance to sliding or shearing.
• Shear Modulus (G): Ratio of shear stress to shear strain—reflects soil stiffness.

Bulk and Elastic Moduli

• Bulk Modulus (K): Resistance to uniform compression; relates volume change to applied pressure.
• Elasticity vs. Plasticity:
  • Elasticity: Ability to return to original shape after stress is removed.
  • Plasticity: Ability to deform permanently without cracking.

Recipe: Identify applied stresses and corresponding strains. Use the appropriate modulus formula to relate them.

Misconception: Assuming soils behave like ideal elastic solids—real soils often exhibit both elastic and plastic behavior.

Water in Soils: Flow and Saturation

Water in soil pores governs many geotechnical phenomena.

Degree of Saturation and Water Content

• Degree of Saturation (S): Percentage of voids filled with water.
• Water Content (w): Ratio of water weight to solid weight.

Permeability and Flow

• Movement of Water: Described by terms like permeability and governed by Darcy's Law.
• Flow direction, rate, and the potential for soil to drain or retain water are critical to stability.

Recipe: Use known masses or volumes to compute water content and saturation.