Overview

Comprehensive PE exam study guide for soil mechanics covering USCS classification, effective stress, consolidation, shear strength, lateral earth pressure, and compaction.

This topic accounts for 6 out of 40 questions on the PE Civil Civil Breadth (AM) exam.

Key Concepts

Soil Classification (USCS)

The Unified Soil Classification System classifies soils by grain size and plasticity. Coarse-grained: >50% retained on #200 sieve. Gravel (G) retained on #4, Sand (S) passes #4. Fine-grained: >50% passing #200. Classified by LL and PI on plasticity chart: CL (lean clay, PI > 7, below A-line), CH (fat clay, LL > 50), ML (silt, PI < 4 or below A-line), MH (elastic silt). Dual symbols: GW, GP, SW, SP (W=well-graded, P=poorly-graded). Cu = D60/D10, Cc = D30^2/(D10 x D60).

Effective Stress Principle

Total stress = effective stress + pore water pressure: sigma = sigma_prime + u. Effective stress controls soil behavior (strength, compressibility). At depth z: sigma = gamma_total x z. Below water table: u = gamma_w x h_w. Effective stress: sigma_prime = sigma - u. For layered soils, sum the contributions of each layer.

Effective Stress Vertical Total Stress At Depth Moist Unit Weight Saturated Unit Weight Buoyant Effective Unit Weight

Consolidation Settlement

Primary consolidation for normally consolidated clay: S = (Cc x H)/(1+e0) x log(sigma_f/sigma_0). For overconsolidated clay (sigma_f < sigma_p): S = (Cr x H)/(1+e0) x log(sigma_f/sigma_0). If sigma_f > sigma_p: two-part calculation using Cr up to sigma_p and Cc beyond. Time rate: U = f(Tv), where Tv = Cv x t / H_dr^2. At U=50%, Tv=0.197; at U=90%, Tv=0.848.

Primary Consolidation Normally Consolidated Primary Consolidation Overconsolidated Time Factor Consolidation Degree Of Consolidation U 60

Shear Strength

Mohr-Coulomb: tau_f = c + sigma_n x tan(phi). Undrained strength (total stress): tau = Su (phi_u = 0). Drained strength (effective stress): tau = c_prime + sigma_prime x tan(phi_prime). Lab tests: UU triaxial (undrained), CU triaxial (consolidated undrained), CD triaxial (consolidated drained). Direct shear gives tau vs sigma_n directly.

Lateral Earth Pressure

Rankine theory: Ka = tan^2(45 - phi/2), Kp = tan^2(45 + phi/2). Active pressure (wall moves away): pa = Ka x gamma x z - 2c sqrt(Ka). Passive pressure (wall moves toward soil): pp = Kp x gamma x z + 2c sqrt(Kp). At-rest: K0 = 1 - sin(phi). Resultant force on wall height H: P = 0.5 x K x gamma x H^2, acting at H/3 from base.

Rankine Active Earth Pressure Coefficient Rankine Passive Earth Pressure Coefficient At Rest Earth Pressure Coefficient Active Earth Pressure Cohesionless Active Earth Pressure Cohesive

Compaction

Standard Proctor (ASTM D698): 12,400 ft-lbf/ft^3. Modified Proctor (ASTM D1557): 56,250 ft-lbf/ft^3. Dry density: gamma_d = gamma_wet / (1 + w). Maximum dry density (MDD) occurs at optimum moisture content (OMC). Relative compaction = field gamma_d / lab gamma_d_max x 100%. Zero air voids: gamma_zav = Gs x gamma_w / (1 + w x Gs). Specifications typically require 95% of maximum.

Dry Unit Weight Dry Density From Wet Density Relative Compaction Zero Air Voids Density Void Ratio Porosity Degree Of Saturation

Common Exam Question Types

Classify a soil using USCS given sieve analysis and Atterberg limits
Calculate effective stress at a depth with water table
Compute consolidation settlement for normally or overconsolidated clay
Determine time for a given degree of consolidation
Calculate active/passive earth pressure using Rankine theory
Determine relative compaction from field and lab data

Exam Tips & Strategies

For effective stress: always draw a soil profile diagram with layers and water table

Ka = tan^2(45 - phi/2) is active (smaller). Kp = tan^2(45 + phi/2) is passive (larger)

Consolidation: Cc for normally consolidated (virgin curve), Cr for recompression (much smaller)

Relative compaction >= 95% is the typical specification. Know the Proctor test differences

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Soil Mechanics Study Guide