Overview

PE exam study guide for site development: earthwork volumes, bearing capacity, retaining wall stability, slope stability, and stormwater detention.

This topic accounts for 5 out of 40 questions on the PE Civil Civil Breadth (AM) exam.

Key Concepts

Earthwork Volumes

Average end area method: V = L(A1+A2)/(2x27) in cubic yards. Prismoidal formula: V = L(A1 + 4Am + A2)/(6x27). Shrinkage factor converts bank to compacted volume (typically 0.80-0.90). Swell factor converts bank to loose (typically 1.20-1.35). Mass diagram plots cumulative earthwork vs. station to optimize haul.

Average End Area Method Prismoidal Formula Shrinkage Factor Bank To Compacted Swell Factor Bank To Loose

Bearing Capacity

Terzaghi for strip: q_ult = cNc + qNq + 0.5*gamma*B*Ngamma. Square: q_ult = 1.3cNc + qNq + 0.4*gamma*B*Ngamma. Allowable = q_ult / FS (FS typically 3). q = overburden at footing depth = gamma*Df. N-factors depend on phi only. For c=0 soils (sand), the cNc term drops. For phi=0 soils (clay), Nc=5.14, Nq=1, Ngamma=0.

Terzaghi Bearing Capacity Terzaghi Bearing Capacity Strip Footing Allowable Bearing Capacity Required Footing Area

Retaining Wall Stability

Check: (1) Overturning about toe: FS_OT = sum(resisting moments)/sum(overturning moments) >= 2.0. (2) Sliding: FS_slide = (W*tan(delta) + c_b*B) / Pa_h >= 1.5. (3) Bearing capacity: ensure base pressure <= allowable. Resultant should fall within middle third (e <= B/6) to avoid tension. Active pressure: Pa = 0.5*Ka*gamma*H^2.

Rankine Active Earth Pressure Coefficient

Slope Stability

Infinite slope (cohesionless, dry): FS = tan(phi)/tan(beta). With seepage parallel to slope: FS = (gamma_b/gamma_sat)*tan(phi)/tan(beta). Taylor's stability chart: N_s = c/(gamma*H*FS). Bishop's simplified method is the standard for circular failure surfaces. Typical minimum FS: 1.5 for permanent slopes, 1.3 for temporary.

Infinite Slope Cohesionless Dry Infinite Slope Submerged Factor Of Safety

Stormwater Detention

Goal: attenuate post-development peak flow to pre-development rate. Storage volume = area between inflow and outflow hydrographs. Modified Rational Method: V = Q_allow*(td - tc)*60 for triangular hydrograph. Routing: Modified Puls method for reservoir routing. Outlet structures: orifice (Q = Cd*A*sqrt(2gh)), weir, or combination.

Detention Time Orifice Equation Rational Method

Common Exam Question Types

Calculate earthwork volumes from cross-sections
Determine ultimate and allowable bearing capacity
Check retaining wall stability (overturning, sliding)
Calculate factor of safety for a slope
Size a stormwater detention basin

Exam Tips & Strategies

Earthwork: V = L(A1+A2)/2, always divide by 27 for cubic yards

Terzaghi: square footing uses 1.3 and 0.4 shape factors. Strip uses 1.0 and 0.5

Retaining walls: FS_overturning >= 2.0, FS_sliding >= 1.5

Infinite slope: FS = tan(phi)/tan(beta). If FS < 1, the slope is unstable

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Site Development Study Guide