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Sabtan Research Programme · Engineering Geology

Geotechnical & Pavement Toolkit

A teaching companion sheet for foundation & flexible-pavement design

Built alongside Applications of Engineering Geology (A. A. Sabtan, KAU). Shallow-foundation bearing capacity, subgrade evaluation, the plate bearing test, and flexible-pavement structural design — computed live, with the working shown.

Module I · Bearing Capacity

Shallow Foundation — Bearing Capacity

Terzaghi-style general bearing capacity for a strip or square footing.

Soil / rock parameters
Footing geometry & safety factor

Results

Bearing factors Nc / Nq / Nγ–
Overburden at base, q = γD–
Ultimate bearing capacity, qult–
Allowable bearing capacity, qallow–

Which term governs qult?

Cohesion · c·Nc Surcharge · q·Nq Self-weight · ½γB·Nγ
Method & assumptions
Nq = eπ·tanφ·tan²(45+φ/2), Nc = (Nq−1)/tanφ, Nγ = 2(Nq+1)·tanφ (Vesić). Strip: qult = c·Nc + q·Nq + 0.5·γ·B·Nγ. Square uses teaching shape factors sc=1.3, sq=1.2, sγ=0.8. Idealised — shape (refined), inclination, groundwater, and settlement effects are not included.
Module II · Subgrade Strength

Subgrade Evaluation — CBR

Rate the natural subgrade and estimate its resilient modulus from the California Bearing Ratio.

Input

Results

Subgrade rating–
Typical use–
Resilient modulus, MR (Powell)–
Resilient modulus, MR (AASHTO)–

CBR strength scale

Method & reference layer values
MR (MPa) = 17.6·CBR0.64 (Powell et al., 1984; best for CBR ≈ 2–12).
MR (psi) = 1500·CBR (AASHTO, CBR ≲ 10).
Indicative CBR for road layers (Sabtan, Ch. 11; general practice):
Layer / materialCBR (%)
Soft / weak subgrade< 5
Wet sand≈ 10
Sub-base (granular)30 – 80
Base course> 80
Crushed limestone≈ 100
Module III · Subgrade Reaction

Plate Bearing Test — Subgrade Reaction k

Modulus of subgrade reaction from a plate load test, with size correction to a design footing width.

Test data
Design correction

Results

Contact pressure, p = P/A–
Plate modulus, ktest = p/Δ–
Corrected to Bf, kdesign–
Method & assumptions
ktest = p/Δ, reported in MPa/m (≡ MN/m³). Size correction (Terzaghi & Peck):
• Cohesive: kf = ktest·(Bp/Bf) — k inversely proportional to width.
• Granular: kf = ktest·[(Bf+Bp)/(2·Bf)]² — generalised Terzaghi sand form (reduces to the standard 0.3 m relation).
Standard reporting plate is 762 mm (30 in) at 1.25 mm settlement.
Module IV · Structural Design

Flexible Pavement — Structural Design

Two design bases. Switch between Sabtan's book method and the AASHTO 1993 equation.

Traffic
Subgrade

Results

Growth factor, F (Table 11-7)–
Design traffic number, DTN = F·ITN–
Full-depth asphalt thickness, TAread Fig 11-6

Growth factor F vs design period (Table 11-7)

TA is chart-based. Sabtan's book reads the full-depth asphalt thickness from Fig 11-6 (Yoder & Witczak, 1975) using the computed DTN together with the subgrade CBR / MR. That nomograph isn't reproduced here, so the tool computes the exact, formula-based steps (F and DTN) and hands off the final thickness to the chart. For a fully computed thickness, use the AASHTO tab.
Method & verification
F = [((1+r)n − 1) / r] / 20, with r as a decimal (for r = 0, F = n/20). This reproduces Table 11-7 exactly — e.g. r=6%, n=20 → F=1.84; r=8%, n=30 → F=5.66; r=10%, n=35 → F=13.55.
DTN = F·ITN (Eq. 11-1). ITN comes from Fig 11-5 (average total vehicle load, daily heavy-vehicle count, max allowable axle load).
AASHTO 1993 is imperial: ESALs, inches, psi. Saudi road practice follows the AASHTO method (Sabtan, Ch. 11).
Traffic & reliability
Serviceability & subgrade
Trial section (optional check)

Results

Subgrade modulus, MR = 1500·CBR–
Required structural number, SNreq–
AC-only thickness, D₁ = SN/a₁–
Trial section provides, SNprov–
Check–

Structural number — required vs provided

Method & assumptions
log₁₀W₁₈ = ZRS₀ + 9.36·log₁₀(SN+1) − 0.20 + log₁₀[ΔPSI/2.7] / [0.40 + 1094/(SN+1)5.19] + 2.32·log₁₀MR − 8.07. SNreq solved by bisection; ΔPSI = p₀ − p_t. Provided SN = a₁D₁ + a₂D₂m₂ + a₃D₃m₃. MR = 1500·CBR (psi). Drainage coefficients m default 1.0.