1. Overview
Compressor foundations transmit static weight and dynamic forces into the supporting soil. The soil must have adequate bearing capacity to support these loads without excessive settlement or bearing failure. Unlike static equipment, compressor foundations impose cyclic and dynamic loads that require additional consideration beyond standard structural foundation design.
Static Loads
Equipment + Foundation Weight
Typically 2-5 ksf contact pressure
Dynamic Loads
Unbalanced Forces
Add 25-50% to static for dynamic allowance
Embedment Depth
D_f = 3-6 ft
Below frost line and organic layers
Groundwater
Reduces Capacity
Use buoyant unit weight below GWT
Design Standards
| Standard | Coverage | Key Requirement |
|---|---|---|
| ACI 351.3R | Machinery foundations | Dynamic analysis, soil-structure interaction |
| ASCE 7 | Load combinations | Dead, live, wind, seismic loads |
| API 686 | Machinery installation | Alignment, grouting, settlement tolerances |
| ASTM D1586 | SPT testing | Standard penetration test procedures |
| ASTM D2850 | Triaxial test | Undrained shear strength |
Critical principle: Soil bearing capacity is typically the controlling design factor for compressor foundations, not the structural capacity of the concrete. A geotechnical investigation is required before final foundation sizing.
2. Bearing Capacity Theory
Bearing capacity is the maximum contact pressure a soil can sustain without shear failure. The Terzaghi general bearing capacity equation is the fundamental relationship for shallow foundations.
Terzaghi Bearing Capacity Equation
Ultimate Bearing Capacity (strip footing):
q_ult = c'N_c + q'N_q + 0.5 * gamma * B * N_gamma
Where:
q_ult = Ultimate bearing capacity (psf)
c' = Effective cohesion (psf)
q' = Effective overburden pressure at foundation level (psf)
q' = gamma * D_f
gamma = Unit weight of soil (pcf)
B = Foundation width (ft)
D_f = Depth of embedment (ft)
N_c, N_q, N_gamma = Bearing capacity factors (function of phi')
Allowable Bearing Capacity:
q_all = q_ult / FS
Where FS = 2.5 to 3.0 (typical for compressor foundations)
Shape Correction Factors
For rectangular or square foundations, apply shape factors to Terzaghi's equation:
Meyerhof Shape Factors:
q_ult = c'N_c * s_c + q'N_q * s_q + 0.5 * gamma * B * N_gamma * s_gamma
For rectangular foundation (B x L):
s_c = 1 + 0.2(B/L)
s_q = 1 + 0.1(B/L) for phi' > 10 deg
s_gamma = 1 - 0.4(B/L)
For square foundation (B = L):
s_c = 1.3
s_q = 1.2 for phi' > 0 deg
s_gamma = 0.8
Bearing Capacity Factors
| phi' (deg) | N_c | N_q | N_gamma | Typical Soil |
|---|---|---|---|---|
| 0 | 5.14 | 1.0 | 0.0 | Soft clay (undrained) |
| 10 | 8.35 | 2.47 | 1.22 | Soft to medium clay |
| 20 | 14.83 | 6.40 | 5.39 | Stiff clay / loose sand |
| 25 | 20.72 | 10.66 | 10.88 | Medium dense sand |
| 30 | 30.14 | 18.40 | 22.40 | Dense sand |
| 35 | 46.12 | 33.30 | 48.03 | Very dense sand |
| 40 | 75.31 | 64.20 | 109.41 | Dense gravel |
Groundwater Effects
Case 1: GWT at or above foundation level
Use buoyant unit weight for gamma in N_gamma term:
gamma' = gamma_sat - gamma_w
gamma_w = 62.4 pcf
Case 2: GWT within depth B below foundation
gamma_eff = gamma' + (d_w / B)(gamma - gamma')
Where d_w = depth of GWT below foundation base
Case 3: GWT deeper than B below foundation
No correction required; use total unit weight.
Dynamic bearing capacity: For compressor foundations with significant dynamic loads, ACI 351.3R recommends reducing the allowable static bearing capacity by 50% for the dynamic load component, or verifying that total (static + dynamic) does not exceed 75% of the static allowable.
3. Soil Classification & Properties
Soil type determines both bearing capacity and dynamic stiffness. The Unified Soil Classification System (USCS) is standard practice for geotechnical work in the oil and gas industry.
Typical Allowable Bearing Pressures
| Soil Type (USCS) | SPT N-value | Allowable (psf) | Suitability |
|---|---|---|---|
| Soft clay (CL, CH) | 2-4 | 500-1,000 | Poor; needs improvement |
| Medium clay (CL) | 4-8 | 1,000-2,000 | Marginal; verify settlement |
| Stiff clay (CL, CH) | 8-15 | 2,000-4,000 | Acceptable for small units |
| Very stiff clay | 15-30 | 4,000-6,000 | Good |
| Hard clay / shale | >30 | 6,000-12,000 | Excellent |
| Loose sand (SP, SW) | 4-10 | 1,000-2,000 | Marginal; check liquefaction |
| Medium dense sand | 10-30 | 2,000-4,000 | Good |
| Dense sand | 30-50 | 4,000-8,000 | Excellent |
| Gravel (GP, GW) | >50 | 6,000-12,000 | Excellent |
| Weathered rock | Refusal | 10,000-20,000 | Excellent |
SPT Correlation for Cohesionless Soils
Meyerhof (1965) for footings on sand:
q_all = N / 4 (ksf) for B <= 4 ft
q_all = N / 6 × [(B+1)/B]^2 (ksf) for B > 4 ft
Where:
N = Corrected SPT blow count (N_60)
B = Foundation width (ft)
SPT Energy Correction:
N_60 = N_field × (ER / 60)
Where ER = hammer energy ratio (%)
Safety hammer: ER ~ 60%
Donut hammer: ER ~ 45%
Auto-trip: ER ~ 70-85%
Dynamic Soil Properties
| Soil Type | Shear Modulus G (ksf) | Poisson's Ratio | Damping Ratio |
|---|---|---|---|
| Soft clay | 50-200 | 0.45-0.50 | 0.03-0.10 |
| Stiff clay | 200-1,000 | 0.40-0.45 | 0.02-0.05 |
| Loose sand | 100-500 | 0.30-0.35 | 0.03-0.07 |
| Medium dense sand | 500-2,000 | 0.30-0.35 | 0.02-0.05 |
| Dense sand/gravel | 2,000-5,000 | 0.25-0.35 | 0.01-0.03 |
| Weathered rock | 5,000-20,000 | 0.20-0.30 | 0.01-0.02 |
4. Settlement Analysis
Even if bearing capacity is adequate, excessive settlement can cause equipment misalignment, piping stress, and operational problems. Settlement analysis is often the controlling criterion for compressor foundations.
Settlement Limits for Machinery Foundations
| Parameter | Limit | Reference |
|---|---|---|
| Total settlement | < 1.0 in (25 mm) | ACI 351.3R |
| Differential settlement | < 0.5 in (12 mm) | ACI 351.3R |
| Angular distortion | < 1/500 | API 686 |
| Tilt | < 0.001 in/ft | API 686 |
Immediate (Elastic) Settlement
Elastic settlement of a rectangular footing:
S_i = q * B * (1 - nu^2) / E_s * I_w
Where:
S_i = Immediate settlement (in or mm)
q = Net contact pressure (psf)
B = Foundation width (ft)
nu = Poisson's ratio of soil
E_s = Elastic modulus of soil (psf)
I_w = Influence factor (function of L/B and depth)
Typical E_s values:
Soft clay: 250-500 ksf
Stiff clay: 500-2,000 ksf
Loose sand: 200-500 ksf
Dense sand: 1,000-3,000 ksf
Gravel: 2,000-5,000 ksf
Consolidation Settlement (Clays)
Primary consolidation for normally consolidated clay:
S_c = [C_c / (1 + e_0)] * H * log10[(sigma'_0 + delta_sigma) / sigma'_0]
For overconsolidated clay (sigma'_0 + delta_sigma < sigma'_p):
S_c = [C_r / (1 + e_0)] * H * log10[(sigma'_0 + delta_sigma) / sigma'_0]
Where:
C_c = Compression index (0.2-0.5 for soft clay)
C_r = Recompression index (C_c / 5 to C_c / 10)
e_0 = Initial void ratio
H = Thickness of compressible layer (ft)
sigma'_0 = Initial effective stress at midpoint (psf)
delta_sigma = Stress increase from foundation (psf)
sigma'_p = Preconsolidation pressure (psf)
Time for consolidation:
t = T_v * H_dr^2 / c_v
T_v = Time factor (0.848 for 90% consolidation)
H_dr = Drainage path length (ft)
c_v = Coefficient of consolidation (ft^2/day)
Practical guidance: For compressor foundations on clay soils, perform consolidation analysis to estimate long-term settlement. If consolidation settlement exceeds 0.5 in differential, consider deep foundations (piles) or ground improvement (stone columns, dynamic compaction).
5. Field Investigation
A site-specific geotechnical investigation is essential. The scope depends on the compressor size and soil variability.
Minimum Investigation Requirements
| Equipment Size | Borings | Depth | Lab Tests |
|---|---|---|---|
| < 500 HP | 1-2 | 20-30 ft or 2B | Classification, Atterberg, moisture |
| 500-2,000 HP | 2-3 | 30-50 ft or 2B | Above + consolidation, triaxial |
| > 2,000 HP | 3-4 | 50-75 ft or 2B | Above + dynamic testing (MASW, crosshole) |
Field Testing Methods
| Test | ASTM Standard | Parameter Obtained | Application |
|---|---|---|---|
| Standard Penetration Test (SPT) | D1586 | N-value, relative density | Bearing capacity correlation |
| Cone Penetration Test (CPT) | D5778 | q_c, f_s, continuous profile | Soil stratification, liquefaction |
| Vane Shear Test | D2573 | Undrained shear strength | Soft clay bearing capacity |
| Pressuremeter Test (PMT) | D4719 | E_s, limit pressure | In-situ modulus for settlement |
| MASW / Crosshole | D7400 | V_s, G_max | Dynamic soil properties |
| Plate Load Test | D1194 | Bearing capacity, modulus | Direct verification |
Best practice: Boring depth should extend to at least 2 times the foundation width below the base, or until competent bearing material is encountered. For vibrating machinery, always include at least one shear wave velocity measurement for dynamic soil stiffness.
6. Worked Examples
Example 1: Bearing Capacity for Recip Foundation on Sand
Given:
Foundation: 12 ft x 8 ft, D_f = 4 ft
Soil: Medium dense sand, phi' = 30 deg, gamma = 120 pcf
GWT at 20 ft depth (no correction needed)
Step 1: Bearing capacity factors (phi' = 30 deg)
N_c = 30.14, N_q = 18.40, N_gamma = 22.40
Step 2: Shape factors (B/L = 8/12 = 0.667)
s_c = 1 + 0.2(0.667) = 1.133
s_q = 1 + 0.1(0.667) = 1.067
s_gamma = 1 - 0.4(0.667) = 0.733
Step 3: Overburden pressure
q' = gamma * D_f = 120 * 4 = 480 psf
Step 4: Ultimate bearing capacity (c' = 0 for sand)
q_ult = 0 + 480 * 18.40 * 1.067 + 0.5 * 120 * 8 * 22.40 * 0.733
q_ult = 9,426 + 7,876 = 17,302 psf
Step 5: Allowable bearing capacity (FS = 3.0)
q_all = 17,302 / 3.0 = 5,767 psf
Step 6: Check applied pressure
Equipment weight = 50,000 lb
Foundation weight = 12 * 8 * 4 * 150 = 57,600 lb
Total = 107,600 lb
q_applied = 107,600 / (12 * 8) = 1,121 psf
Result: q_applied (1,121 psf) << q_all (5,767 psf) -- OK
Example 2: Settlement Estimate on Clay
Given:
Foundation: 10 ft x 10 ft, D_f = 3 ft
Net applied pressure: q_net = 2,000 psf
Clay layer: 15 ft thick below foundation
C_c = 0.35, e_0 = 0.80, sigma'_0 = 2,500 psf (at midpoint)
Step 1: Stress increase at midpoint of clay
Depth to midpoint = 3 + 7.5 = 10.5 ft below grade
Using 2:1 stress distribution:
delta_sigma = q_net * B * L / (B + z)(L + z)
delta_sigma = 2,000 * 10 * 10 / (10 + 7.5)(10 + 7.5)
delta_sigma = 200,000 / 306.25 = 653 psf
Step 2: Consolidation settlement
S_c = [0.35 / (1 + 0.80)] * 15 * 12 * log10[(2500 + 653) / 2500]
S_c = 0.194 * 180 * log10(1.261)
S_c = 35.0 * 0.1007 = 3.52 in -- EXCEEDS LIMIT
Recommendation: Settlement exceeds 1.0 in limit.
Options: deep foundations, preloading, or ground improvement.
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