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24 in pipe under 8 ft of cover with an H-20 wheel: Marston trench load, D-load of a concrete pipe, Iowa deflection and buckling of a steel pipe

Tool	Buried Pipe Loads
Source	Soil Conservation Service (1958). The Structural Design of Underground Conduits. Technical Release No. 5, U.S. Department of Agriculture, Washington, DC (eqs 1-1, 1-4 to 1-6a). U.S. Army Corps of Engineers (1997). Conduits, Culverts, and Pipes. Engineer Manual EM 1110-2-2902, Washington, DC (Figure 2-5, eqs 3-2, 6-3, 6-7). Bureau of Reclamation (2019). Method for Prediction of Flexible Pipe Deflection, 3rd ed. M-25, Denver, CO (eq. 3.1, Table 5, Appendix E). Naval Facilities Engineering Command (1986). Soil Mechanics. NAVFAC DM-7.01, Alexandria, VA (Figure 18(e), eq. 4-2).
Level	Professional

Problem

A 24 in pipe lies under 8 ft of cover in a 4.5 ft wide trench backfilled with ordinary clay (120 lb/ft³) and is crossed by an H-20 wheel. Find the earth and live loads, the three-edge-bearing D-load a concrete pipe with a 3 in wall needs on Class B bedding, and the deflection, ring compression and buckling of a steel pipe with a 3/16 in wall in moderately compacted clean sand.

Inputs to Enter

Trench installation: inside diameter 24 in, cover 8 ft, trench width 4.5 ft, soil 120 lb/ft³, ordinary clay Kμ′ 0.130; embankment values Kμ 0.19, settlement ratio 0.7, projection ratio 0.7; no ground water
Live load: H-20 / HS-20 wheel, 16,000 lb on a 10 in by 20 in print, highway impact rule of Reclamation M-25 (1.0 at 8 ft)
Rigid pipe: wall 3 in (B_c 30 in), Class B bedding, load factor 1.9, factor of safety 1.25, pipe D-load 1,350 lb/ft per ft (ASTM C76 Class III), 150 lb/ft³
Flexible pipe: steel wall 0.1875 in, E 29,000 ksi, F_y 36 ksi; Class II embedment at 85 to 95 percent compaction, E′ 2,000 lb/in², F_d 0.75, T_f 2; D_L 1.5, K 0.1, limit 5 percent, prism load; factors 2.0 on crushing and buckling, B′ = 1
Flotation factor 1.5; bend of 45° at 100 lb/in², soil bearing 2,000 lb/ft², block factor 1.5

Open the Buried Pipe Loads tool (loaded with this example)

Answers

Trench load: H/B_d = 1.778, C_d = [1 − exp(−2 · 0.13 · 1.778)]/0.26 = 1.4235, W = 1.4235 · 120 · 4.5² = 3,459 lb/ft
Embankment load: H_e/B_c = 1.458, C_p = 4.9795, 3,735 lb/ft; transition width 4.795 ft, so the trench load governs: W_E = 3,459 lb/ft (prism load 2,400 lb/ft)
Live load: Newmark coefficient I = 0.0026, crown pressure 0.820 lb/in² (118 lb/ft²), mean across the pipe 116 lb/ft², W_L = 289 lb/ft
Required D-load (3,459 + 289) · 1.25 / (1.9 · 2.0) = 1,233 lb/ft per ft against 1,350: satisfied, factor of safety 1.37
Steel pipe: EI/r³ = 9.006 lb/in², prism pressure 6.667 lb/in²; Iowa deflection 0.1 · (1.5 · 6.667 + 0.820)/(9.006 + 122.0) = 0.83 percent; Reclamation equation 1.41 percent
Ring compression 487 lb/in² against 18,000; buckling q_cr = 268.4 lb/in², allowable 134.2 against 7.49 lb/in²
Flotation with water at the surface: factors 4.63 (concrete) and 4.87 (steel); minimum cover 1.35 ft and 2.18 ft
Thrust at the bend 2 · 100 · 452.4 · sin 22.5° = 34,624 lb; block bearing area 25.97 ft²; the total pressure on the pipe is least near 4.2 ft of cover

Notes

The tool's default inputs are this case; press Submit. The case is illustrative, not a printed example. Checked by test_buried_pipe_loads.php (1,245 checks) against the worked example of SCS Technical Release 5 (C_d 2.92, C_p 15.13, 22,240 lb/ft), the Appendix B examples of EM 1110-2-2902, the Appendix A examples and the live-load tables of Reclamation M-25, and an independent numpy / scipy evaluation.