Problem. A two-cell reinforced concrete box culvert under earth, water and traffic loads is solved separately with MindFEM and with ETABS. Earth and water pressure are applied as surface loads growing linearly with depth. Moments, displacements and soil reaction are compared for the load cases and for two combinations, with the culvert empty and full.
Reference document. The reference is the same culvert modelled in ETABS 20.1.0 with its own objects. The pressures that vary with depth are given in ETABS as non-uniform area loads.
Numerical model. The wall axes are 3.5 + 3.5 m apart and the slab axes 3.0 m; the outer walls are 0.40 m, the middle wall 0.30 m, the top slab 0.40 m and the base slab 0.45 m thick; the culvert is 10 m long with both ends free, meshed with 0.25 × 0.25 m quadrilateral elements. The base rests on a subgrade of modulus 20 000 kN/m³ vertically and 10 000 kN/m³ horizontally, under 2 m of fill weighing 19 kN/m³; lateral earth pressure uses the at-rest coefficient 0.5, the groundwater is 2.0 m above the base and the water inside is 2.5 m deep.
Two-cell box culvert
Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects
32-row table · largest deviation 1.09%
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| G: total soil reaction [kN] | 4,927.79 | 4,927.79 | < 0.001% |
| G: vertical displacement at top slab mid-span [mm] | -3.85884 | -3.85526 | 0.0927% |
| G: moment at top slab mid-span [kNm/m] | -31.4635 | -31.4476 | 0.0506% |
| G: top slab moment over the middle wall [kNm/m] | 73.3094 | 73.3766 | 0.0918% |
| G: top slab moment at the outer wall [kNm/m] | 10.0839 | 10.0145 | 0.689% |
| G: moment at base slab mid-span [kNm/m] | 43.9292 | 43.8941 | 0.0798% |
| G: base slab moment under the middle wall [kNm/m] | -62.9239 | -63.0077 | 0.133% |
| G: moment at outer wall mid-height [kNm/m] | -19.3147 | -19.268 | 0.242% |
| G: moment at the outer wall base [kNm/m] | -28.6899 | -28.6745 | 0.0534% |
| H: horizontal displacement at outer wall mid-height [mm] | 0.110158 | 0.108962 | 1.09% |
| H: moment at outer wall mid-height [kNm/m] | 20.4697 | 20.4489 | 0.102% |
| H: moment at the outer wall top [kNm/m] | -14.9866 | -14.9998 | 0.0876% |
| H: moment at the outer wall base [kNm/m] | -16.6646 | -16.6746 | 0.0598% |
| Q: total soil reaction [kN] | 700 | 700 | 0% |
| WD: total soil reaction [kN] | -1,400 | -1,400 | 0% |
| WI: total soil reaction [kN] | 1,750 | 1,750 | 0% |
| Empty: total soil reaction [kN] | 4,227.79 | 4,227.79 | < 0.001% |
| Empty: largest soil pressure [kPa] | 64.1941 | 64.158 | 0.0562% |
| Empty: moment at top slab mid-span [kNm/m] | -33.6956 | -33.6888 | 0.0205% |
| Empty: top slab moment over the middle wall [kNm/m] | 75.7272 | 75.7587 | 0.0416% |
| Empty: top slab moment at the outer wall [kNm/m] | 33.8614 | 33.81 | 0.152% |
| Empty: moment at base slab mid-span [kNm/m] | 44.3266 | 44.3019 | 0.0556% |
| Empty: base slab moment under the middle wall [kNm/m] | -67.1666 | -67.2157 | 0.0732% |
| Empty: moment at the outer wall base [kNm/m] | -54.429 | -54.4211 | 0.0145% |
| Full: total soil reaction [kN] | 6,677.79 | 6,677.79 | < 0.001% |
| Full: largest soil pressure [kPa] | 99.1614 | 99.1295 | 0.0321% |
| Full: moment at top slab mid-span [kNm/m] | -28.6856 | -28.6774 | 0.0284% |
| Full: top slab moment over the middle wall [kNm/m] | 67.1373 | 67.1765 | 0.0585% |
| Full: top slab moment at the outer wall [kNm/m] | 21.8454 | 21.7929 | 0.241% |
| Full: moment at base slab mid-span [kNm/m] | 40.2246 | 40.1984 | 0.0651% |
| Full: base slab moment under the middle wall [kNm/m] | -57.7931 | -57.8483 | 0.0955% |
| Full: moment at the outer wall base [kNm/m] | -41.5113 | -41.504 | 0.0177% |
The cross-section at mid-length (y = 5 m), on the wall and slab axes. The moments and displacements are read at the marked nodes. Dimensions are in metres.
Note. The pressures use the coordinates of the mid-planes. Below the water table the earth pressure uses the effective unit weight, so H is the sum of two load patterns: H1 is the pressure of dry soil and H2 the correction below the water. The Empty combination G + H + WD + Q is the culvert empty with groundwater present. The Full combination G + H1 + WI is the culvert carrying 2.5 m of water in a dry season with no groundwater. Both cells are full, so the water pressures on the middle wall balance and it carries no load. The section under the table shows where each row is read. The moments are the mean of the values of the elements sharing the node; Mxx in the slabs and the vertical bending moment in the walls. The ETABS moment sign convention is the opposite of MindFEM's, and the table uses MindFEM's sign. In the Empty and Full combinations the moment at the outer wall mid-height is between 3 and 4 kNm/m and is left out of the table, because its percentage difference grows without meaning.
Model files
The ETABS model that produced the results in the table can be downloaded. It opens in ETABS 20 and
later with File > Import > ETABS .e2k File.