Raft foundation, comparison with ETABS

Results.

Problem. The raft foundation of a six-storey concrete building with shear walls and a core is solved separately with MindFEM and with ETABS on a Winkler subgrade. Settlements, soil pressure and raft moments are compared under vertical and lateral load cases. In the second example the vertical subgrade springs act in compression only and one edge of the raft lifts under the earthquake load; the third example compares the effect of that uplift with linear springs.

Reference document. The reference is the same raft modelled in ETABS 20.1.0 with its own objects, with the subgrade given as an ETABS area spring.

Numerical model. The column grid is 4 × 6 m in X and 3 × 6 m in Y; the raft extends 0.6 m beyond the axes and is 25.2 × 19.2 m, 0.80 m thick, C30/37, meshed with 0.30 × 0.30 m quadrilateral elements. Two 6 m rectangular walls on the long facades and a 3.6 × 3.6 m lift core with a door opening stand on the raft as one-storey shells; the subgrade modulus is 20 000 kN/m³ vertically and 10 000 kN/m³ horizontally; the loads are G and Q at the column axes and the wall bases, and a lateral load EX given by its shear and overturning moment.

Raft, walls and core#

Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects

Where the numbers are read, the same in all three examples. The moments are read in the marked quadrilateral elements, the settlement and uplift at the marked nodes. The grid is in metres.

Note. The column load is applied to the single node on the column axis. The top edges of the walls are free. The ETABS moment sign convention is the opposite of MindFEM's, and the table uses MindFEM's sign. The subgrade is an area spring in ETABS and nodal springs in MindFEM; building the subgrade with the element shape functions changes the results by less than one per mille. In the element at the column face the difference rises to 1.8 per cent, because under a point load the moment depends on the mesh and the two programs' thick plate elements give different values there. Under EX the corner lies near where the settlement changes sign, and the difference at the corner is 0.015 mm. The plan under the table shows where each row is read.

Raft losing contact with the soil, compression-only subgrade#

Independent calculation. ETABS 20.1.0, the same structure modelled with ETABS's own objects

Note. The structure and the mesh are those of the first example, and the plan under the first example shows where each row is read. The vertical subgrade springs act in compression only in both programs; in ETABS the U3 direction of the area spring is given the compression-only option. The horizontal springs are linear. The base shear of the earthquake load is 16 per cent of the total G. Both cases are nonlinear and each is solved on its own, because the results cannot be added. Under G + Q the whole raft is in contact and the result is that of the first example. Under 0.9G + EX the edge of the raft behind the tension end of walls W1 and W2 lifts. The uplift is the difference between the settlement under 0.9G and the lift under EX, −4.29 mm and +5.53 mm at the edge behind W1. The two programs differ by 0.1 mm in the EX part, and in the small uplift this becomes 9 per cent. The same difference is there when the springs are linear.

Compression-only springs against linear springs#

Compared model. MindFEM, the same raft, linear subgrade springs

Note. This table is not a verification. The same raft under the same 0.9G + EX load, with the earthquake base shear at four levels, is solved in MindFEM once with linear and once with compression-only vertical subgrade springs. The reference column is the result with linear springs, the computed column the result with compression-only springs, and the deviation is the size of the redistribution. Linear springs assume the springs in the lifting zone carry tension; that tension totals 1907 kN at 0.24 G and 9202 kN at 0.40 G. Compression-only springs carry none, and the upward pull at the ends of the walls is carried by the bending of the raft instead of by the ground. The largest soil pressure therefore falls, while the span and column moments in the lifting zone grow several times. At 0.16 G 3 per cent of the raft lifts and the difference stays within a few per cent. At 0.48 G the contact area falls to 43 per cent and the uplift passes 70 mm; that level is left out of the table. The plan under the first example shows where each row is read.

Model files#

The ETABS models that produced the results in the tables can be downloaded. They open in ETABS 20 and later with File > Import > ETABS .e2k File.

• Raft, walls and core (.e2k)
• Raft losing contact with the soil, compression-only subgrade (.e2k)