PSI - Issue 33

Anas Ibraheem et al. / Procedia Structural Integrity 33 (2021) 942–953 Anas Ibraheem, Yulia Pronina / Structural Integrity Procedia 00 (2019) 000–000 where � is Young’s modulus of the undrained soil under the foundation; � is the net applied pressure on the foundation; A � is a function of H/B and B ; A � is a function of � ; B is the width of the footing; L is the length of the footing; � is the base level depth; H is stiff stratum depth. Here, the functions A � and A � are detailed by Das (2010, 2011). The elastic settlement of a rigid foundation can be estimated from equation (1). 4.3.2.2. Consolidation settlement. Consolidation settlement occurs due to the expulsion of water from the soil and dissipation of excess pore water pressure. In a clay layer with a thickness of and a void ratio of � , the final consolidation settlement � due to the applied pressure can be estimated by formulas of Das (2009, 2010): 947 6

e

 

S

H

c 



c

1

e

0

 

0    av

log(

)

c e C

 

0

0 s D H       ( f s

1)

2

av    where Δe is the change in the void ratio due to the applied pressure ; � is the soil compression index; � is the average effective pressure on the clay layer before the construction of the foundation; � is the base level depth; � is the unit weight of soil; Δ �� is the average increase in effective pressure on the clay layer caused by the construction of the foundation; �� (detailed by Das (2009)); µ � is the correction factor for three-dimensional effect on primary consolidation settlement (detailed by Das (2009)). 5. Calculation example To solve the foundation–soil interaction problem, we consider simple four-storey structure shown in Fig. 3. The structural beams are of rectangular sections (height is 40cm, width is 25cm). The structural columns are square sections (width is 35cm). The concrete material properties are: Poisson’s ratio is 0.2, compressive strength is 27.58MPa, and modulus of elasticity is 24855.58MPa. The gravity loads on beams are dead load (10kN/m in addition to self-weight). The load pattern (inserted to calculate the settlements) is the dead load pattern. For comparison we created the same models using two methods:  The first method (Fig. 3) with uncoupled springs assigned to the joints located at the base level of the structure;  The second method (Fig. 4) with footings created under the joints located at the base level of the structure. The settlements are calculated according to the relationships of shallow foundations on granular soil (settlement calculation based on theory of elasticity) for sand soil patterns, and the settlements are calculated according to the relationships of shallow foundations in cohesive soils for clay soil patterns. The goal is to calculate the value of settlements in the base of structure according to the two methods, the footing type and the soil pattern in each model being the same. We performed the analysis using three types of square footing:  Type 1 height is 1.6m, width is 1.6m, and thickness is 0.5m.  Type 2 height is 1.8m, width is 1.6m, and thickness is 0.5m. av qI