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

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4.2. The calculation scheme In this method a new load pattern is defined which named SETTLEMENT. In this pattern the user selects the load combination of LIVE and DEAD loads that will be used for calculating the settlements. For example, the settlements of the foundations can be calculated based on the forces (base reactions) resulted from 100% of dead loads and 25% of live loads (related to dead load value). Here, the dead loads include self-weight, cover loads, cladding etc.; and the live loads include weight of people, weight of furniture etc. The program analyzes the structure under the influence of the selected load combination within the SETTLEMENT load pattern, and calculates the displacements in the ground joints of the structure (the structure's supports). The program then assigns these displacements in the ground joints and analyzes the structure under the influence of these displacements only, calculates the internal forces and the deformed shape of the structure, and stores these values within the results data of the SETTLEMENT load pattern. This method allows introducing the effect of settlement of footings on sandy soils (elastic settlement) and on clay soils (elastic and consolidation settlement), which is an option that does not exist in other programs. The calculation scheme is depicted in Fig. 2. 4.3. Relationships used in this method There are several methods in the geotechnical literature (theoretical and experimental) for the prediction of the settlement of footings on several types of soil described by Das (2009, 2010, 2011). They are all related to the characteristics of the underlying ground soil, the applied loads, and the dimensions of the footing that have been chosen. 4.3.1. Shallow foundations on granular soil (settlement calculation based on theory of elasticity). 4.3.1.1. Elastic settlement of flexible and rigid foundations. The elastic settlement of a shallow foundation can be estimated by using the theory of elasticity. Theoretically, if the foundation is perfectly flexible, the settlement for center of foundation may be expressed as (see Das (2010))

(2 ) 1 s S q B I I E    s f e

where q is the net applied pressure on the foundation; ν is Poisson’s ratio of the soil; � is the average modulus of elasticity of the soil under the foundation; I � , � are the shape and depth factors (detailed by Das (2010));. The elastic settlement of a rigid foundation can be estimated as (see Das (2010))

0.93

S

S



(1)

( e rigid

)

( e flexible

)

4.3.2. Settlement of shallow foundations in cohesive soils. 4.3.2.1. Elastic settlement (immediate settlement). Elastic settlement is instantaneous, i.e. it occurs immediately after the load is applied. The average immediate settlement under a flexible footing on saturated clay soils generally is estimated using the theory of elasticity, using the following equation of Das (2010):

0 u S q B A A E  1 2 e