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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1. Introduction Taking into account the soil behavior under isolated foundations is an important issue during the analysis and design process of frame buildings. That is because additional bending moments of structural elements, originating from differential settlements affect the overall stability of the structure. Conventional analysis and design methods treat structure as independent of foundation as well as the supporting soil. However, in reality, the structure, structural foundation, and supporting soil act as one integral compatible unit; therefore, analysis of the soil–foundation interaction problem is quite essential to study the response of a system. Generally, structural engineers use commercial finite elements software (CSI programs, Autodesk programs, Bentley systems programs). These programs perform the analysis of the foundation–soil interaction problem using the discrete approach described by Das (2011) in which the soil mass is replaced by a finite number of equivalent springs, resulting in the simplest model using this approach. In the mathematical model of the structure, these springs elastically connect the joints to the ground (joints located at the base level of the structure model which called the structure supports). Spring model represents the elastic behavior of foundation on non-cohesive soils (elastic settlements), but does not represent the behavior of foundation on cohesive soils (consolidation settlements). Our solution to the foundation–soil interaction problem is based on analysis assuming a rigid base connection between the joints and the ground, and calculating the foundations settlements according to the resulting forces. These settlements can be calculated by theoretical and experimental equations introduced by Das (2009, 2010, 2011), and expressed as vertical translation values in the ground joints (structure supports). Then we reanalyze the structure using iterative process by introducing the effect of these translations. This method allows introducing the effect of foundations settlements on cohesive soils (elastic and consolidation settlements) in analysis and design. 2. Overview of the Program The presented program performs the analysis of the foundation–soil interaction problem in two ways:  Foundations may be modeled as flexible-base foundations using uncoupled spring model (discrete approach) described by Das (2011).  Using a new procedure that takes into account the influence of foundation settlements in the analysis and design. The program allows the user to define different models of foundations. In each model, the dimensions, thickness, footing material, embedment depth and the soil pattern under the footing must be predefined. In the soil pattern, the basic parameters such as weight per unit volume, bearing capacity, modulus of elasticity, shear modulus, Poisson’s ratio, stiff stratum depth, initial void ratio, recompression index, compression index, pore water pressure parameter, and friction angle must be given. 2.1. Formation of the stiffness matrix of fixed beam elements In order to calculate the deformed shape and the internal forces (moments, shear forces, axial forces) in the structural elements using finite elements method, the program first calculates the 3D elastic stiffness matrix [k] for frame elements including shear and bending effects in local coordinates, and then assemble the general stiffness matrix of the structure according to Bathe (1996) finite element procedure. Using direct solver (sparse Cholesky skyline decomposition by Dereniowski et al. (2003)), it solves the system of linear equations to calculate the displacements. 2.2. Designing using the program The program designs the frame elements according to American Concrete Institute and Computer and Structure Inc. standards (ACI 318M (2014), CSI (2016)) using the load and resistance factor design (LRFD). Beams elements