Finite element modeling of masonry wall with mortar 1pc : 4 lime : 10 sand under lateral force

This paper gives a detailed presentation of three-dimensional Finite Element Model that has been constructed for Masonry Wall under lateral force by using Abaqus software. This research aimed to investigate the behavior of Masonry Walls under lateral force and developed load-displacement curve. From the result that The numerical model using the Abaqus Software can represent the load-displacement curve of Masonry Walls due to lateral forces, Numerical Results with the Abaqus Software obtained that the magnitude of the load on condition of Plastic is 82.13 KN and experimental results obtained of 81 KN. There is a difference of 1.4%, Based on Abaqus Software with Numerical results obtained a compressive strength of masonry wall f'm = 1.8 MPa with a modulus of elasticity = 150 MPa, Calculation of the natural frequency of structures with Abaqus Software is obtained as the difference of 2.13-2.92% with the test results Hakas (2017)


Introduction
When structure receives earthquake, the biggest damage is non-engineering structure. Masonry Wall in their planning are often not calculated. Research on Masonry structure that receives the lateral force has been done, Boen (1994), P2KP (2006) and Siddiq (2004) examined the walls of unfettered with beam column with lateral force to find out an acceptable load by the wall. Hakas (2017) researched the prediction lateral in a plane through changes natural frequency and the damping of the structure of Masonry Wall ½ brick with mortar 1 Pc: 4 Lime: 10 Sand. Satyarno (2008) researched Masonry strength due to static and cyclic load.
The Finite Element Method has been widely used by researchers to analyse Masonry walls, the researchers using the Finite Element Method in analysing Masonry walls such as Stavridis and Shing (2010)  The aims of this research are to comprehensively investigate the behavior of Masonry Walls with ½ brick 1 pc: 4 Lime: 10 sand due to lateral force with (1) 3dimensional modeling using ABAQUS Software. (2) Find the load and displacement Curve, (3) The compressive strength of masonry wall (4) Find the modulus of elasticity of walls. The results of this modeling are compared with a study conducted by Hakas (2017) 2 Experiment Model Experiment Model Tests are 1:1 scale Masonry wall with dimensions of 3 x 3 x 0.15 m placed on reinforced concrete slabs. The masonry walls contain concrete frames with beam and column sizes of 0.15 x 0.15 m and there are plastering on both sides with a mortar of 1PC: 4 Lime: 10 sand. With 2 cm thick. The details of the reinforcement can be seen in Figure 1.
Models of Masonry was given lateral load gradually with the stages of loading which can be seen in table 1. Laboratory test was carried out on the structure of the Faculty of civil engineering of GADJAH MADA UNIVERSITY. The test settings can be seen in Figure 2.

Structural Modelling
Masonry walls are modeled using ABAQUS software, geometric details, loads and materials applied to Abaqus software described below:

Geometric and load modelling
A masonry wall with mortar was modeled with a homogeneous material. Used constrain tie to connect between the Masonry walls and concrete. Reinforcement is modeled using 2 nodes, linear truss element and embedded in concrete material performed, measure displacement is done in line with the lateral load and do unrestrain in some direction of load and restrain in another direction. Figure 3 shows the masses in modeling.
The loading of the Abaqus software is given in accordance with the experimental test results, the lateral force is given at a distance of 50 cm from the top of the masonry wall (See Figure 4).

Material in The Abaqus Model
Data Material of concrete and reinforcing used for the modeling in accordance with the results of material testing. Material data used can be explained as follows:

Steel for reinforcement.
Steel for reinforcement used grade U39 for the diameter of 8 and a diameter of 6. Figure

Masonry
For the calculation of compressive strength masonry walls using T. Paulay et al (1991). where parameters used are the size of a brick, the distance between the thicknesses of the mortar, compressive strength of brick, compressive strength of mortar. Equations used for calculation are: Where:   Table 3. Compressive strength of masonry walls

Modulus of Elasticity Of Masonry
Based on the compressive strength of the Masonry wall then determined the modulus of elasticity masonry wall based on Table 2 and the following results are obtained: Based on the Compressive strength and elastic modulus of masonry wall then compared with experimental results in the laboratory, Figure 7 shows the comparison of Load-displacement curve with a various modulus of elasticity variance with laboratory test result 90 KN lateral load Based on Figure 7 it can be seen that the elastic modulus of the experimental results has a lower value compared to the rules contained in Table 4 Figure 8 shows the load-displacement ratio between the Abaqus results and the Hakas experiment on the lateral force of 90 KN. From the Figure 9 can be seen that the experimental results of the test object experienced plastic condition at 81 KN load and Abaqus results obtained began to experience plastic conditions at the load 82.13 KN there is a difference of 1.4% between the experimental results and the Abaqus results.

Natural Frequency
Based on an analysis using Abaqus obtained results defined for some conditions, Figure 11 shows the natural frequency is defined on the structure of a brick wall without Load condition, it can be seen that the greatest frequency is 39, 6255 Hz. Figure 12 shows a graph of the frequency due to the imposition of 90 KN, of graphs can be seen that the frequency of 33.12 Hz. And Figure 13 shows a graph of the frequency due to the imposition of 70 KN, it can be seen that the natural frequencies of structures are 37.72 Hz, and in Figure 14 Table 5: Table 5. Natural Frequency of masonry wall Based on Table 5 it can be seen that there is a difference of average 2.47% from Abaqus program results and experimental results Hakas (2017).

Conclusions
Based on the results of this research, using integrated modeling Finite Element Models of a masonry wall with the Abaqus software. The obtained results are discussed: