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Open Journal of Geology, 2017, 7, 731-743 http://www.scirp.org/journal/ojg
ISSN Online: 2161-7589 ISSN Print: 2161-7570
Probabilistic Analysis of Shallow Foundation Settlement considering Soil Parameters Uncertainty Effects
Mahmoud Nazarzadeh, Soheil Sarbishe-ee
Department of Civil Engineering, Geotechnical, E-Campus Branch, Islamic Azad University E Campus, Tehran, Iran
Abstract One of the most important challenges in the design of the foundation of the Earth layer below the surface is the Summit Foundation, which can be a very large impact on the sustainability and the structure of the desired user. Based on this analysis and design criteria of two successive ruptures (load bearing) and settlement, due to the nature of non-homogeneous soil and its parameters uncertainty, relying on one number as the amount of foundation settlement doesnt seem logical. This is while in the methods of the probability distribu-tion function by taking the probability for each of the input parameters, or the characteristics of each parameter, the parameter values are likely to have the chance of occurrence. In this research, effort is made using the method of probabilistic Monte Carlo simulation, the effect of the uncertainty of parame-ters influencing the mechanical behavior following the successive layers of earth and examined. In the event that non-deterministic model input va-riables for describing, not non-deterministic model output as well. So the output of each method to analysis of the concept of the probability distribu-tion function for the input variables is a function of the probability distribu-tion for the target function. In this study, the reliability of the settlement for the three modes of settlement center, corner of rigid foundation is fitted with two types of normal probability distribution and the log-normal distributions. For this purpose, the parameters of the effect of the transition on the analy-sis of soil modulus of elasticity of foundation, such as settlement and the coefficient of Poisson ratio distribution in probability using probabilistic log-normal and normal have been considered. Analysis indicated that the set-tlement in the center of the wake is flexible critical than the other two and has a higher probability of occurrence of the settlement in this part of the founda-tion. In the case of the normal distribution and the normal distribution graph of the log was used, the probability density function of the normal distribution is related to the log has a greater dispersion.
How to cite this paper: Nazarzadeh, M. and Sarbishe-ee, S. (2017) Probabilistic A- nalysis of Shallow Foundation Settlement considering Soil Parameters Uncertainty Effects. Open Journal of Geology, 7, 731- 743. https://doi.org/10.4236/ojg.2017.75049 Received: March 3, 2017 Accepted: May 24, 2017 Published: May 27, 2017 Copyright 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/
Open Access
DOI: 10.4236/ojg.2017.75049 May 27, 2017
http://www.scirp.org/journal/ojghttps://doi.org/10.4236/ojg.2017.75049http://www.scirp.orghttps://doi.org/10.4236/ojg.2017.75049http://creativecommons.org/licenses/by/4.0/
M. Nazarzadeh, S. Sarbishe-ee
Keywords Settlement Foundation, Reliability, Uncertainty, The Log-Normal Distribution, Normal Distribution
1. Introduction
One of the major challenges in designing shallow foundations is subsidence of layers of earth under the foundation that can have a huge impact on the stability and use of the structure in question. Accordingly, in the analysis of foundations, failure criteria (bearing capacity) and subsidence are used [1]. Monte Carlo si-mulation method for the determination of model uncertainty, a little bit for each of the input random variables is a function of the probability distribution is con-sidered.
In these analyses, in the first case, the amount of force that the foundation can transfer to the layers of subsoil, or the maximum bearing capacity of the subsoil should be determined, and in the second case, maximum subsidence happened in the subsoil should be determined using the effective parameters [2]. In the de-signing foundation, usually the subsidence determined is more critical than the force that foundation can transfer to the subsoil. As a result, usually in designing foundation, subsidence will be decisive [2]. This kind of simulation is uncertain-ty in different aspects of the issue clearly show slightly. Monte Carlo methods to quantify uncertainties in model, a probability distribution function for each in-put random variables is considered. If uncertain input variables as described in the model, the model outputs are necessarily uncertain. The output of each me-thod for analyzing the concept of probability distribution function for input va-riables using a probability distribution function for the objective function [3].
2. Problem Statement
The load of a building is borne by the foundation and in some cases is trans-ferred to the soil and borne by soil layers. Given that in case of failure of this part of the structure, there is less possibility to repair, rebuild, etc., designing of this part of the structure must be done with great precision [4].
Normally, by carrying out a few tests, the mechanical parameters affecting soil behavior are determined at some points and by averaging the analyses are made based on these parameters [3]. The other method is using probabilistic methods and combining them with geotechnical engineering analysis methods. In these methods, the effect of all possible parameters will be included in the calculations, so analyses precision will increase and share of all the errors will be considered in these analyses [5].
In this research, effort will be made to use probabilistic Monte Carlo simula-tion method to assess the effect of uncertainties parameter affecting the me-chanical behavior of successive layers of earth underneath. This is a kind of si-
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M. Nazarzadeh, S. Sarbishe-ee
mulation where uncertainty in various aspects is shown clearly and quantita-tively [6]. In Monte Carlo method, a probability distribution function is consi-dered for each input random variable to quantify uncertainties in the model. If the input variables are described as uncertain, model outputs are necessarily un-certain [7]. Thus, the output of each method that uses the concept of probability distribution function for analyzing for the input parameters will be a probability distribution function for the objective function [8].
2B3. Review of Literature
Studies by Griffith et al. In this paper, a study is conducted to investigate the probabilistic bearing ca-
pacity of strip foundations on the earth without weight by using the theory of random field. Modeling is done in two forms: (Figure 1), in a case, strip founda-tion is used and in another case, two strip foundations are considered in parallel [9].
Stochastic finite element method has been used in this article. This method is a combination of finite element method, random field theory, and probabilistic Monte Carlo simulation method. Soil shear strength is considered in probabilis-tic form by using lognormal probability distribution [9].
The study by Fenton et al. In this article, the reliability of subsidence under foundation has been ana-
lyzed in three-dimension mode. For this purpose, the modulus of elasticity of the soil is considered using the probability distribution of normal log [9]. The sub-sidence under single and double square foundations has been determined using
Figure 1. Models studied [9].
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three-dimensional finite element method. The model used in the analysis is pre-sented in the (Figure 2) below [10].
Using limited random running method the desired results are determined and compared with the results provided by the Monte Carlo method [1]. Determined probabilistic distribution for th

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