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Settlement is an important criterion in the design of the foundations. It is classifying into immediate (or elastic) settlement and consolidated settlement (primary and secondary). The factors that affect the shallow foundation settlement are the applied loads, soil stiffness, and geometric shape of foundation. Calculations of settlement depend on the parameters of soil which can be obtained from field and laboratory tests. Field and laboratory tests were conducted for twenty three sites in three different regions in Iraq (Mosul, Baghdad, and Basrah). In this research, field and laboratory tests results adopted for two sites from each region depended on the maximum and minimum bearing capacity values. Settlement for each site was calculated using numerical (mathematical) calculations and PLAXIS software under different added loads. The results of settlements beneath the foundation were competing for the sites with maximum value of bearing capacity in Mosul; Baghdad and Basrah. Also, the comparison conducted for sites of minimum bearing capacity value and the results showed different settlement values of each site. The change of settlement values under different loads was linearly in the six sites using numerical (mathematical) calculations. While, the settlement values obtained from PLAXIS software for sites with maximum bearing capacity value showed that Mosul site had the highest value due to the type of soil layers and the difference models of soil used in the software. Basrah site had a settlement value higher than Baghdad site due to the soil layers of sand type only. PLAXIS results for sites with minimum bearing capacity showed that for Basrah site the soil went to failure. While, the settlement values for Mosul and Baghdad sites were close to each other due to have nearly same soil layers. Therefore, high rise buildings could not be used in some sites. Also, soil in some locations and under some added loads needed to be improved before the implementation of any constructions.

Settlement is an important criterion in the design of the foundations. Foundation settlement must be estimated carefully to ensure stability of buildings, towers, bridges, and any high cost structures. The main reason for the settlement occurrence is the compressive deformation of the soil. According to [

• Immediate (or elastic) settlement: It takes place rapidly after adding loads without any change in the moisture content and volume.

• Consolidation: This type includes two phases:

1) Primary consolidation phase: This phase is a consolidation settlement results from the change of volume due to water extrusion from soil voids. It occurs in saturated cohesive soils and the change happens slow and takes place over a long period of time.

2) Secondary consolidation phase: This phase is compression settlements which consider as a plastic adjustment observe in saturated cohesive soils. It is an extra deformation of soil occurs due to constant adding loads. It follows the primary consolidation phase.

The major factors affect shallow foundation settlements are: applied loads, soil stiffness, width, depth, and shape of foundation [

Foundation settlement (immediate, consolidation) are estimated depending on the calculating stresses in the mass of the soil related to foundation pressure. The settlements and stresses distribution and their values are calculating with the assumption that soil model is homogeneous, isotropic, and linearly elastic. They are playing an important role in the foundations design [

Immediate settlement usually estimates according to elastic theory, which assumes that the soil may behave elastically under stresses at any point in soil mass. There are usually three types of methods to calculating the elastic settlement [

Empirical methods: They are depending on observation settlement of structure and full scale prototypes. They are depending on correlations of the results from the standard tests in situ such as the cone penetration test (CPT) and the standard penetration test (SPT). Moreover, they contain steps improved by Terzaghi and Peck (1948, 1967), Meyerhof (1956, 1965), DeBeer and Martens (1957), Hough (1969), Peck and Bazaraa (1969), and Burland and Burbidge (1985) [

Semi-Empirical methods: They are based on the integration of the theoretical studies and the field observations. The methods contain steps outlined by Schmertmann (1970), Schmertmann et al. (1978), Briaud (2007), and Akbas and Kulhawy (2009) [

Theoretical relationship methods: They are relating to the theory of elasticity. The settlement calculations depend on the modulus of elasticity (E_{s}) [

The consolidated settlement is estimating from the consolidation test (Triaxial or oedometer). These tests are the way of estimating the magnitude and time of consolidation to obtain settlement for normally consolidated and over consolidated cohesive soils [

The objective of this paper is evaluating shallow foundation settlement under different added loads in three regions of Iraq (Mosul northern, Baghdad central, and Basrah southern parts). The evaluations were conducted using numerical (mathematical) calculations and finite elements (PLAXIS 2D) models. The work was conducted by collecting samples from different sites in the three regions of Iraq. And the behaviour of soil layers is evaluated under the different added loads.

The study areas were located in Mosul northern, Baghdad central, and Basrah southern parts of Iraq (

• Mosul region situated in the northern part of Iraq. It is occupying part of the foothill zone and north part of Al-Jazira zone (

3 m depth [

• Baghdad region is the capital of Iraq, situated in the upper part of Mesopotamian plain (

• Basrah region situated in the lower part of Mesopotamian plain southern of Iraq. The sediments of this plain

are related to the Quaternary period. Multi-sources of sediments have been classified as fluvial, deltaic and marine. These sediments are of economic value because they used in constructions. Most of the sediments of fluvial type and composed of sand, silt and clay. Tigris and Euphrates Rivers were the main sources of these sediments, also contain carbonates and gypsum grains. The ground water table in Basrah region is less than 1 m to less than 5 m [

Samples were taking from the three regions of Iraq (Mosul, Baghdad, and Basrah). Boreholes drilled to different depth ranges between 3 m to 24 m depend on depth of dense soil layers, to obtained disturbed and undisturbed samples from all sites.

Different types of tests conducted for these samples to define the soil classification and mechanical properties. The tests were: physical test, index properties (Atterberg limits and grain size), shear strength test (direct shear and unconfined compression), and oedometer test. Two sites selected from each region (Mosul, Baghdad, and Basrah) depended on the bearing capacity value (maximum and minimum) obtained from the field and laboratory tests [

Computations of soil settlement under different added loads for the three regions of Iraq conducted and explained in the following sections:

The analytical calculations were conducted based on the oedometer tests for cohesion soil layers. While, for cohesionless soil layers the immediate settlement calculations were conducted based on the SPT field tests:

1) The calculations of consolidated settlement were depending on a plot of the void ratio (e) against (log scale) effective pressure (σ'), which is obtaining from oedometer test [

From curves shown in Figures 3-5: the compression index C_{c}, swelling index C_{s}, and void ratio e values were obtaining. Boussinesq equation used to determine the effective stress at the corner of rectangular foundation Δσ' (KPa) for the different layers of soil mass of 75 m depth. The following equation used to calculate the normal

Region | Location | No. of samples | Depth (m) |
---|---|---|---|

Mosul | Al-Hamedat | 3 | 1, 2, 3 |

Al-Rashidia | 3 | 1,2, 4 | |

Baghdad | Al-Karada | 4 | 2, 4, 8, 13 |

Al-Jadrea | 4 | 2, 4, 8, 13 | |

Basrah | Al-Rumaila | 3 | 1, 5, 10 |

Al-Hartha | 4 | 2, 6, 13, 24 |

consolidated cohesion soil [

where: S_{c} = consolidated settlement (mm).

H = thickness of soil layer (m).

For overconsolidated cohesion soil the following equations used [

2) The immediate or elastic settlement for cohesionless soil layers carried out using the following formula which depends on Standard Penetration Test (SPT). This test was performed in the fields. The calculations assumed that the foundation is flexible [

where: S_{e} = immediate settlement for flexible foundation (mm).

μ' = Poisson’s ratio.

I_{s} = influence factor.

B = width of foundation (m).

q_{o} = applied pressure (kPa).

E_{s} = Young’s Modulus of Elasticity (kPa).

The immediate settlement of a rigid foundation estimated according to the following formula [

The Young’s modulus of elasticity of soil obtained from the following equation [

where: N = the value of blows of SPT test.

The influence factor calculated from the following formula:

where:

Poisson ratio of soil (μ') calculated according to the following relation [

All the calculations were done for the six sites under different loads of values 56; 63.5; 68; 75 and 93 kPa. Theses loads present the dead and live load for buildings with two, three and four stories, respectively.

The finite element method is the most used method for analysis in engineering works. PLAXIS 2D software is a finite element tool which is used for geotechnical works. In view of the fact that soil is a material behaves differently under loading, unloading and reloading [

Estimation of settlement under foundation for different loads conducted using numerical (mathematical) calculations and PLAXIS software. The equation used in the numerical calculation was the Boussinesq equation for the

Soil parameters | Mosul Region Hamedat Rashidia | Baghdad Region Karada Jadrea | Basrah Region Rumaila Hartha | |||
---|---|---|---|---|---|---|

Material model | HS | HS & MC | HS & MC | HS & MC | MC | HS & MC |

Unsaturated weight (γ_{unsat}), kN/m^{3} | 19 | 19, 20 | 20,21, 19 | 18 | 17.55, 18.7, 19.66 | 18.6, 19, 19 |

Saturated weight (γ_{sat}), kN/m^{3} | 20 | 23, 24 | 20, 21, 19 | 19, 20 | 17.55, 18.7, 19.66 | 23, 23.4, 25 |

Compression index (C_{c}) | 0.126 | 0.21 | 0.0156 0.109 | 0.108 | − | 0.191, 0.224 |

Swelling index (C_{s}) | 0.019 | 0.022 | 0.054 0.027 | 0.0067 | − | 0.029, 0.027 |

Initial void ratio (e) | 0.650 | 0.677 | 0.647 0.455 | 0.741 | − | 0.8, 0.93 |

Modulus of elasticity (E), kN/m^{2} | − | 32,500 | 32,167 | 32,500 | 26,833 32,500 | 32,500 |

Passion’s ratio (μ') | − | 0.35 | 0.35 | 0.37 | 0.31, 0.28, 0.26 | 0.36 |

Cohesion (C), kN/m^{2} | 40 | 0 | 185.3 | 38 | 4, 2, 0 | 12 |

Friction angle (ϕ˚) | 20 | 28 | − | − | 33, 38, 41 | 26 |

Dilatancy angle (ψ˚) | − | − | − | − | 3, 8, 11 | 0 |

purpose of the calculated settlement in each layer of soil. Equations (1)-(3) used to calculate the consolidation settlements for cohesion soil layers. The immediate settlement was calculated using Equations (4)-(8) for cohesionless soil layers. The Hardening Soil (HS) model was used in PLAXIS for cohesion soil layers. And Mohr- Coulomb (MC) model was used for the cohesionless soil layers. All the results were obtained from the two methods as following:

The results obtained from numerical calculations were performed by dividing mass of soil into layers. The data depended on the field and laboratory tests and the groundwater level was taking into consideration through the calculations of

The results shown in

The same soil properties and type of foundation used in the numerical calculations also used for PLAXIS model. The data used in the programme shown in

Whilst, the results obtained from PLAXIS software for Basrah region (Al-Rumaila and Al-Hartha) illustrated in

All the sites in the three regions were consisting of soil layers of cohesion and cohesionless type except two

sites. Al-Hamedat (Mosul region) which was completely consisting of cohesion soil (brown clay) and Al-Ru- maila (Basrah region) was completely consisting of cohesionless soil (sand). Also, the differences in layers of the soil obtained various behaviours under the added loads.

The results obtained from the PLAXIS software were depended on the elastic-plastic behaviour of the soil layers under different added loads. The level of groundwater was stated in the model of each site. Soil parameters which obtained from the experimental tests (field and laboratory) used in the software. The settlement values were affected according to the water content and grain size of the soil that is change depending on the geology and climatic of the locations. The models of soil used in the software were: Hardening soil (HS) and Mohr Coulomb (MC). HS model depends on the stiffness parameter of the soil obtained from the oedometer tests. MC model depends mainly on the elastic parameters are the Modulus of elasticity and the Poison’s ratio of the soil. The results presented in

software for the different sites in the three regions. The comparison show that the values of settlements in

The results obtained from PLAXIS were higher than vales obtained from mathematical calculations for all sites in the three regions for different reasons such as the difference of the soil models used for the different sites HS and MC. For some sites, both HS and MC models were used. While, for other sites used only HS model or only MC models.

Numerical (mathematical) and finite element (PLAXIS) methods are means depending on the field and the la- boratory tests. They used to estimate the settlement values beneath foundation for different added loads. The results obtained from the numerical (mathematical) calculations for the six sites in the three regions and under different loads were increases linearly. The difference of settlement values was depending on the soil layers types, water table depth and bearing capacity values. PLAXIS models were an approximation of the reality. The results obtained from PLAXIS software showed the approximate real behaviour for the soil under different loads. The software was using soil parameters of stiffness and strength, depending on the elastic theory and clarified the elastic-plastic behaviour of the soil layers. PLAXIS results were explaining that soil in some sites of the three regions needed to be improved before implementation of any buildings. Finally, the numerical (mathematical) calculations for the settlement values showed that some sites were not suitable for high rise buildings. Whilst, PLAXIS software results of settlement values under different loads were not linearly for some sites depending on the layers type and compressibility of soil and ground water level. Also, it shows almost the realistic

behaviour of the soil under load. PLAXIS software is a good tool which must be used to explain the deformation and soil behaviour under different loads.

Entidhar Al-Taie,Nadhir Al-Ansari,Sven Knutsson, (2016) Evaluation of Foundation Settlement under Various Added Loads in Different Locations of Iraq Using Finite Element. Engineering,08,257-268. doi: 10.4236/eng.2016.85022