Chapter 6: Design of Foundations 79 6.1 INTRODUCTION The substructure or foundation is the part of a structure that is usually placed below the surface of the ground. Footings and other foundation units transfer the loads from the structure to the soil or rock supporting the structure. Because the soil is generally much weaker than the concrete columns & walls that must be supported, the contact area between the soil & the footing is much larger than that between the supported member & the footing. The more common types of footings are illustrated in figure (6.1). Strip footings or wall footings display essentially one-dimensional action, cantilevering out on each side of the wall. Spread Footings are pads that distribute the column load to an area of soil around the column. These distribute the load in two directions. Sometimes spread footing have pedestals, are stepped, or are tapered to save materials. A pile cap transmits the column load to a series of piles, which in turn, transmit the load to a strong layer at some depth below the surface “hard strata”. Combined footings transmit the loads from two or more columns to the soil. Such a footing is often used when one column is close to a property line. A mat or raft foundation transfers the loads from all the columns in a building to the underlying soil. Mat foundations are used when very weak soils are encountered. The choice of foundation type is selected in consultation with the geotechnical engineer. Factors to be considered are: • The soil strength, • The soil type, • The variability of the soil type over the area and with increasing depth, and • The susceptibility of the soil and the building to deflections. The most basic and most common types are strip, spread, combined footings. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi Chapter 6: Design of Foundations 80 Figure 6.1: (Types of Footings) The two essential requirements in the design of foundation are that the total settlement of the structure be limited to a tolerably small amount and that differential settlement of the various parts of the structure be eliminated as nearly as possible. With respect to possible structural damage, the elimination of differential settlement, i.e., different amounts of settlement within the same structure, is even more important than limitations on uniform overall settlement. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi in some multi-story structures with basement and in retaining walls. As a general rule of thumb. overhead water tanks. etc. earthquake design. Chapter 6: Design of Foundations 81 To limit settlements as indicated. Because mats are monolithic. • Spread the load over a sufficiently large area of that stratum to minimize bearing pressure. The same is true of mats on highly expansive soils to prone to differential heaves. they are much easier to waterproof. The structural continuity & flexural strength of a mat will bridge over these irregularities. due to the heavy load. so waterproofing is an important concern. 9 The soil is very erratic & prone to excessive differential settlements. and some of the previous provisions the mat foundation might be used. A raft foundation is also called as mat foundation. A shallow single Foundation unit that supports all columns & walls of a structure or parts of a structure may be called a raft foundation. The raft foundation is usually designed as a flat slab. 9 The uplift loads are larger than spread footings can accommodate. the structural continuity and flexural strength of the mat will absorb these irregularities. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . 9 The structural loads are erratic. 9 Lateral loads are not uniformly distributed through the structure and thus may cause differential horizontal movement in spread footing or pile caps. etc. and thus increase the likelihood of excessive differential settlement. chimneys. A raft foundation becomes unavoidable in submerged structure. The continuity of a mat will resist such movements. Again. In this project. The weight of the mat also helps resist hydrostatic uplift forces from the groundwater. it is necessary to: • Transmit the load of the structure to a soil stratum of sufficient strength. Foundation engineering often consider mats when dealing with any of the following conditions: 9 The structural loads are so high or the soil conditions so poor that spread footings would be exceptionally large. They are usually provided for multi-story buildings. if spread footings would cover more than about one-third of the building footprint area a mat or some type of deep foundation will probability be more economical. and 9 The bottom of the structure is located below the ground table. The greater weight and continuity of a mat may provide sufficient resistance. chimneys.supported mats. (T).3: (A Pile or Shaft – Supported Mat Foundation) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . the thickness. Mats are also to support storage tanks and large machines. Typically. Although most mat foundation are directly supported on soil. sometimes engineers use pile –or shaft. is 1-2 m (3-6 ft). these foundation are often called piled rafts. and other types of tower structures.2: (a Mat Foundation Supported Directly on Soil) Figure 6. so mats are massive structural elements. as are soils. and they are hybrid foundations that combine features of both mat and deep foundations. Figure 6. Chapter 6: Design of Foundations 82 Many buildings are supported on mat foundations. Although this type of analysis is appropriate for spread footings.2 RIGID VS. They can be divided into two categories: RIGID METHOD & NON-RIGID METHODS.4: (Bearing Pressure Distribution for Rigid Method) This simple distribution makes it easy to compute the flexural stresses and deflections (differential settlements) in the mat. Figure 6. and deflection may be easily computed using the principles of the structural mechanics. this is the same simplifying assumption used in the analysis of spread footings. The engineer can then select the appropriate mat thickness & reinforcement.1 Rigid method: The simplest approach to structural design of mats is the rigid method (also known as the conventional method or the conventional method of static equilibrium).2. which means the shears. 6. moments. the mat becomes an inverted and simply loaded two-way slab. it doesn't accurately model mat foundations becomes the width-to-thickness ratio is much greater in mats and the assumption of rigidity is no longer valid. For analysis purposes. and either uniform across the bottom of the mat (if the normal acts through the centroid and no moment load is present) or varies linearly a cross the mat (if eccentric or moment loads are present) as shown in figure (6. Chapter 6: Design of Foundations 83 6. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . NON-RIGID There are various methods have been used to mat foundations. which means any distortion in the mat are too small to significantly impact the distribution of bearing pressure depends only on the applied loads and the weight of mat. This method assumes the mat is much more rigid than the underlying soils.4). Chapter 6: Design of Foundations 84 Portions of a mat beneath columns and bearing walls settle more than the portions with loss load. which means the bearing pressure will be greater beneath the heavily- loaded zones. as shown in figure (6. Figure 6.6: (The distribution of Bearing Pressure under a Mat Foundation) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . Figure 6.5).6). but is present to some degree in all soils.5: (The distribution of Soil Bearing Pressure) This redistribution of bearing pressure is most pronounced when the ground is stiff compared to the mat as shown in figure (6. These are called non-rigid methods. the bearing pressure is greater on the edges and smaller in the center than shown in this figure. Although we use the same units to wt. unfortunately non-rigid analyses also are more difficult to implement because they require consideration of soil-structure interaction and because the bearing pressure distribution is not as simple. δ = Settlement. The sum of these spring forces must equal the applied structural loads plus the wt. even if the mat was perfectly rigid. Chapter 6: Design of Foundations 85 Because the rigid method does not consider this redistribution of bearing pressure. q = Bearing pressure. Coefficient of subgrade reaction: Because non-rigid method consider the effects of local mat deformations on the distribution of bearing pressure. Ks = Where: Ks = coefficient of subgrade reaction. as shown in fig (6.. Portions of the mat that experience more settlement produce more compression in the "springs. and deformations in the mat." which represents the higher bearing pressure. Ks (also known as the modulus of subgrade reaction. of the mat: ∑ + . it doesn't produce reliable estimates of the shear.2. 6. whereas portions that settle less don't compress the springs as for and thus have less bearing pressure.2 Non-Rigid methods: To become the in accuracies of the rigid method by using analyses that consider deformations in the mat and their influence on the bearing pressure distribution. it is necessary to define the relation slip between settlement & bearing pressure. moments.uD = = Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . This is usually done using the coefficient of subgrade reaction. and they are not numerically equal. or the subgrade modulus). In addition. The interaction between the mat and the underlying soil may there be represented as a "bed of springs" each with a stiffness Ks per unit area. and produce more accurate values of mat deformations and stresses.6) are not correct-in reality. the simplified bearing pressure distribution in figure (6. The coefficient Ks has units of force length cubed.7). Ks is not the same as the same as the unit wt. Wf = Pore of the mat. Finite element method. 4. Figure 6. Winkler method. Pseudo-coupled method. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . δ = settlement at a point on the mat. uD = Bearing pressure between mat & soil. Coupled method. 3. Chapter 6: Design of Foundations 86 Where: ∑ = sum of structural loads acting on the mat. Methods in non-rigid: 1. 5. and the mat deformations depends on the bearing pressure.7: (The Coefficient of Subgrade Reaction – bed of springs) This method of describing bearing pressure is called a soil-structure interaction analysis because the bearing pressure depends on the mat deformations. Multiple-parameter method. 2. A = mat-soil contact Area. Therefore. there is no single ks value. E (Vesic & Saxena. Unfortunately. so the settlement is also smaller and ks is greater. ks need to be larger near the edges of the mat and smaller near the center. Time . 3. it may be necessary to consider both short-term and long-term cases. including the following: 1. 1970). Plate load tests include dubious assumption that the soils within the shallow zone of influence below the plate are comparable to those in the much deeper zone below the mat. The depth of the loaded area below the ground surface – At greater depths. this task is not as simple as it might first appear because Ks is not a fundamental soil property. therefore. The shape of the loaded area: The stresses below long narrow loaded areas are different from those below square loaded areas therefore. plate load test generally do not provide good estimates of ks for mat foundation design. Ks. Its magnitude also depends on many other factors. 2. 4. shape. 5. Some rely on plate load test to measure ks in situ. they too are limited. the change in stress in the soil due to q is a smaller percentage of the initial stress. ks will differ. Therefore. Chapter 6: Design of Foundations 87 Determination of the coefficient of subgrade reaction: Most mat foundation designs are currently developed using either the Winkler method or the pseudo-coupled method. Actually. even if we could define these factors because the q-δ relationship is nonlinear and because neither method accounts for interaction between the springs. The position on the mat – To model the soil accurately. both of which depend on our ability to define the coefficient of subgrade reaction. Others have derived relationships between ks and the soils modulus of elasticity. and depth of the plate and the mat. Engineers have tried various techniques of measuring or computing ks. the test results must be adjusted to compensate for the differences in width. Although these relationships provide some insight.Much of the settlement of mats on deep compressible soils will be due to consolidation and thus may occur over a period of several years. Another method consists of computing the average mat settlement using the techniques of settlement and expressing the results in the form of ks using equation: ks = Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . each has a different (ks). However. The width of the loaded area: A wide mat will settlement more than a narrow one with the same q because it mobilizes the soil to a greater depth. when all “springs” have the same Ks) and the geometry of the problem can be represented in two-dimensions. In effect. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . 6. However. and variations in the soil stiffness. When the loading is complex. As with spread footings.e. it is possible to develop closed-form solutions using the principles of structural mechanics. This requires two separate analyses. these deformations are the equivalent of differential settlement. the principle of superposition may be used to divide the problem into multiple simpler problems.2 Closed-Form solutions: When the Winkler method is used (i. T. These solutions produce values of shear. and reinforcement to satisfy resists these loads.3. as follows: Step (1): Evaluate the strength requirements result from the load combinations and LRFD design methods (which ACI calls ultimate strength design). possible non-uniformities in the mat.1 General Methodology: The structural design of mat foundations must satisfy both strength and serviceability requirements. If they are excessive. Chapter 6: Design of Foundations 88 6. These deformations are the result of concentrated loading at the column locations. These closed-form solutions were once very popular.3 STRUCTURAL DESIGN: 6. the advent and widespread availability of powerful computers and the associated software now allows us to use other methods that are more precise and more flexible. T should be large enough that no shear reinforcement is needed. moment. then the mat must be made stiffer by increasing its thickness. Step (2): Evaluating mat deformations (which is the primary serviceability requirement) using the unfactored loads. The mat must have a sufficient thickness.3. and deflection at all points in the idealized foundation. because they were the only practical means of solving this problem.. Typically. The mat elements are connected to the ground through a series of “springs. such analyses are substantially more complex and time-consuming. and the weight of the mat itself. and it is very difficult to develop accurate soil properties for such models. and this downward movement is resisted by the soil “springs. it assumes the superstructure is perfectly flexible and offers no resistance to deformations in the mat. Each element has certain defined dimensions. The loads on the mat include the externally applied column loads.” which are defined using the coefficient of subgrade reaction. applied area loads. The finite element analysis can be extended to include the superstructure. in principle. the design is modified accordingly and reanalyzed.” These opposing forces along with the stiffness of the mat can be evaluated simultaneously using matrix algebra which allows us to compute the stresses. However. strains. and the underlying soil in a single three-dimensional finite element method. a specified stiffness and strength (which may be defined in terms of concrete and steel properties) and is connected to the adjacent elements in a specified way. This is conservative. these extended finite element analyses are rarely performed in practice. These loads press the mat downward. This method would. If the results of the analysis are not acceptable. In other words.3 Finite Element Method: Today. This method divides the mat into hundreds or perhaps thousands of elements. Therefore. and thus may produce a more economical design. and distortions in the mat. This type of finite element analysis does not consider the stiffness of the superstructure. applied line loads. Chapter 6: Design of Foundations 89 6. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . be a more accurate model of the soil structure system. the mat. most mat foundations are designed with the aid of a computer using the finite element method (FEM).3. one spring is located at each corner of each element. 5 m down.4. the base plan then imported with all loads and load combinations to SAFE software in order to analyze the base as raft foundation.0 m to the left. and • 1. • 1. all results were obtained. Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi .3 m up.4 m to the right. F Starting with depth.4 DESIGN PROCESS: 6. Figure 6. T = 500 mm and by trial and error procedure a depth of T = 700 mm was selected. F The raft covers the base plan with the following offsets relative to the above raft sketch: • 2. Chapter 6: Design of Foundations 90 6. for economic wise a suitable drop of 600 mm was made under heavy load columns. F Due to large variation in loads on columns. • 1.1 General Description: After performing analysis on 3-D ETABs software Model.8: (Undeformed Shape for Raft Foundation) Raft dimensions were selected in order to primarily achieve no bearing capacity and punching shear problems then serviceability criteria to be checked based on the selected dimensions. Chapter 6: Design of Foundations 91 6.9: (Deformed Shape of Raft Foundation for Ultimate Combination) Figure 6.2 SAFE Outputs: Figure 6.4.10: (Bearing Pressure for Soil beneath the Raft Foundation for Service Combination) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . Chapter 6: Design of Foundations 92 Figure 6.12: (Punching Shear Ratios under all Columns for Ultimate Combination) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi .11: (Punching Shear Ratios under Interior Columns for Ultimate Combination) Figure 6. Chapter 6: Design of Foundations 93 Figure 6.14: (Bending Moment Diagrams for Given Y‐Strips) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi .13: (Bending Moment Diagrams for Given X‐Strips) Figure 6. 15: (Shear Diagrams for Given X‐Strips) Figure 6.16: (Shear Diagrams for Given Y‐Strips) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . Chapter 6: Design of Foundations 94 Figure 6. This depends on the values of moment in each strip in both X & Y directions.0018 b h = (0. min = 0.0018) (1000) (1300) = 2340 mm2 / m 268 mm2/ 200 mm Use 1Φ25/ 200 mm … Top & Bottom • Wherever minimum reinforcement exceeded.0018 b h = (0.3 Sample Calculation: • General Raft (depth = 700 mm): As.4.2: (Reinforcement Guideline for Drops) Reinforcement Bars Area of Steel (mm2 per meter) 5Φ25 2454 5Φ25 + 5Φ12 3020 5Φ25 + 5Φ14 3224 5Φ25 + 5Φ16 3459 5Φ25 + 5Φ18 3726 5Φ25 + 5Φ20 4025 5Φ25 + 5Φ25 4908 5Φ25 + 5Φ32 6475 Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . min = 0.1: (Reinforcement Guideline for General Raft) Reinforcement Bars Area of Steel (mm2 per meter) 5Φ18 1272 5Φ18 + 5Φ12 1838 5Φ18 + 5Φ14 2042 5Φ18 + 5Φ16 2277 5Φ18 + 5Φ18 2544 5Φ18 + 5Φ20 2843 5Φ18 + 5Φ25 3173 5Φ18 + 5Φ32 3726 Table 6. Table 6. an additional reinforcement must be added. The following tables can ease this mission. Chapter 6: Design of Foundations 95 6.0018) (1000) (700) = 1260 mm2 / m 252 mm2/ 200 mm Use 1Φ18 / 200 mm … Top & Bottom • Drop (depth = 600 mm) : As. bottom = 2150 kN.806 . . = 0. . = (1– 1 ) . ′ . = 0.0045 As.0020 * 1000 * 575 = 1150 mm2 As req < As min ……… Use As.0045 * 1000 * 1150 = 5175 mm2 Use 5Φ25 + 5Φ32 F Mu.840 .Top = . .min = 1272 mm2 Use 5Φ18 Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi .0020 As req = ρ * b * d = 0. . = (1 – 1 ) . . . Chapter 6: Design of Foundations 96 • For X-strip: F Mu.m / m h = 1300mm d = 1150mm M Ru = = = 1. ′ . required = ρ * b * d = 0. ′ R ρ = (1– 1 ) .m / m h= 700mm d= 575mm M Ru = = = 0. ′ R ρ = (1– 1 ) .250 kN. .416 . ′ . ′ .0035 As req = ρ * b * d = 0.Top = . ′ R ρ = (1– 1 ) .00406 * 1000 * 575 = 2338 mm2 Use 5Φ18 + 5Φ18 Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . . . = 0. = (1– 1 ) .bottom = 1686 kN. . = (1– 1 ) .00348 * 1000 * 1150 = 4025 mm2 Use 5Φ25+ 5Φ25 F Mu. = 0. .647 .m / m h = 700mm d = 575mm M Ru = = = 1. Chapter 6: Design of Foundations 97 • For Y-strip: F Mu.m / m h= 1300mm d= 1150mm M Ru = = = 1.490 kN. .00406 As req = ρ * b * d = 0. ′ R ρ = (1– 1 ) . 78 "OK" ΦV Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi .4 kN F Punching Shear Ratio = = 0. F d = 1150 mm. F C = 800 mm. “ assumed” F b0 = c +d = 800 + 1150 =1950 mm F Mu= 3110 kN.m "From SAFE Model" F Pu= 8791 kN “ from ETABS Model” F Vuc = ) . F ΦVc = Φ ′ = (0.2 kN .75) 1950 1150 √28 = 3955. . = = 3085. . Chapter 6: Design of Foundations 98 • Check Punching shear: For the purpose of checking punching shear. an Equivalent 800 mm side Square column corresponding to the circular column of diameter of D = 900 mm was taken. 17: (Raft Foundation Details) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi . Chapter 6: Design of Foundations 99 Figure 6. Chapter 6: Design of Foundations 100 Figure 6.18: (Sections in Raft) Eng Ahmad Al Omari Eng Essam Ghaith Eng Qutaiba Hameedi .