Design of Raft Foundations – Methods and Calculations

Design of Raft Foundations – Methods and Calculations

The design criteria for raft footings as specified in IS – 2950:1965 state that maximum differential settlement in foundation should not exceed 40mm for clayey soils and 25mm for sandy soils. In addition, the maximum settlement values for raft foundation on clay should be limited to 65-100mm and for sand to 40-65mm.

It is important to adhere to these design criteria to ensure the stability and durability of the foundation. If the settlement exceeds the specified limits, it may result in structural damage and compromise the overall integrity of the building. Therefore, careful consideration and evaluation of the soil conditions and structural requirements are crucial in the design and construction of raft footings.

Two techniques are available for creating raft foundations: the Conventional Method and the Soil Line Method. The Conventional Method and the Soil Line Method are two distinct methods for designing raft foundations.

1. Conventional Method of Raft Foundation Design

Assumptions:

The given context refers to a method for calculating the allowable bearing pressure of a foundation, based on certain assumptions. The first assumption is that the soil pressure can be considered as a plane, and that the centroid of the soil pressure aligns with the line of action of the resultant force of all the loads on the foundation. The second assumption is that the foundation is infinitely rigid, which means that the actual deflection of the foundation does not affect the pressure distribution beneath it.

Based on these assumptions, a formula can be used to calculate the allowable bearing pressure of the foundation. However, it is important to note that this method relies on specific assumptions that may not hold true in all situations. Factors such as soil variability, foundation flexibility, and load distribution can all impact the pressure distribution and ultimately affect the accuracy of the calculated allowable bearing pressure. Therefore, it is important to consider the specific conditions and limitations of each situation when using this method.

 Where 

 and 

 = allowable soil pressure under raft foundation in 

 (use a factor of safety of three). The smaller values of 

 and 

should be used for design. 

and 

The given context is related to determining the equivalent penetration resistance in saturated silts for design purposes. The formula used for this purpose involves various parameters such as the reduction factor on account of subsoil water and the value of penetration resistance denoted by N.

According to the context, if the value of N is greater than 15 in saturated silts, an equivalent penetration resistance should be taken into consideration for design purposes. To determine this equivalent resistance, the formula provided can be used.

The formula involves the reduction factor on account of subsoil water and the value of N. These parameters are important in determining the overall equivalent penetration resistance. By using this formula, one can accurately determine the appropriate penetration resistance for design purposes.

In summary, the context provided focuses on the determination of equivalent penetration resistance in saturated silts for design purposes. The formula provided takes into account the reduction factor on account of subsoil water and the value of N to accurately calculate the equivalent resistance.

The context given is about calculating the pressure distribution (q) under a raft using a specific formula. To rewrite this in paragraphs, it can be said that there is a need to determine the pressure distribution beneath a raft structure, which can be done by utilizing a formula provided for this purpose.

The pressure distribution is an important parameter that needs to be calculated to ensure the stability and safety of the raft structure. The formula provided is a mathematical expression that can be used to calculate this distribution accurately.

To determine the pressure distribution using this formula, certain input parameters such as the size and shape of the raft, as well as the properties of the underlying soil, must be known. Once these parameters are known, they can be used in the formula to obtain the pressure distribution values at various points under the raft.

The accuracy of the pressure distribution calculations is crucial as it can affect the overall stability and load-carrying capacity of the raft. Hence, it is important to use a reliable and well-established formula such as the one provided to ensure the accuracy of the calculations. By using this formula, engineers and designers can design and construct raft structures that are safe, stable, and can withstand the loads and forces they are subjected to.

The given context describes an equation involving several variables related to a raft. The equation expresses the total vertical load on the raft, denoted by Q, in terms of the co-ordinates of any given point on the raft, represented by x and y, with respect to the x and y axes passing through the centroid of the area of the raft. Additionally, the equation includes the total area of the raft, denoted by A.

To understand the equation, it is important to know that the centroid is the geometric center of a shape, and the x and y axes are the horizontal and vertical reference lines used to locate points on a graph. The equation provides a mathematical relationship between the load on the raft and the location of any point on the raft relative to its centroid.

By rewriting the given context, we can clarify the meaning of the equation and provide a more detailed explanation of the variables involved. The equation relates the total vertical load on the raft, denoted by Q, to the co-ordinates of any given point on the raft, represented by x and y. These co-ordinates are measured relative to the x and y axes passing through the centroid of the area of the raft.

The centroid is the center of gravity of the raft, and the x and y axes are the horizontal and vertical reference lines used to locate points on the raft. The equation also includes the total area of the raft, denoted by A. This is the sum of all the individual areas of the components that make up the raft.

Overall, the equation provides a way to calculate the total vertical load on the raft based on the location of any point on the raft and the total area of the raft. It is a useful tool for engineers and designers who need to understand the load-bearing capacity of rafts and other structures.

The given context refers to the eccentricities of a section with respect to the principal axis that passes through its centroid. To rephrase it, we can say that the section has certain deviations from its geometric center along the axis that is considered the most significant. These deviations are referred to as eccentricities and are measured in relation to the centroid of the section. Therefore, the eccentricities of the section are a measure of how far the mass is distributed from the central axis passing through its centroid.

The given context is about the moment of inertia of a section. The moment of inertia is a physical property of an object that describes how resistant it is to rotational motion. In the context of a section, it refers to the resistance of the section to rotational motion about a particular axis.

In this case, the moment of inertia is being measured about the principal axis that passes through the centroid of the section. The centroid is the point at which the section’s area is evenly distributed. The principal axis is the axis that passes through the centroid and has the highest moment of inertia.

To calculate the moment of inertia about the principal axis, one needs to use the formula that takes into account the section’s shape and dimensions. This formula involves integrals that are evaluated over the section’s area. Once the integral is computed, the result is multiplied by the density of the section to obtain the moment of inertia.

In summary, the moment of inertia of a section is a measure of its resistance to rotational motion. The moment of inertia is being measured about the principal axis that passes through the section’s centroid. To calculate the moment of inertia, one needs to use a formula that involves integrals evaluated over the section’s area and multiplied by the density of the section.

,

 can be calculated by the following equations: 

 Where 

and 

The provided context describes the eccentricities of a load with respect to the centroid in both the x and y directions. To rephrase this information, one could say that the load is not perfectly centered with respect to its centroid and is offset in both the horizontal and vertical planes. This offset or eccentricity is measured as the distance between the centroid and the load in the respective directions. Therefore, the load has a specific eccentricity value in the x direction and another value in the y direction, which must be taken into account when analyzing its effects on the structure or system it is placed upon.

and 

The given context is related to the moment of inertia of an area, specifically a raft, around the x and y axes through its centroid. The moment of inertia is a property of an object that represents the resistance to rotational motion around a particular axis.

In this case, the moment of inertia of the raft is being discussed with respect to the x and y axes, which are both passing through the centroid of the area. The centroid is the geometric center of the area, which is calculated by finding the average position of all the points in the area.

The moment of inertia of the raft is a measure of how difficult it is to rotate the raft around the x and y axes. The moment of inertia is different for different axes and depends on the distribution of mass within the object. The moment of inertia around the x and y axes through the centroid of the raft can be calculated using standard formulas that take into account the shape and size of the raft.

Overall, the moment of inertia is an important concept in physics and engineering, as it is used to understand and design structures that are resistant to rotational forces. In the case of the raft, understanding its moment of inertia around the x and y axes can help in determining its stability and how it will behave in different conditions.

It seems that the given context is missing or incomplete. Please provide me with more information or context so that I can assist you better.

2) Soil line Method (Elastic Method) of Raft Foundation Design

There are two approaches to foundation design that have been proposed: the simplified elastic foundation and the truly elastic foundation. The simplified elastic foundation replaces the soil with an infinite number of isolated springs, while the truly elastic foundation assumes that the soil is a continuous elastic medium that follows Hooke’s law. These methods are suitable for foundations that are relatively flexible and where loads tend to concentrate over small areas.

One important factor that these methods consider is the modulus of subgrade reaction, which is determined through tests. This modulus is assumed to be known in order to apply these methods. Table-1 provides the modulus of subgrade reaction (Ks) for cohesionless soils, specifically for loads applied through a plate of size 30 cm x 30 cm or beams that are 20 cm wide on soil area. Similarly, Table-2 provides the modulus of subgrade reaction (Ks) for cohesive soils.

Knowing the modulus of subgrade reaction is crucial for designing foundations that can withstand loads without excessive settlement or failure. By using the appropriate modulus value from these tables, engineers can apply the simplified or truly elastic foundation methods to design foundations that will adequately support the loads and maintain stability.

 Table -1: Modulus of subgrade reaction K_s for cohesionless soils

Soil Characteristics		Ks(Kg/cm2)
Relative Density	Values of N	Dry or moist state	Submerged state
1. Loose	<10	1.5	0.9
1. Medium	10 to <30	4.7	2.9
3. Dense	30 and over	18	10.8

Table – 2: Modulus of subgrade reaction K_s for cohesive soils

Soil Characteristics		Ks(Kg/cm2)
Consistency	Unconfined compressive Strength (Kg/cm2))	–
1. Stiff	1 to <2	2.7
1. Very Stiff	2 to <4	5.4
3. Hard	4 and over	10.8

The given context describes a set of values for Ks that correspond to a square plate of size 30 cm x 30 cm. However, it is noted that these values may not be applicable to plates of different sizes or shapes. Therefore, the context provides relationships that can be used to find the values of K for different sizes and shapes.

The first relationship provided is regarding the effect of size. This relationship suggests that the size of the plate will have an impact on the value of K. Therefore, to find the value of K for a plate of a different size, this relationship needs to be taken into consideration.

The context does not provide the exact formula for calculating the effect of size on K, but it implies that the formula exists and needs to be used. It is important to note that the effect of size may differ depending on the shape of the plate.

Overall, the context highlights the importance of considering the size and shape of the plate when determining the value of K. It provides a starting point in the form of values for Ks for a specific plate size and shape, but emphasizes that these values may not be directly applicable to plates of different sizes and shapes.

 for cohesionless soil 

The given equation is used to determine the modulus of subgrade reaction for different types of footings on cohesive soils. The equation takes into account the width of the footing and the modulus of subgrade reaction for a square plate of width 30cm x 30cm.

The variables in the equation are defined as follows: K represents the modulus of subgrade reaction for a footing with a width of B cm, Ks represents the modulus of subgrade reaction for a square plate with a width of 30cm x 30cm, and K’ represents the modulus of subgrade reaction for a footing with an unknown width.

By using this equation and solving for K’, the modulus of subgrade reaction for a footing of any width can be determined based on the known values of K and Ks. This information is useful in designing foundations for structures on cohesive soils, as it helps ensure that the foundation is stable and can withstand the loads placed upon it.

cm. (b) Effect of shape 

 for cohesive soils Where 

The modulus of subgrade reaction is a parameter used in geotechnical engineering to model the response of soil to the loading of a foundation. It represents the stiffness of the soil and is typically denoted by the symbol k. For a rectangular footing with dimensions length L and width B, the modulus of subgrade reaction can be calculated based on the soil properties and the geometry of the foundation.

The modulus of subgrade reaction is an important factor in the design of foundations, as it affects the settlement and bearing capacity of the soil. It is a measure of the soil’s ability to resist deformation under load and is typically expressed in units of force per unit length.

For a rectangular footing, the modulus of subgrade reaction can be determined using various methods, including plate load tests, pressuremeter tests, and empirical correlations based on soil properties. The value of the modulus of subgrade reaction is influenced by factors such as soil type, moisture content, density, and the depth of the foundation.

In summary, the modulus of subgrade reaction is a fundamental parameter in the analysis and design of foundations. For a rectangular footing, it is influenced by soil properties and the dimensions of the foundation, and can be determined using various methods.

The modulus of subgrade reaction is a parameter used to characterize the stiffness of the soil beneath a foundation. For a square footing with a side length of B, this parameter can be determined through various methods. However, when it comes to footing on cohesionless soils, the effect of shape on the modulus of subgrade reaction is considered negligible. In such cases, the shape of the footing does not significantly impact the soil’s stiffness, and the modulus of subgrade reaction can be assumed to be the same regardless of the shape of the footing.