# Bearing capacity of shallow foundation solved examples

Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.

There are three modes of failure that limit bearing capacity: general shear failure, local shear failure, and punching shear failure. Terzaghi's bearing capacity method is the earliest method proposed in There are more advanced and accurate methods proposed later by Meyerhofand Brinch and Hansen Concepts and Formulas.

Figure 1. The first term in the equation is related to cohesion of the soil. The second term is related to the depth of the footing and overburden pressure. The third term is related to the width of the footing and the length of shear stress area.

Note: from Bowles' Foundation analysis and design book, "Terzaghi never explained. Watch Videos. Soil Bearing Capacity Failure Demonstration. Solved sample problems.

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### Determination of Bearing Capacity of Shallow Foundations

No files available for this topic. Suggest one!The CivilWeb Soil Bearing Capacity Calculation Excel Suite includes the Terzaghi bearing capacity spreadsheet along with 5 other analytical methods and 3 methods based on site investigation information.

The Terzaghi bearing capacity method was the first analytical method to be developed and while it has been extended many times, the Terzaghi method is still often used today.

This can also be purchased at the bottom of this page. The earliest bearing capacity analysis method to be widely adopted was developed by Terzaghi. This is based on the work of Prandtl in the s which was derived from the punching resistance of metals.

Terzaghi adapted this work in the s to apply the principles to the problem of shallow foundations bearing on soils. He used this plasticity theory and an assumed shear failure surface to calculate the required pressure to achieve shear failure in the soil.

For his plastic analysis Terzaghi assumed that the failure surface of the soil would take the form shown in the below diagram. Below the foundation a wedge of soil remains intact and is pushed downwards by the loads acting on the foundation.

This wedge of moving soil creates a radial shear zone extending from each edge of the wedge. Terzaghi takes the shape of this radial shear zone as a series of logarithmic spirals. The third shear zone forms as a linear shear zone where the soils are able to shear along planar surfaces. Terzaghi initial analysis of infinite strip foundations was later adapted to three equations which estimate the bearing capacity of the soil for square, circular or strip foundations.

These equations take the common bearing capacity analysis form of three parts which consider the effects of soil cohesion, surcharge, and the weight of the soil. Terzaghi defined these bearing capacity factors using the below equations.

The Terzaghi bearing capacity factors have often been presented in tabular or graphical form in the past to simplify the calculations before computers. These tables and graphs are presented below. Terzaghi assumed the following parameters in order to model the shear failure of the soils beneath the foundation.

Terzaghi also produced amended equations for calculating the bearing capacity of soils subject to local shear failure. This involves reducing the cohesion and the angle of internal friction using the following equations. These amended values are then used to calculate the Terzaghi bearing capacity factors in the same way as for the general shear failure conditions explained above.

Many graphs and tables have also been produced to illustrate the values for the bearing capacity factors for local failure in the same way as those for general shear failure.

Examples of these tables and graphs are presented below. The Terzaghi bearing capacity analysis is still in use today, particularly for preliminary analysis. This is because the analysis is well known and relatively straightforward. It does not however take account of a number of common problems such as eccentric or inclined loading and has been improved several times over the following decades to increase the accuracy and increase the range of conditions which can be accommodated.

Generally the Terzaghi bearing capacity theory has been superseded by subsequent methods though the Terzaghi bearing capacity equation could still be used in simple cases where the design conditions are appropriate. This spreadsheet suite includes 9 different methods of calculating the bearing capacity including both analytical methods and methods based on site investigation information.

The spreadsheet suite also includes unique comparison tools which complete the bearing capacity calculations for all 6 analytical methods. This allows the designer to compare results and to choose the most appropriate bearing capacity value or even an average of all 6 methods. To try out a fully functional free trail version of this software, please enter your email address below to sign up to our newsletter. Your Email required. Terzaghi Bearing Capacity Theory The earliest bearing capacity analysis method to be widely adopted was developed by Terzaghi.

Terzaghi Bearing Capacity Equations Terzaghi initial analysis of infinite strip foundations was later adapted to three equations which estimate the bearing capacity of the soil for square, circular or strip foundations.Sign Up to The Constructor to ask questions, answer questions, write articles, and connect with other people.

**Shallow Footings Bearing Capacity**

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The bearing capacity of soil is defined as the capacity of the soil to bear the loads coming from the foundation.

The pressure which the soil can easily withstand against load is called allowable bearing pressure. The gross pressure at the base of the foundation at which soil fails is called ultimate bearing capacity. By neglecting the overburden pressure from ultimate bearing capacity we will get net ultimate bearing capacity. By considering only shear failure, net ultimate bearing capacity is divided by certain factor of safety will give the net safe bearing capacity.

When ultimate bearing capacity is divided by factor of safety it will give gross safe bearing capacity. The pressure with which the soil can carry without exceeding the allowable settlement is called net safe settlement pressure.

## BEARING CAPACITY FOR SHALLOW FOUNDATIONS

This is the pressure we can used for the design of foundations. In the reverse case it is equal to net safe settlement pressure. For the calculation of bearing capacity of soil, there are so many theories. This theory is only applicable to shallow foundations. He considered some assumptions which are as follows. As shown in above figure, AB is base of the footing.

He divided the shear zones into 3 categories. Zone -1 ABC which is under the base is acts as if it were a part of the footing itself. P p y is derived by considering weight of wedge BCDE and by making cohesion and surcharge zero. P p c is derived by considering cohesion and by neglecting weight and surcharge.Soil investigation is one of the most important activities carried out before the commencement of any construction project.

In the soil test report, the geotechnical engineer is expected to state the strength of the soil at different layers, and ultimately recommend a suitable foundation. One of the parameters used in describing the strength of a soil formation for purposes of foundation design is the soil bearing capacity, which is based on the shear strength of the soil. In this post, we are going to present an example on how to determine the bearing capacity of a soil using the general bearing capacity equation.

Background Terzaghi in extended the plastic failure theory Bof Prandtl to evaluate the bearing capacity for shallow strip footings. This modification allowed for depth factor, shape factor and inclination factors. Solved Example Let us determine the bearing capacity of a simple pad foundation with the following data. Using a factor of safety FOS of 3. Save my name, email, and website in this browser for the next time I comment.

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Password recovery. Forgot your password? Get help. Create an account. Sunday, October 11, About Us. Foundations Geotechnical Engineering.

Sheet Pile Walls and their Uses. Recommended Depth of Exploration for Site Investigation. Please enter your comment! Please enter your name here.Geotechnical Info Search.

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Ultimate bearing capacity is the theoretical maximum pressure which can be supported without failure. Allowable bearing capacity is what is used in geotechnical design, and is the ultimate bearing capacity divided by a factor of safety.

Theoretical Ultimate and allowable bearing capacity can be assessed for the following: Shallow Foundations strip footings square footings circular footings Deep foundations end bearing skin friction For comprehensive examples of bearing capacity problems see:.

Notes: Effective unit weight, gis the unit weight of the soil for soils above the water table and capillary rise. For saturated soils, the effective unit weight is the unit weight of water, g w9. Find more information in the foundations section. The first equation is for ultimate bearing capacity, while the second two are factored within the equation in order to provide an allowable bearing capacity. Linear interpolation can be performed for footing widths between 1.

Notes: Determining effective length requires engineering judgment. The effective length may also be the length of a pile segment within a single soil layer of a multi layered soil. Effective unit weight, gis the unit weight of the soil for soils above the water table and capillary rise.

Example 1 : Determine allowable bearing capacity and width for a shallow strip footing on cohesionless silty sand and gravel soil. Loose soils were encountered in the upper 0. Use a factor of safety, F.

## Possible Failure Cases of Layered Soil

Three is typical for this type of application.View Cart Checkout. The bearing capacity of a shallow foundation can be defined as the maximum value of the load applied, for which no point of the subsoil reaches failure point Frolich method or else for which failure extends to a considerable volume of soil Prandtl method and successive.

Prandtl, has studied the problem of failure of an elastic half-space due to a load applied on its surface with reference to steel, characterizing the resistance to failure with a law of the type:.

Within zones ABF and EBC failure occurs along two families of lines, the ones made up of straight lines passing through points A and E, and the other consisting of arcs of families of logarithmic spirals. The poles of these are points A and E. Having thus identified the soil tending to failure by application of the ultimate load, this can be calculated expressing the equilibrium between the forces acting in any volume of soil whose base is delimited by whichever slip surface.

Based on this theory, admittedly of little practical value, all the various investigations and developments have proceeded. Terzaghicontinues on the same lines as Caquot but adds modifications to take into account of the real characteristics of the foundation-soil system.

Under the action of the load transmitted by the foundation, the soil at the contact with the foundation tends to move laterally, but is restrained in this by the tangential resistances that develop between the soil and the foundation. This results in a change of the stress state in the ground placed directly below the foundation. Further on the basis of experimental data, Terzaghi introduces factors due to the shape of the foundation.

Again Terzaghi refines the original hypothesis of Prandtl who considered the behaviour of soil as rigidâ€”plastic. Terzaghi instead assigns such behaviour only to very compact soils. Failure is instantaneous and the value of the ultimate load is easily identifiable general failure.

For very loose soils therefore Terzaghi introduces in the previous formula the reduced values for the mechanical properties of the soil:. Meyerhof obtained the N factors by making trials on a number of BF arcs see Prandtl mechanism whilst shear along AF was given approximate values. Shape, depth, and inclination factors for the Meyerhof bearing-capacity.

Shape and depth factors for use in either the Hansen or Vesic bearing-capacity equations. Table of inclination, ground, and base factors for the Hansen equations. Where V d the design load at ultimate limit state normal to the footing, including the weight of the foundation it self and R d is the foundation design bearing capacity for normal loads, also taking into account eccentric and inclined loads.

When estimating R d for fine grained soils short and long term situations should be considered. Where eccentric loads are involved, use the reduced area at whose center the load is applied. In addition to the correction factors reported in the table above will also be considered the ones complementary to the depth of the bearing surface and to the inclination of the bearing surface and ground surface Hansen.

Sliding considerations The stability of a foundation should be verified with reference to collapse due to sliding as well as to general failure. For collapse due to sliding, the resistance is calculated as the sum of the adhesion component and the soil-foundation friction component. Lateral resistance arising from passive thrust of the soil can be taken into account using a percentage supplied by the user. Resistance due to friction and adhesion is calculated with the expression:.

There where eccentric loads are involved, use the reduced area at whose centre the load is applied. Bearing capacity for foundations on rock Where foundations rest on rock, it is appropriate to take into consideration certain other significant parameters such as the geologic characteristics, type of rock and its quality measured as RQD. It is the practice to use very high values of safety factor for bearing capacity of rock and correlated in some way with the value of RQD Rock quality designator.

For example for a rock whose RQD is up to a maximum of 0. These coefficients should be used with form factors from the formula of Terzaghi.Congratulations to our 2016 graduates. Find Out More About Our PSTAT Graduate Programs. Previous Pause Next PSTAT Points of Excellence PSTAT's Actuarial Program is an SOA Center of Actuarial Excellence Home to the Center for Financial Mathematics and Actuarial Research Operating the UCSB StatLab since 1985.

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