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Foundation Bearing Failure Modes and Capacities

Weight to Volume relationships in soils

Mohr's Circle for 2D Stresses

3D Mohr's Circle 

Geotechnical Engineering

 by the CalcTree engineering team on July 20, 2024

The ultimate bearing capacity is defined as the 

critical pressure at which failure occurs

, where the applied loads exceed the soil's supporting (bearing) capacities. The structure-soil interaction is affected by the soil's density and shear strength as well as the depth of the footing supporting the structure above. Failure occurs when the soil bearing capacity is exceeded: in this article, we will elaborate on the three different modes of bearing failure.

Jump to Meyerhof and Terzaghi bearing capacity calculators here:

General shear failure manifests as an abrupt and devastating collapse marked by a distinct failure pattern. This involves the formation of a clearly defined failure surface extending from the edge of the footing to the ground surface. Notably, the failure is characterized by ground surface upheaval and footing tilting, unless there is an obstructing structure. Typically occurring when the foundation rests on compact sand and rigid clay, this failure scenario can have significant consequences.

Settlement develops progressively with the incremental application of the load. Once the load per unit area attains the ultimate bearing capacity, a sudden failure occurs in the soil supporting the foundation. This failure is marked by the development of a failure surface within the soil extending to the ground surface, accompanied by noticeable bulging of adjacent soils on either side of the foundation.

Localised shear failure occurs when the foundation is situated on soil with medium compaction, composed of sandy or clayey characteristics. The discernible failure pattern is only observable beneath the footing, resembling the general shear failure. This pattern entails visible wedge and slip surfaces at the footing's edges.

Upon reaching the ultimate bearing capacity, abrupt shifts occur in the foundation's movement, and subsequent incremental load increases lead to significant increases in foundation settlement. The failure surface subsequently extends outward from the foundation, and the load-settlement curve does not have a prominent peak.

Punching failure occurs when the foundation is significantly deep beneath the ground surface and the situated on loose soils with low compressibility. Unlike the above shear failures, there is no upheaval or tilting of adjacent soils, and the ground beneath essentially 'punches through' the soil when the capacity is exceeded. 

Unlike other failures, punching failure results in substantial settlement without a clearly defined ultimate bearing capacity. The compression of soil beneath the footing occurs suddenly with load increase and the failure surface does not extend above the ground surface. Hence, punching shear is difficult to observe and prevent.

In summary, general shear failure, local shear failure, and punching failure are characterised by their distinctive failure patterns and settlements. Detailed soil assessment and good design and construction processes are essential to avoid and prevent these failures.

To accurately calculate the bearing capacity of a founding material, a thorough assessment of its properties and behaviour is necessary. This includes conducting in-situ and lab tests, which propose the following challenges:

Various empirical and theoretical methods have been proposed and refined to allow engineers to estimate (to a satisfactory standard) bearing capacities. In particular, Terzaghi and Meyerhof methods are widely used. 

The Terzaghi method focuses on soil shear strength components, considering cohesion, effective stress and the angle of internal friction. It offers a comprehensive formula for determining the ultimate bearing capacity 

 of soil beneath a foundation. This equation incorporates cohesion 

. Terzaghi's method assumes relatively simple foundation shapes and loading conditions while accounting for multiple soil parameters. Terzaghi's ultimate bearing capacity is given by:

In contrast, the Meyerhof method takes a more empirical approach, relying on field observations and simplified equations for estimating bearing capacity. Meyerhof added factors to the ultimate bearing capacity 

 to account for the footing shape, depth and load inclination. Meyerhof's ultimate bearing capacity is given by:

Learn about foundation elements bearing failure and calculate soil capacities using Meyerhof & Terzaghi Approaches.

Calculate Bearing Failure Modes and Capacities using Meyerhof & Terzaghi Approaches

This calculator computes the volume and weight relationships in soils, which are useful relationships used in soil mechanics.

Soil Sample Values

Weight-Volume Relationship

 is shown below with its three phases of soil mass (soil solids, air and water).

In most cases you will know the soil sample mass 

 (based on the test tube dimensions) and soil specific gravity 

👉Note, you can either work in mass (with units 

). If you work in mass, your densities will be in 

 while if you work in weight, your densities will be in 

We can then determine the remaining mass and volume quantities:

 is typically within the range 2.65 (average from granular soils) and 2.80 (average for cohesive soils).

We now know all our mass and volume quantities (

). We can then define the following weight-volume relationships commonly used in soil mechanics:

Useful weight-volume relationships can be developed by considering a soil sample with 

Weight-volume relationships can then be derived in terms of 

The derivation of the above equations are found in 

Useful weight-volume relationships can also be developed by considering a soil sample with 

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Weight-Volume Relationships For Soils

σave

τmax

Mohr's Circle

The Mohr's Circle is the graphical representation of the stress transformation equations and is useful in visualizing the relationships of the normal and shear stresses inclined at a given angle. 

There may be times we would like to rotate our stress element to get the stress at a certain angle. The stress transformation equations are used to determine the normal and shear stress inclined at a particular angle.  

The principal stresses are the maximum and minimum normal stresses that occur when the stress element is rotated to the degree that the shear stress is zero. 

Use this page to calculate the 2D mohrs circle for given stresses.

τxy

τyz

τxz

3D Mohr's Circle

The 3D stresses are usually given by six stress components, the normal stresses at the x- y- and z- directions and the shear stresses at the xy , yz, and xz planes. These stresses are then put in a 3 x 3 symmetric matrix shown below. 

In order to get the maximum normal and shear stresses, we get the eigenvalues of the matrix above. Say, that the cut plane has the following directional cosine:

We can find the normal stress on this plane by,

To find the eigenvalues and eigenvectors, we use the following characteristic polynomial equation: 

We can then find the normal stresses using the following system of equations:

For a more graphical approach, we can use the following approach:

The obtained values will serve as the centers of our circles. The radii of the circles can be obtained by:

Mech of Materials Ch 07 lecture 04 Transformation of 3D Principal Stress with Mohr Circles by Cheng-fu Chen 

Use this page to calculate the 3D mohrs circle for given stresses.