1. Bearing Capacity
of Layered Soils

2. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: Stronger Soil overlying a Weak soil
With reference to the figure shown for a continuous footing, Meyerhof and Hanna (1978) treated this case of a stronger layer over a weaker layer semi-analytically.
The mode of failure depends on the relative thickness, H/B, below the foundation

3. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: 1. Stronger Soil overlying a Weak soil
For small values of H/B, punching-type shear failure takes place in the upper layer followed by a general shear failure in the lower layer.
Since the problem – strip foundation – is considered as a plane-strain problem, a unit length is considered so that for limit equilibrium
qb: bearing capacity of the bottom layer
Ca= caH: adhesion force
Pp: passive resistance
(See figure above)

4. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: 1. Stronger Soil overlying a Weak soil
qb is determined in the usual way at the depth of Df+H for general shear failure:
The passive resistance can be expressed as
Inserting these expressions in the equilibrium equation, one obtains the b.c. equation sought:
where Ks is the punching shear coefficient given by

5. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: 1. Stronger Soil overlying a Weak soil
The punching shear coefficient is provided in the graph as a function of q2/q1 and φ1.
q1 and q2 are the bearing capacities of the two layers obtained in the usual manner assuming each soil was deep and uniform in the respective cases
qt=q1: upper bound

6. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: 1. Stronger Soil overlying a Weak soil
The adhesion, ca, is obtained as a fraction of the soil cohesion of the top layer and as a function of the ratio of the two limiting bearing capacities.

7. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: 1. Stronger Soil overlying a Weak soil
For a large H/B, the failure surface is entirely in the upper layer so that the bearing capacity is dependent only on this layer properties (see figure).
This case gives the upper bound, qt, indicated above:

8. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: 1. Stronger Soil overlying a Weak soil
Going back to the case of small H/B for rectangular foundations, the equation is modified to include shape and depth factors; i.e.
where
Meyerhof’s and/or Hansen’s shape factors,λ, can be used in the above equations using the respective friction angles.

9. Bearing Capacity of Layered Soils: 1
Bearing Capacity of Layered Soils: Stronger Soil overlying a Weak soil
The qualitative variation of qult is as shown: it increases with increasing H?B and is bounded by the two values.

10. Bearing Capacity of Layered Soils: 2
Bearing Capacity of Layered Soils: weaker Soil overlying a strong soil
Meyerhof and Hanna (1978) also treated this case in a semi-analytical manner.
In the case of relatively small H/B (left), the slip surface passes through both layers, and its shape is different from the case of large H/B (right), which is the classic half-space case.

11. Bearing Capacity of Layered Soils: 2
Bearing Capacity of Layered Soils: weaker Soil overlying a strong soil
For the case of small H/B, the ultimate bearing capacity is given by
where

12. Bearing Capacity of Layered Soils: 2
Bearing Capacity of Layered Soils: weaker Soil overlying a strong soil
D is the maximum depth of failure surface in the top (weaker) layer
Based on model tests, Meyerhof and Hanna suggested
The qualitative variation of qult is as shown: it decreases with increasing H/B and bounded by the two values

13. Particular Cases and Examples
Recommended reference:
Das, B. M.; Shallow Foundations: Bearing Capacity and Settlement, CRC Press, 2009
Baban, T. M.; Shallow Foundations: Discussions and Problem Solving, Wiley Blackwell, 2016

14. Bearing Capacity of Foundations on rocks
Recommended reference:
Bowles, J. E.; Foundation Analysis and Design, McGraw-Hill,1997
Baban, T. M.; Shallow Foundations: Discussions and Problem Solving, Wiley Blackwell, 2016

15. Bearing Capacity of Foundations in Slopes
Recommended reference:
Das, B. M.; Shallow Foundations: Bearing Capacity and Settlement, CRC Press, 2009
Baban, T. M.; Shallow Foundations: Discussions and Problem Solving, Wiley Blackwell, 2016