Shallow Foundation Design

In foundation engineering, there are two main modes of failure that the engineer needs to design against with safety and economy in mind:

1.           Bearing Capacity Failure: caused by the exceedance of the shear strength of soil; this mode of failure is abrupt and catastrophic.

2.           Excessive Settlement: defined as the exceedance of a specified maximum acceptable amount of settlement. For typical structures with isolated spread footings, a total foundation settlement of 2.5 cm is a common design value resulting in acceptable differential settlements. Thus, the allowable stress is defined as the stress resulting in 2.5 cm of total settlement. The consequences of this mode of failure are not catastrophic as is the case for the bearing capacity criterion.

In the following, typical design procedures in engineering practice for each failure criterion are presented and used in the reliability analyses.

Bearing Capacity

For a granular, non-cohesive material, the ultimate bearing capacity q_ult of a saturated soil having a buoyant unit weight γ_b, under a foundation of width B, founded at a depth D, is often taken as (also known as the Terzaghi Bearing Capacity equation):

N_γ, N_q are coefficients that depend on the effective friction angle of the soil, φ’. It is commonly accepted that (Bowles, 1996):

However, for calculating N_γ, different equations have been recommended. One of the most popular equations is that of Brinch-Hansen (1970):

Because of the difficulties in measuring the effective friction angle of the sand in the laboratory, in- situ index tests such as the Standard Penetration Test, are almost always used to estimate the friction angle (Naval Facilities Engineering Command, 1986). Many researchers provided recommendations correlating the effective friction angle of granular material with the SPT blow-count (e.g. Meyerhof, 1956, Peck et al. 1974, Schmertmann, 1975). Most recently, Hatanaka and Uchida (1996) collected high quality “undisturbed” freezing samples and provided a correlation of the blow-count measured in-situ with the friction angle evaluated in the laboratory. The authors noted that “almost all of the data falls within the range of ±3°” of the best fit line to these data, but did not provide a more quantitative expression of this uncertainty. A regression analysis using their data was performed to evaluate the standard error in the correlation. The resulting equation was also modified to adjust the resulting N-value using the Japanese equipment to the normalized N₆₀ value used in the United States (Mayne, 2003). The best fit of the resulting equation was compared against the equation suggested by Hatanaka & Uchida (1996) and there was no difference in the predicted friction angle. The form of equation used is:

where ε is the standard error from the regression analysis, which has a zero mean and a standard deviation of 2.3.

The design procedure for the bearing capacity criterion used in practice can be summarized in the following steps: the SPT blow-count measured in the field is corrected and normalized to an effective overburden pressure of 1 atmosphere using the Liao and Whitman (1985) recommendation, the deterministic corrections based on Youd et al. (2001), and the energy correction according to equation 5. The Hatanaka and Uchida (1996) correlation (equation 4) is then used to estimate the friction angle from the corrected SPT value N_1,60 .

where N is the number of blows measured in the field, and N₆₀ is the equivalent number of blows for a hammer energy ratio of 60%. Different energy correction factors C_E are applied depending on the type of hammer used. For a safety hammer C_E is between 0.7 and 1.2 (Youd et al. 2001). ASTM D6066-96 notes that even when the energy is measured in the field, the energy ratio may still vary overall around 10% from the initially measured value.

The resulting friction angle is then applied in the Terzaghi equation (equation 1) using equations 2 and 3, and the ultimate bearing capacity is estimated. Recognizing the uncertainties involved, factors of safety are applied to reduce the estimated ultimate bearing capacity from equation 1. The bearing capacity allowable design stress is:

The factor of safety (FS) is a function of the importance of the structure, the consequences of failure, and the uncertainty of the subsurface investigation. The factor of safety approach gives the false impression that when two structures are designed with the same factor of safety the degree of conservatism in the design is the same.

Excessive Settlement

Because of the difficulties in obtaining undisturbed samples in sands to evaluate the compressibility of the soil in the laboratory, the use of in-situ tests are again popular, and various recommendations have been made based on field data. The Burland and Burbidge (1985) procedure involves one of the most comprehensive efforts in this regard. The method was based on a statistical analysis of 200 records of settlement of foundations, tanks, and embankments on sands and gravels. For an allowable settlement of 2.5 cm the allowable stress q_2.5 (in kPa) is given by the following equation:

where B is the width of foundation in meters, N is the average N-value of the SPT over the depth of influence (about one foundation width), and T is a statistically evaluated random variable that has the normal distribution with a mean of 2.23 and a standard deviation of 0.26. The standards at the time the data were collected were ASTM 1586-67, which failed to recognize many of the sources of uncertainty. Thus, it can be reasonably assumed that any uncertainty involved in the SPT blow-count is included in the uncertainty of the T variable. A simple design equation having a 30% probability of exceeding the settlement of 2.5 cm based on the Burland and Burbidge (1984) approach, which is used in this reliability analysis, is:

You can put all this into practice and compare various design methods with our new SPTfoundation app, which can be found here:

SPTfoundation

Reference:

Zekkos, D.P., Bray, J.D., Der Kiureghian, A. (2004), “Reliability of shallow foundation design using the standard penetration test”, 2nd International Conference on Site Characterization Proceedings, 19-22/9/2004, Porto, Portugal, Vol.2, pp. 1575-1582.