# Bearing Capacity of Ring Foundations on Sand Overlying Clay
## 4 Comparisons of Previous Studies
### For Strip and Circular Footings on Sand Overlying Clay  
In Table 3, the results of the normalized bearing capacity, \(p_{u}\)/(\(\gamma B\)), for a strip foundation on sand overlying clay are compared with the solutions reported by (1) [PERSON] and [PERSON] [8] by using the semi-empirical solution, (2) [PERSON] and [PERSON] [12] by using the upper bound rigid-block method, and (3) [PERSON] et al. [3] by using finite-element upper- and lower-bound limit-analysis methods. The present result is particularly close to those of [PERSON] et al. [3]. Both solutions of [PERSON] and [PERSON] [8] and [PERSON] and [PERSON] [12] overestimate the bearing capacity \(p_{u}\)/(\(\gamma B\)) by up to 16% and 22% compared to the presented upper bounds and lower bounds, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\varphi\) = 30\({}^{\circ}\) & \(\varphi\) = 35\({}^{\circ}\) & \(\varphi\) = 40\({}^{\circ}\) & \(\varphi\) = 45\({}^{\circ}\) \\ \hline [PERSON] (1985) \({}^{\mathrm{a}}\) & 15.73 & 42.38 & 124.46 & 418.93 \\ [PERSON] and [PERSON] (2002) \({}^{\mathrm{b}}\) & – & 45.00 & 130.00 & 456.00 \\ [PERSON] (2004) \({}^{\mathrm{a}}\) & 15.54 & 41.97 & 124.10 & 419.44 \\ [PERSON] et al. (2007) \({}^{\mathrm{c}}\) & 14.10 & 37.18 & 106.60 & 338.00 \\ [PERSON] et al. (2007) \({}^{\mathrm{d}}\) & 19.84 & 52.51 & 157.20 & 539.20 \\ [PERSON] and [PERSON] (2009) \({}^{\mathrm{e}}\) & 15.80 & 42.00 & 122.20 & 405.50 \\ [PERSON] and [PERSON] (2011) \({}^{\mathrm{c}}\) & 14.65 & 39.97 & 116.20 & 379.79 \\ [PERSON] and [PERSON] (2015) \({}^{\mathrm{c}}\) & 14.80 & 40.10 & 116.57 & 380.08 \\ Present study \({}^{\mathrm{c}}\) & 15.06 & 40.15 & 115.03 & 373.37 \\ Present study \({}^{\mathrm{d}}\) & 15.62 & 42.21 & 124.97 & 422.68 \\ \hline \hline \end{tabular} Note. \({}^{\mathrm{a}}\) method of characteristics; \({}^{\mathrm{b}}\) finite difference method; \({}^{\mathrm{c}}\) lower bound solution; \({}^{\mathrm{d}}\) upper bound solution; \({}^{\mathrm{e}}\) finite element method.  
\end{table}
Table 2: Comparison of bearing capacity factor (\(N_{\gamma}\)) for a rough circular foundation on homogeneous sand.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{\(c_{u}\)/\(\gamma B\)} \\ \cline{2-7}  & **0.5** & **1.0** & **2.0** & **3.0** & **4.0** & **5.0** \\ \hline [PERSON] and [PERSON] (1980) \({}^{\mathrm{a}}\) & 18.28 & 27.00 & 41.55 & 51.23 & 59.62 & 67.69 \\ [PERSON] and [PERSON] (1995) \({}^{\mathrm{b}}\) & 20.06 & 26.36 & 41.06 & 52.21 & 61.24 & 68.82 \\ [PERSON] et al. (2003) \({}^{\mathrm{b}}\) & 20.71 & 27.81 & 38.80 & 48.97 & 57.84 & 66.39 \\ [PERSON] et al. (2003) \({}^{\mathrm{c}}\) & 16.17 & 23.44 & 34.59 & 43.95 & 52.34 & 59.43 \\ Present study \({}^{\mathrm{b}}\) & 16.85 & 24.79 & 36.90 & 46.91 & 55.89 & 64.09 \\ Present study \({}^{\mathrm{c}}\) & 15.59 & 23.15 & 34.43 & 43.59 & 51.74 & 59.97 \\ \hline \hline \end{tabular} Note. \({}^{\mathrm{a}}\) limit equilibrium method; \({}^{\mathrm{b}}\) upper bound solution; \({}^{\mathrm{c}}\) lower bound solution.  
\end{table}
Table 3: Comparison of normalized bearing capacity, \(p_{u}\)/(\(\gamma B\)), for a rough strip foundation on sand overlying clay (\(H\)/\(B\) = 2, \(\varphi\) = 45\({}^{\circ}\)).  
Table 4 provides the obtained values of \(p_{u}\)/(\(\gamma R_{0}\)) for a circular foundation on layered sand-clay media and compares them with the analyses of [PERSON] and [PERSON] [30] using the lower bound solution and [PERSON] et al. [9] using the limit equilibrium method. The comparisons of the present results have been also provided with the centrifuge test results of [PERSON] et al. [19]. It can be observed that the present results compare reasonably well with the results of [PERSON] et al. [9, 19] and [PERSON] and [PERSON] [30].