# Comparative Analysis of Kazakhstan and European Approaches for the Design of Shallow Foundations
## 2 Review of the Design Codes  
### Bearing Capacity  
When adhering to SP RK 5.01-102-2013: 'Foundations of buildings and structures', the bearing capacity of soil under the foundation base is determined in accordance with the following equation:  
\[R=\frac{\gamma_{c1}\gamma_{c2}}{k}\Big{[}M_{y}k_{z}b\gamma_{II}+M_{q}d_{I} \gamma^{\prime}{}_{II}+\Big{(}M_{q}-1\Big{)}d_{b}\gamma^{\prime}{}_{II}+M_{c}c_{ II}\Big{]}, \tag{1}\]  
where \(\gamma_{c1}=1.25\), \(\gamma_{c2}=1.0\), \(k=1.0\), \(M_{y}=0.61\), \(M_{q}=3.44\), \(M_{c}=6.04\), \(k_{z}=1.0\), \(b=1.5\) m for pad foundation or 2.0 m for strip foundation, \(\gamma_{II}=\gamma^{\prime}{}_{II}=19.42\) kN/m\({}^{3}\), \(c_{II}=15\) kPa, \(d_{I}=1.0\) m, and \(d_{b}=0\). The ultimate limit state analysis (ULS) of a shallow foundation requires the average pressure under the foundation base (\(p\)) not to exceed the bearing capacity of soil (\(R\)):  
\[p\leq R, \tag{2}\]  
The average pressure under the foundation base is determined using the following equation:  
\[p=\frac{N+G_{f}+G_{g}}{b}\, \tag{3}\]  
where \(N\) is the average pressure per 1 m of foundation under the foundation base, kN/m, \(G_{f}\) is the foundation weight per 1 m, kN/m and \(G_{g}\) is the weight of soil on the foundation slab per 1 m of foundation, kN/m. The analytical method for the calculation of bearing capacity is provided in Annex D of EC 7. In drained conditions, the design bearing capacity for a shallow foundation is determined using the following equation:  
\[R/A^{\prime}=c^{\prime}N_{c}b_{e}s_{c}i_{c}+q^{\prime}N_{q}b_{q}s_{q}i_{q}+ \frac{1}{2}\gamma^{\prime}B^{\prime}N_{\gamma}b_{\gamma}s_{\gamma}i_{y}, \tag{4}\]  
where \(A^{\prime}=3.0\) m\({}^{2}\) for a pad foundation or 20.0 m\({}^{2}\) for a strip foundation, \(\gamma^{\prime}=19.42\) kN/m\({}^{3}\), \(N_{q}=7.82\) (DA1-1 and DA2) and 5.06 (DA1-2 and DA3), \(N_{c}=16.88\) (DA1-1 and DA2) and 12.79 (DA1-2 and DA3), \(N_{\gamma}=5.51\) (DA1-1 and DA2) and 2.57 (DA1-2 and DA3), \(b_{q}=b_{c}=b_{\gamma}=1.0\), \(s_{q}=1.28\) (DA1-1 and DA2) and 1.23 (DA1-2 and DA3) for a pad foundation or 1.07 (DA1-1 and DA2) and 1.06 (DA1-2 and DA3)  
Figure 1: Distribution of building regulations around the world. for a strip foundation, \(s_{c}=1.32\) (DA1-1 and DA2) and 1.28 (DA1-2 and DA3) for a pad foundation or 1.09 (DA1-1 and DA2) and 1.08 (DA1-2 and DA3) for a strip foundation, \(s_{\gamma}=0.78\) for a pad foundation or 0.94 for a strip foundation, \(i_{c}=i_{q}=i_{\gamma}=1.0\). Due to the design procedure of limit state analysis with the combination of partial factors according to EC 7, the designer should ensure that the design value of bearing capacity (\(R_{d}\)) is larger than/equal to the design value of the vertical load acting on the foundation base (\(V_{d}\)) as follows:  
\[V_{d}\leq R_{d}, \tag{5}\]  
EC 7 involves three design approaches (DA1, DA2, and DA3), which require the application of different values of partial factors. For the design of shallow foundations, partial factors are used for the calculation of actions (A), material properties (M), and resistances (R). The combinations of partial factors corresponding to different design approaches are presented in Table 1. There are two combinations of DA1 which involve the application of partial factors on actions only and variable actions and soil parameters for DA1-1 and DA1-2, respectively. For DA2, the partial factors are applied on actions and resistances, rather than soil properties, whereas, for DA3, the partial factors are applied on actions and soil parameters simultaneously. The material strength design (MSD) method is used by DA1 and DA3 so that the partial factors are applied on actions and material strength parameters. As the partial factors for DA2 are applied on actions and resistance simultaneously, this approach is based on the load and resistance factor design (LRFD) method.