## 2 Experimental Program for Field Tests
### Test Results  
The purpose of the field test is to evaluate the pile section with the maximum bending moment and to verify the plane cross-section assumption. From the deflection profiles in Figure 4a, we can see that the data from inclinometers and those from sliding micrometers agreed with each other, which means that the casing and the concrete body of the pile bent as an assembly. The bending moment along the pile and the casing is shown in Figure 4b. Figure 3: The layout of the instrumentations. From the bending moment profile curves, we can be assured that the maximum bending moment existed in the casing-covered pile section at depths from 11 to 14 m. The larger the applied force was, the deeper the maximum bending moment appeared. It should be noted that the value may not be the real bending moment, and we merely care about the position where the maximum bending moment appeared. Therefore, as seen from Figure 2, the depth of 12 m where the strain gauges were attached was the nearest measurement section in the pile body. The distribution of strain along the cross section is given in Figure 5.  
Figure 4: (**a**) Deflection vs. depth and (**b**) bending moment vs. depth. Figure 5: The distribution of strain along pile cross-section. In Figure 5, the x-label is the distribution of strain along the cross section of the DSPC at the depth of 12 m; the values were from sliding microtiters, vibrating-wire strain gauges, and inclinometers found in Figure 4. The y-label is the height of the pile section. All the points are linearly distributed at different loading stages; the closer the measurement points were to the surface of the pile body, the larger the strain was. It is obvious that there was no relative displacement between the concrete and the casing during the loading process. This means that the casing and the concrete body deformed as an assembly. It is reasonable to use the plane cross-section assumption in the calculation of the bending stiffness. For the rigid stiffness of steel-concrete piles, the calculation method is as follows:  
\[EI=E_{s}I_{s}+\eta E_{p}I_{p} \tag{1}\]  
where \(E_{s}\) is the modulus of elasticity of the steel casing, \(I_{s}\) is the moment of inertia of the steel casing, \(E_{p}I_{p}\) is the bending stiffness of the concrete pile, and \(\eta\) is the correction coefficient. There are different \(\eta\) values for different criteria, such as Chinese codes [13], with a value of 1.0. In Japan [14], this value is 0.2, and in Europe [15], it is 0.6. The initial bending stiffness \(E_{p}I_{p}\) of the DSPC is calculated as follows:  
\[EI=E_{s}I_{s}+E_{p}I_{p}=5.92\times 10^{10}\;\mathrm{N}\cdot\mathrm{m}^{2} \tag{2}\]  
where \(E_{s}I_{s}=E_{s}\pi(d_{1}^{\;4}-d^{4})/64\); \(E_{p}I_{p}=0.85\;E_{c}\pi d(d^{2}+2(a_{E}-1)\rho_{g}d_{0}^{\;2})/32\); \(d_{1}\) is the diameter of the outside casing, \(d_{1}=2.0\) m; \(d\) is the pile diameter, \(d=1.8\) m; \(d_{0}\) is the net diameter that does not include the thickness of the cover, \(d_{0}=1.64\) m; \(a_{E}\) is the ratio of the modulus of elasticity of the steel bar to that of the concrete, \(a_{E}=E_{s}/E_{c}=5.56\); \(\rho_{g}\) is the reinforcement ratio of the pile body, \(\rho_{g}=0.57\)%, \(E_{s}=2.1\times 10^{5}\) MPa; and \(E_{c}\) is the modulus of elasticity of the concrete, \(E_{c}=3.6\times 10^{4}\) MPa. Figure 6 shows the bending moment-stiffness response of pile section 0.3 below the loading point. The x-label is the ratio of the bending moment at the pile section and the maximum value, \(M/M_{\mathrm{max}}\), where \(M=F\!I_{t}\), \(F\) is the lateral force, \(h\) is 0.3 m, and \(M_{\mathrm{max}}\) is 240 kNm. The y-label is the ratio of bending stiffness (\(\alpha\)) at the pile section and the maximum value, where \(\alpha=(EI)_{\mathrm{measured}}/EI\), \((EI)_{\mathrm{measured}}=M/(\mathrm{d}w^{2}/\mathrm{d}^{2}z)\), \(w\) is the deflection of pile (Figure 4), and \(z\) is the depth (m). Figure 6: The bending moment-stiffness response of pile section 0.3 below loading point.