# Case Study of an Underpinning Pile Foundation for an Interval Tunnel Crossing an Existing Bridge
## 2 Project Overview
### Engineering Geological Conditions  
The interdistrict tunnel at the pile foundation underpinning belongs to a mound and valley landform of the dissolution type. According to the engineering geologic investigation report, the main strata at the pile foundation underpinning are miscellaneous fill, plastic red clay, and medium-weathered limestone. The uppermost layer is \(<\)1-2\(>\) miscellaneous fill (Q4 ml), mainly composed of construction waste and artificial backfilled gravel, etc. The gravel blocks are mainly dolomite, the voids are filled by clayey soil, and the structure is looser. The middle layer is \(<\)4-1-3\(>\) plastic red clay (Q4 el+dl); the soil is brownish-yellow, maroon, etc., and is locally distributed in the stratum, with engineering properties such as softening in water, fissure development, and easy flaking. The lower layer is \(<\)20-2-3\(>\) medium-weathered limestone (P1m), with a greenish gray, gray-black, medium-layered structure. The rock is relatively complete, and the mineral composition is mainly composed of calcite and biological debris.  
To determine the deformation modulus of the rock formation, we conducted an indoor rock test, as shown in Figure 3. The uniaxial compressive strength of the rock was measured to be 37.909 MPa, while the rock integrity index provided by the geological survey report was 0.44 and the rock wave speed was 3.42 km/s. In this paper, research results from the literature [27] are used to determine the deformation modulus of the rock mass, which is calculated by Equation (1).  
\[E_{\text{m}}=\left\{\begin{array}{c}\left(\frac{1+K_{\text{v}}}{2}\right) \sqrt{\frac{\sigma_{\text{c}}}{100}}\cdot 10\left(\frac{15V_{\text{p}}-17.5}{40} \right),\left(\sigma_{\text{c}}\leq 100\text{ MPa}\right)\\ \left(\frac{1+K_{\text{v}}}{2}\right)\cdot 10\left(\frac{15V_{\text{p}}-17.5}{40} \right),\left(\sigma_{\text{c}}>100\text{ MPa}\right)\end{array}\right. \tag{1}\]  
where \(E_{\text{m}}\) is the deformation modulus of the rock mass; \(\sigma_{\text{c}}\) is the uniaxial compressive strength of intact rock masses; \(K_{\text{v}}\) is the rock integrity index; and \(V_{\text{P}}\) is the rock body wave speed.  
Finally, the deformation modulus of the medium fractionated limestone is estimated to be 3.75 MPa. Combined with the field monitoring data and the experience of metro construction in the Guiyang area, the deformation modulus of this paper is taken as 2 MPa. The cohesion and internal friction angle of the rock layer and other parameters of the soil layer are taken from the geological survey report and the experience of metro construction in the Guiyang area.  
The main mechanical properties of the strata are listed in Table 1. The thickness of the soil strata shown in Table 1 is the thickness of the soil strata at the time of modeling. Since the actual stratum is not a homogeneous stratum, the stratum thickness is taken as the average thickness of the actual stratum for the simplification of numerical modeling.  
Figure 3: Indoor rock test: (**a**) rock samples for testing; (**b**) rock uniaxial compression test.  
Regarding the swelling angle of the soil, the empirical formula is as follows: swelling angle = internal friction angle \(-30^{\circ}\). When the internal friction angle is less than \(30^{\circ}\), the expansion angle can be regarded as close to \(0^{\circ}\). Therefore, the swelling angle of the soil is not considered in this paper. Soil cohesion is denoted by c, and the angle of internal friction by \(\varphi\). Standard statistical values for the consolidation of fast shear tests were used according to the ground investigation report.