## 1 Introduction  
Hydropower plays an important role in the transition to clean power. In order to achieve the goal of net zero emissions in time, the construction of hydroelectric power plants (HPPs) has been accelerated [1; 2; 3]. Spiral case structure (SCS) is one of the major structures in HPP, where hydro energy is converted into electricity [4]. A SCS usually consists of steel spiral case (SSC) and mass concrete with engineered reinforcement, and it provides a circumferentially uniform water intake for a [PERSON] or Francis turbine. In general, there are three types of SCSs, which are the P-type SCS, M-type SCS and N-type SCS. The P-type SCS stands for the method where SSC is embedded in concrete under temporarily water-pressurized condition, while the M-type SCS and N-type SCS are embedded under an unwatered condition. The difference between the M-type and N-type SCSs is that the N-type SCS is embedded in a natural state, while the M-type SCS has a compressible membrane covering the SSC. In most medium and high head HPPs with storage or pumped-storage facilities, P-types SCS is always adopted for its abundant engineering practices as a well-established technology [5]. The standard construction procedure of P-type SCS is shown in Figure 1. The first-phase concrete and pedestal of the SSC are constructed previously to provide necessary support for the SSC. Then, the SSC is placed in position and sealed with the test head and test barrel. The test head is set at the inlet of the SSC, and the test barrel is set between the upper and lower stay rings. Meanwhile, the SSC is fixed to the concrete with tie rods around it to prevent the uplift of SSC during the construction of the second-phase concrete. Then, temporary internal water pressure (IWP) is specified in the SSC, and second-phase concrete is constructed with the SSC under pressurized conditions. Finally, after the set of second-phase concrete, the temporary IWP is released, the sealing devices are removed and the construction of a P-type SCS is, thus, finished. However, at the present rate of hydropower development, the global energy pathway to net zero emissions will not be realized [6]. Considering that M-type SCSs do not need pressurization equipment in the construction period, it is believed that they can simplify the construction procedure and help reduce the span of the powerhouse [7; 8; 9]. Accordingly, several attempts have been made to install M-type SCSs in high head HPPs, such as all five SCSs in the Lijiaxia HPP and nine out of thirty-two SCSs in the Three Gorges HPP [10; 11]. The standard construction procedure of M-type SCS is shown in Figure 2. The construction of the first-phase concrete and pedestal of the SSC is similar to that of P-type SCS. Then, after the SSC is placed in position with inner supporting rods, the top portion of it is covered with a compressible membrane. After that, the second-phase concrete is constructed, with no need for sealing devices or pressurization. Despite the merits of M-type SCSs, there exists some concerns about them, such as the long-term mechanical properties of compressible membrane, which has been investigated during the feasibility study of the Three Gorges HPP [12; 13]. Besides, for an average P-type SCS, the mass of the water inside it during pressurization can reach \(1\times 10^{6}\) kg, which might help a lot resisting the raising displacement of the SSC during the construction of concrete. However, the current study concerning temporary IWP mainly focuses on its effect on the contact between the SSC and the concrete [14; 15; 16; 17], and the effect of the gravity of water inside has been long neglected. Figure 1: Standard construction procedure of P-type SCS. During the construction period of a 700 MW class turbine set with M-type SCS in China, a structural deformation accident happened with the maximum raising deformation of 45 mm of the SSC, and it took over four months to remove about 1200 m\({}^{3}\) concrete before reconstruction, causing severe economic loss [18].