## 5 Conclusions  
In this investigation, numerical finite element calculations were adopted to analyze the stability of a deep foundation pit with hard surrounding rocks under fixed vertical supports of drilled grouting piles and varied transverse supports of steel bracings and prestressed anchorages. The parameters used for stability evaluation included the lateral displacement of the surrounding rocks, settlement of the surrounding ground, axial forces of the steel bracings, and displacement at the tops of the drilled grouting piles. According to the simulation results, the following conclusions could be drawn. (1) After setting the two-layer prestressed anchorages to 8 m and 22.5 m underground and one-layer steel bracings to 16 m beneath ground, the lateral displacements of the surrounding rocks were the lowest, while setting the one-layer steel bracings to 9 m underground and one-layer prestressed anchorages to 22.5 m beneath the ground led to the highest lateral displacements of the surrounding rocks. (2) The four different transverse supporting schemes of different layers of steel bracings and prestressed anchorages were effective in terms of controlling lateral displacements of the surrounding rocks and settlement of the surrounding ground, the values of which at different excavation stages were relatively lower compared to those required in the Chinese standard of GB50007-2011. (3) Though the transverse supporting scheme consisting of setting two-layer prestressed anchorages at 8 m and 22.5 m beneath ground and one-layer steel bracings at 16 m underground could effectively control lateral displacements of the surrounding rocks and settlement of the surrounding ground, the corresponding construction techniques were rather complicated, and the foundation pit was over-supported compared with the other three transverse supporting schemes, leading to a waste of supporting elements and labor resources, prolonged construction durations, and increased construction costs. (4) Though the displacements of the surrounding rocks were the second smallest when setting four-layer steel bracings at 4 m, 8 m, 12 m, and 16 m underground and one-layer prestressed anchorages at 22.5 m underground, the four-layer steel bracings occupied too much space for excavation, which obviously negatively influenced the excavation techniques applied to the foundation pit. (5) Though the lateral displacements of the surrounding rocks and settlement of the surrounding ground were the highest when setting one-layer steel bracings at 9 m underground and one-layer prestressed anchorages at 22.5 m beneath ground, the corresponding values were relatively lower compared to those illustrated in the Chinese standard of GB50007-2011. (6) Compared with the deformations of the retaining structures for excavating deep foundation pits in soft soils or soft rocks, those for excavating the deep foundation pit with hard surrounding rocks were significantly reduced when adopting a conventional support scheme of retaining structures and inner supports. Therefore, when excavating deep foundation pits with hard surrounding rocks, appropriately reducing inner supports could be beneficial for lowering costs, construction duration, and so on. Conceptualization, Z.M. ; methodology, Y.L. and K.L. ; software, K.L. ; validation, Z.M. and Z.G. ; formal analysis, Y.L. and Z.M. ; writing--original draft preparation, F.G. and K.L. ; writing--review and editing, F.G.; funding acquisition, Z.M. and P.G. All authors have read and agreed to the published version of the manuscript. This research is supported by the National Key Research and Development Program of China (No. 2019 YFE0118500), the National Natural Science Foundation of China (No. U22A20598), and the Natural Science Foundation of Jiangsu Province (No. BK20200634). The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors. Authors [PERSON] and [PERSON] were employed by the company China State Construction Infrastructure, Co., Ltd.