# Bearing Capacity of a Concrete Grouting Pad on the Working Surface of a Highway Tunnel Shaft
## 6 Conclusions  
This paper first analyses the punching shear failure mode of a grouting pad under symmetric load. Secondly, the unified solution of the plastic limit load for grouting pad punching shear failure is deduced, and the influence law of the plastic limit bearing capacity parameter of a grouting pad is discussed; finally, the plastic limit design method of grouting pad thickness is proposed. The results of this study are applied to the optimal design of grouting pad thickness in shaft 2-2 of the Tianshan Shengli Tunnel, which solves the frequent cracking of the grouting pad. The main conclusions of this paper are as follows:  
1. The grouting pad failure mode is punching shear failure. The formation of annular holes or \"weak rings\" due to peripheral grouting holes is the basic condition for failure. The bearing capacity is insufficient to withstand the lifting force produced by grouting and the water pressure on the working surface. These two factors work together to lead to punching shear failure. 2. A uniform solution for the bearing capacity of the grouting pad is derived and verified to be reasonable. When \(b\) is set to 0 and 0.5, it can degenerate to the Tresca and Mises yield criteria, respectively. The bearing capacity \(q_{\text{u}}\) shows a trend of first decreasing and then increasing as the value of \(b\) increases. The minimum value is reached when \(b\) = 0.4, and the maximum value is achieved when \(b\) = 1. Therefore, the unified solution is recommended for design calculations, as it better utilises the the potential of material strength. 3. When the thickness is certain, the bearing capacity of the grouting pad is inversely proportional to the ratio of the diameter to the area of the loaded area at the bottom. It is important to follow the principle of \"division, interval, and hole skipping\" during grouting construction. When designing a grouting pad, the maximum bearing capacity is achieved when the \(r_{2}\)/\(r_{1}\) ratio is close to 1.25. As the ratio of \(r_{2}\)/\(c\) increases, the value of \(r_{1}\) exhibits a three-stage trend of first decreasing, then increasing, and finally decreasing. 4. The bearing capacity of a grouting pad increases with its thickness under the same load conditions. When the diameter of the grouting pad is \(2r_{2}\) and the thickness \(B_{0}\) is constant, the bearing capacity \(q_{\text{u}}\) increases with an increase of the tensile strength de sign value \(f_{\rm t}\) of the grouting pad concrete material. Following the principle of \"large thickness, unified strength yield criterion, high-strength material\" in the design is recommended to obtain better bearing performance of the grouting pad. * The new method for bearing capacity design proposed in this article has been applied in engineering practice, effectively solving the problem of frequent cracking of grouting pads during shaft grouting construction, and confirming its good feasibility and practicality. The findings have practical guidance significance for the design and construction of grouting pads for deep and large shafts of extra-long tunnels. Formal analysis and writing\(-\)original draft preparation, T.F. ; resources and funding acquisition, Z.Z. ; conceptualisation and methodology, J.C.; supervision and project administration, Y.L. ; investigation, W.L. ; validation, D.L. ; writing\(-\)review and editing, R.Y. ; writing\(-\)review and editing, J.L. All authors commented on previous versions of the manuscript. All authors have read and agreed to the published version of the manuscript. This work was supported by the Key Project of the High-Speed Rail Joint Fund of the National Natural Science Foundation of China (Grant No. U2268214), National Natural Science Foundation of China (Grant No. 52308390), Natural Science Basic Research Program of Shaanxi Province (Grant No. 2023-JC-QN-0383), Scientific Research Project of CCCC First Highway Engineering Company (Grant No.