## 6 Conclusions  
In this study, the convergence-constraint method was adopted to calculate the stability of the surrounding rock support structure of a vertical shaft in a large deep fault crushing area using two mechanical models. The following conclusions are drawn.  
(1) When the ideal elastoplastic model is used for calculation, the calculation results show that when joint deformation of the shaft-surrounding rock and the supporting structure reaches 33 mm, the surrounding rock and the supporting system are in balance. Actual monitoring results showed that the shaft wall had been damaged, and deformation of the supporting structure on the 23 rd day of installation exceeded 300 mm. The result calculated by the ideal elastoplastic model differs from that of the on-site supporting effect.  
(2) In this study, the displacement release of surrounding rock was 100 mm as the opportunity for secondary support of the shaft wall. The well wall secondary support parameters were a well ring (No. 28 A-shaped I-beam), shed distance \(d_{1}\) = 1.2 m, and C35 concrete thickness \(t\) = 700 mm. The calculation results using the strain-softening model show that the surrounding rock characteristic curve and the elastic part of the supporting structure characteristic curve intersect, indicating that the surrounding rock and the supporting system are in balance. The field application results showed that 35 days after the supporting structure was constructed, the deformation rate of the surrounding rock was less than 1 mm/day and the deformation was finally controlled at 140 mm. The calculation results were in line with actual observations.  
(3) Actual application of the models shows that the strain-softening model for equivalently jointed plutons, built on the continuum media theory of plutons and the GSI rock grading system, is more realistic than conventional ideal elastic-plastic models for reflecting the post-peak non-linear mechanical properties of deep and weak plutons. Aiming at stability control of shaft-surrounding rock in deep and large fault fractured areas, the key to the support technology based on the post-peak strain-softening model of rock mass is to introduce the idea of high-resistance yielding, improve the stiffness of the primary support, reasonably release the stress of the surrounding rock, and provide high-strength secondary support in a timely manner.  
Conceptualization, J.Z.; data curation, Y.W. and B.Y.; formal analysis, J.Z. and C.S.; funding acquisition, J.Z.; investigation, Y.W., B.Y., D.C. and B.J.; methodology, J.Z. and Y.W.; project administration, J.Z., Y.W., B.Y. and B.J.; resources, J.Z. and Y.W.; software, Y.W., B.Y., D.C. and C.S.; supervision, J.Z. and D.C.; validation, J.Z., Y.W. and C.S.; writing--original draft, J.Z. and Y.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by The Education Department of Liaoning Province (grant number LJ2017 QL037), National Key R&D Projects (grant number 2017 YFC1503101), National Natural Science Foundation of China (grant number 51704144), and The Discipline Innovation Team of Liaoning Technical University (grant number LNTU20 TD08). The APC was funded by The Discipline Innovation Team of Liaoning Technical University.  
Not applicable.  
All data from this study are included in the submitted manuscript.  
We thank [PERSON], and [PERSON] for editing the language in the drafts of this manuscript.  
The authors declare no conflict of interest.