{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T14:02:59Z","timestamp":1783605779157,"version":"3.55.0"},"reference-count":21,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T00:00:00Z","timestamp":1601510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant No 51778576"],"award-info":[{"award-number":["Grant No 51778576"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In order to reduce the disturbance to adjacent tunnels caused by tunnel crossing, the existing tunnels are often reinforced by setting grouting rings along the pipe piece ring. In this context, the volume expansion of the grouted soil has to be taken into account, and a mechanical model of the volume expansion of the grouting rings is proposed here to study the effect of the grouting rings of new tunnels on the additional stress on the existing tunnels as well as their vertical displacement. The additional stresses on and the vertical displacement of the axis of the existing tunnels caused by the expansion of the grouting rings were deduced based on the stochastic medium theory. The influences of various volumetric expansion rates (Q) of the grouting rings, different lengths of the grouting rings, and different tunnel crossing angles on the settlement of and the additional stress on the existing tunnels were studied. The results demonstrate that the grouting rings can effectively reduce the impacts of the additional stress and the settlement deformation on the existing tunnels. The results of the tunnel settlement obtained from the calculation method proposed in this paper are in good agreement with the measured engineering data.<\/jats:p>","DOI":"10.3390\/sym12101623","type":"journal-article","created":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T09:04:12Z","timestamp":1601543052000},"page":"1623","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Method of Calculating the Vertical Displacement and Additional Stress of Existing Tunnels under the Influence of Grouting Rings of New Tunnels"],"prefix":"10.3390","volume":"12","author":[{"given":"Yongjie","family":"Qi","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, Zhejiang University City College, Hangzhou 310015, China"},{"name":"School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Zhejiang University City College, Hangzhou 310015, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Zhejiang University City College, Hangzhou 310015, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sun, L., Liu, G., Wang, Z., Wu, S., and Hong, C. 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