###### Abstract  
Tunneling under existing underground buildings has become a common issue in densely populated urban areas. The current elastic analysis for ground displacement from new tunnel construction focuses on circular tunnels. However, theoretical analysis for non-circular chamber excavations is lacking. This paper aims to develop an elastic analysis for ground deformation from non-circular chamber excavations using the 'equivalent radius' theory, [PERSON]'s formula, and [PERSON]'s model. It adjusts the ellipticization parameter \(\hat{s}\) and uniform radial displacement \(\epsilon\) in [PERSON]'s formula. Additionally, equivalent stiffness values for diverse existing hollow structures are considered using various approaches. A comparison of the theoretical results from field measurements and simulations shows the modified equations predict ground deformation well. Finally, parametric analysis explores the impacts of non-circular cavern excavations on existing structures under different factors.  
non-circular tunnel; existing underground structure; elastic foundation beam; mechanical response +
Footnote †: journal: applied sciences  
0000-0001-5000-5000-0000]X.X.  
for numerical simulations, and swiftly and efficiently calculating the response of existing structures remains challenging.  
Compared with model tests and numerical simulations, the theoretical method boasts clear conceptual mechanisms, straightforward calculations, and easy generalization. It is suitable for analyzing the response of existing structures during the preliminary engineering evaluation stage, offering efficient and stable calculation results. Theoretical analysis studies encompass elastic foundation models [20; 21; 22; 23; 24; 25; 26; 27], including the Euler-Bernoulli beam calculation for vertical deformation of existing tunnels under underpasses, derived from the Winkler model [28], and settlement methods for homogeneous structures during tunnel excavation [29]. For example, based on the analytical solution of shield tunnels influenced by additional ground loads derived from the Pasternak model [30], dynamic modeling of partially embedded structures' PNF in soil was performed [31]. Furthermore, Timoshenko beams have been employed by researchers to model the response of existing tunnels to shield crossing [32; 33; 34; 35] alongside the application of the Fuss-Winkler model [36]. However, these studies primarily focus on analyzing the influence of circular tunnels passing beneath structures, with a lack of accurate analysis of irregular cavern sections. In fact, as urbanization progresses, irregular cavity cross-sections have become widely used [37; 38; 39; 40]. The excavation of these irregular sections' impact on existing structures warrants further exploration.  
In this paper, an underground subway tunnel is used as an example to analyze existing structures from non-circular chamber excavation utilizing the two-stage method incorporating the \"equivalent radius\" theory. The interaction between the new tunnel, soil mass, and existing structure is decoupled into two separate analysis stages. First, the existing structures are ignored, and only the new tunnel is considered. The free-soil displacement at the location of the future existing tunnel, due to the excavation, is analyzed and computed. In the second stage, the additional displacement load arising from this free-soil displacement is applied to the existing structure. Subsequently, the interaction between the soil and the existing structure is analyzed to determine the mechanical response of the latter. Field monitoring and numerical simulation validate the method. Parametric studies investigate the effects of factors like the clear distance between the new single-cavity tunnel and the existing underground structure's floor, the excavation area of the new tunnel, and the spacing between twin-cavity tunnels. The presented analysis and theoretical models offer valuable insights for engineers tackling non-circular cavern excavations through existing hollow structures.