Analytical solutions and in-situ measurements on the internal forces of segmental lining produced in the assembling process

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Abstract

Most of the traditional design methods assumed shield tunnel lining as a perfectly formed ring, without special attention to the effect of pre-deformations and inaccuracies produced in the assembling process before the segmental ring is closed. However, these factors can significantly affect the mechanical performance and durability of the tunnel. To make up for the deficiencies of conventional design models, we contributed a new method to evaluate the internal forces of tunnel lining produced in the assembly, in which the key idea is to appropriately assume the assembly tolerance of bolt holes and pre-deformations of the lining ring. By applying the principle of minimum potential energy, analytical solutions for three cases (ALS-FF, ALS-FC, ALS-CC) were developed to determine the internal forces of segments produced in the assembly process. Then, an in-situ measurement was conducted to validate the method, and it showed a favorable agreement with the theoretical results. Furthermore, the critical parameters of the proposed model were verified by parametric studies, which revealed that the higher the tolerance space Tsp, the lower the internal forces induced by the assembly inaccuracy. According to the research results, the reasonable tolerance space Tsp and other critical design parameters can be determined for a shield tunnel to achieve optimal performance. The simplicity and practicability of the analytical method, as well as the quantitative evaluation of the effects of assembly inaccuracy on tunnel lining, would undoubtedly contribute to the improvements and optimizations of the design of segmental tunnel lining.

Introduction

Shield tunnel lining is formed by assembling the precast segments in the site to form a closed ring to resist the ground pressures. Compared with the cast-in-place concrete lining, the segmental lining could significantly improve the construction efficiency and quality on the presumption that the lining is assembled perfectly. There have been numerous approaches for segmental lining design in the available design guidelines or codes [14], [23]. Most of the general design methods of tunnel lining supposed the external loads as the earth and water pressure at the serviceability stage. However, field measurements showed that loads from the construction stage, especially during the segments assembling, were inherently different from those at the serviceability stage [4], [19]. Still, few of these provide a quantitative justification to the criteria considered for the construction effects or loads on the segment.

The increasing damages of segments during the construction stage indicated that the construction loads were one of the dominant factors for segments [16], which deserved our special attention. Japan Society of Civil Engineers [15] established a technical committee working on the effects of construction loads and found that construction loads were complex with coupling effects. Sugimoto [21] summarized the causes of segments damages of shield tunnel lining during construction. Cavalaro et al. [5] also found frequently occurred cracks caused by the contact deficiencies between the segments. Based on a case study in Shanghai shield tunnel, Yang et al. [25] found that different kinds of segment cracking or damage will occur during the construction stage caused by improper assembling loads. Using a ground-spring model as the joint connector, Chaipanna and Jongpradist [6] investigated the responses of a segmental lining considering the construction loads. Zakhem and Naggar [29] simulated the staged construction sequence of shield tunneling by finite element method (FEM) and found that the earth pressure on the segmental tunnel lining decreased with the grouting consolidation. Several other researchers had employed analytical method [11], [10], [24], FEM [9], [2], [1], [4], [3], [22], [7], [8], model test [4] as well as in-situ measurement [9], [19], [12] to investigate the effects of construction loads on lining behaviours. Most of the research focused on the apparent loads (earth and water pressures, grouting pressures, jack forces, etc.), and interaction forces between shield and tunnel lining, ignoring the actions induced by segment assembly deviations. Although some of the research considered the effects of segment dislocations and pre-deformations in the models [4], [3], they were still assumed as wished in place without considering the assembly process.

Up to date research and design models assumed shield tunnel lining as a perfect ring in place, with various construction loads considered but without special attention to the effects of pre-deformations and the inaccuracies produced in the process. The ignorance and simplification might be reasonable for small diameter tunnels in simple geological conditions. However, with large diameter and deep tunnels emerging around the world, the present design methods are now facing much more difficulties in defining the actual state of tunnel lining imposed by construction uncertainties than before. The new challenges have caused detrimental effects on the tunnel lining.

It is noted that all the effects of the construction-related process should be considered in design; otherwise, the effect of dislocations and inaccuracy of construction will be amplified so much on the design results that the conventional design methods would be no longer applicable in practice. To find a solution to the problem, we contributed an innovative idea, which was to assume appropriately the assembly tolerance of bolt holes and pre-deformations of the lining ring. Then by applying the principle of minimum potential energy, three analytical solutions were established to calculate the internal forces of different boundary conditions induced in the assembly process. Furthermore, the proposed method was verified and validated by an in-situ test on a large underwater tunnel in China.

Section snippets

Basic models and assumptions

As shown in Fig. 1, the basic model consists of the completed lining ring (CLR) and the assembling lining ring (ALR). The ALR includes two kinds of segments, the completed lining segments (CLS) and the assembling lining segment (ALS). Fig. 2 shows the assembling process of the segmental lining, in which the standard segments (B1 ~ B7) are firstly assembled one by one, and then the two adjacent segments (L1 and L2) and lastly, the key segment (K). For simplicity, each segment was assumed to be

In-situ measurement verification

To validate the proposed method, an in-situ measurement was conducted on a large segmental tunnel, and the internal forces of lining produced in the whole process of segments assembly were all successfully measured and recorded for verifications and comparison of the theoretical results with the in-situ measurement.

Conclusions and discussions

This paper developed an analytical method to evaluate the internal forces of segmental lining induced by pre-deformations and assembly inaccuracy. The analytical solutions to the internal forces were obtained for three kinds of segments (ALS) with constraint ALS-FF, ALS-FC, ALS-CC, respectively. Furthermore, an in-situ measurement was conducted to corroborate the proposed method. The main conclusions are summarized as follows:

  • (1)

    The effect of assembly inaccuracy and pre-deformations on the

CRediT authorship contribution statement

Meng-bo Liu: Investigation, Data curation, Writing - original draft. Shao-ming Liao: Supervision, Conceptualization, Writing - review & editing, Funding acquisition. Jin Xu: Methodology, Validation. Yan-qing Men: Formal analysis, Software.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to express their sincere thanks to the supports of the National Basic Research Program of China (973 Program) (Grant No. 2015CB057806) and the projects (Grant No. 17DZ1203804, No. 19511100802) supported by Shanghai Committee of Science and Technology.

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