Determination Method of Reasonable Reinforcement Parameters for Subsea Tunnels Considering Ground Reinforcement and Seepage Effect
Round 1
Reviewer 1 Report
The paper discusses the effect of the reinforcement zone around subsea tunnels by using an existing analytical solution and numerical method.
The content and structure is good. However, there are several main and minor issues that need to be fixed as follow:
Comments:
In line 74, the seepage field change due to the excavation is introduced to be R0 = min{20r0,h0}. How this range is decided? If there is any approved reference, it should be mentioned. In Eq. (1) for internal pressure using unconfinement factor, Pa (seepage pressure) is included in Eq. (1). In the case of λ = 0, Pi = P0 + Pa at r = r0. This is against the assumption made in Eq. (10) that at r = r0, Pa = 0. Also, in reference [18] Eq. (1), the same equation is shown without Pa. This inconsistency should be cleared. What is the difference in definition between two references? Equation (2) shows stress equilibrium in a small element assuming stress components and seepage volume force do not vary with the angular orientation θ. This assumption should be mentioned in the same part. In the numerical analyses using FLAC 3D, type of analyses (consolidation analyses?) and soil models for RG and NG zones should be specified. In Fig.6(b), the zone shown by a dashed line for RG seems to be not correct. The range between r0 = 1 m to ra = 1.5 m is RG. In Fig.6(b), for the case of processing path 6 (1-2-5-6), the plastic zone should expand RG, and the by a reduction in internal pressure, plastic zone in NG should develop without reaching the full plastic zone in RG. The calculation results are shown in Fig.6(b) do not represent this sequence. Also, for the case of processing path 9 (1-3-4-6), from 1 to 3, the first plastic region in NG is developed. The line that represents plastic radii for NG starts from r < 1.5 m. This seems to be incorrect. In Table 3, how the first, second, and third rounds decision are made? Enough explanation should be provided in this part? 6(b) shows plastic radii by internal pressure values obtained from numerical analyses. The results of plastic radii by internal pressure values for an analytical solution shall be shown and compared.
Minor comments:
Almost most of the Equation shown in analytical solution part is taken from previous studies including [17] and [19] and are not original. The reference better to be mentioned in each equation. In Table 1, process path 11, the numbers are shown in development history should be 1-4-6 not 1-4-4. In Fig. 3, for the development of the plastic zone in NG and RG zones, the λ56 should be shown in Fig.3-c, not in Fig.3-d. In line 98, the word “larger” in sentences “When λ is larger than λ*12, both RG and NG remain elastic” should change to “smaller”. In Eq. (9), the range for seepage quantity should be corrected to ra =< r <= R0.Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript presents i) an analytical model for subsea tunnelling, ii) an optimisation-procedure for determining reinforcement parameters using this analytical model, and iii) an application of this optimisation to a configuration derived from an existing tunnelling project. The analytical model is developed for deep circular tunnels surrounded by two layers of different materials. It accounts for seepage effects via a Terzaghi-effective-stress assumption. The analytical solution for this model is compared to numerical results which indicate that the derived solution is correct. It is furthermore compared to analytical solutions for simplified settings from literature (*).
In general, the paper is well structured, and the language level is acceptable.
MAJOR REMARKS:
1) The description of the optimisation procedure is too short and simplistic. For instance, the authors indicate that they are "taking the tunnel radial displacement with more complex constraint conditions as the first target". What are these "more complex constraint conditions"? What are the parameters which are used for optimisation? Which are the constraints? How do the authors obtain for instance the displacement (based on their analytical model or based on a numerical model)?
The reviewer suggests that the authors revise this part substantially.
2) The configuration used in section 5 can be classified as a shallow tunnel. The rock cover is 30m, which according to section 2.1 defines the outer radius R0 of the domain investigated in the analytical model. In that case, the pressure on the boundary will be far from the constant value assumed in the analytical model.
It is unclear to which extent the newly developed analytical model can be applied in this context. The analogy to [17], which the authors use to justify the applicability of their approach in the first paragraph of section 5.2, is insufficient since the second material adds a further length scale to the problem.
The reviewer suggests firstly I) a more thorough description of the model which is solved in the course of the optimisation procedure and secondly II) an additional comparison of the analytical solution to a numerical solution, this time the setting for numerical solution to be chosen as the setting of the shallow tunnel investigated in section 5.
3) The abstract can be improved. For instance, the term "existing analytical solutions" is misleading because it refers to solutions of different, simplified problems, see (*) above. It would also be good to indicate (just briefly) what kind of ground reinforcement is considered.
MINOR REMARKS:
A) Author names, fang needs capital letter
B) Table 1, processing path 11, development history is I-IV-VI
C) Equation (10): I assume r_g is r_a
D) Caption of table 2 reads "Calculation of parameters ..."; are these selected parameters (as indicated in the text) or calculated parameters?
E) Legend of figure 6b): Please explain the meaning of the key "on the interface" or omit it. As far as I can see there is no separate interface plasticity formulation in the model, the plasticity is associated with the (sub-)volume(s) only.
F) In section 3.2., what is the pressure boundary condition in the far field under "dry conditions". Does it contain the water pressure?
OVERALL RECOMMENDATION:
I suggest the paper for publication once the optimisation method is adequately described and section 5 is enhanced such that the shallow-tunnel setting is correctly accounted for.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
