Research on Construction Optimization of Three-Connected-Arch Hydraulic Underground Cavities Considering Creep Property

1 Chongqing Key Laboratory of Geomechanics & Geoenvironmental Protection, Department of Civil Engineering, Logistical Engineering University, Chongqing 401311, China 2Department of Civil Engineering and Architecture, Chongqing University of Science & Technology, Chongqing 401331, China 3 Key Laboratory of Hydraulic & Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, China


Introduction
Since the construction period of large-scale underground cavity engineering is long, the creep property of rock mass is relatively obvious, and many large-scale underground cavities collapse and finally break down due to deformation which is continuously developing with time.The selection of reasonable construction scheme is one of the main ways to prevent and control surrounding rock's creep of the underground cavity.
In the past years, numerous scholars at home and abroad acquired lots of achievements in underground cavity construction safety [1,2] and its optimization [3,4] and acquired abundant accomplishment in rock mass creep constitutive model [5], creep parametric inversion [6], engineering application [7], and so forth as well.Meanwhile, lots of mathematical softwares or numerical methods were used to solve engineering problems, such as finite element method [8], meshless or meshfree method [9,10], discrete element method [11,12], and Fast Lagrangian Analysis of Continua (FLAC) [13].FLAC 3D is a three-dimensional software that uses full dynamics equation and has a good secondary development interface, which can simulate and help analyze the three-dimensional structure behavior and plastic flow of soil, rock, and other materials.FLAC has become the fastest and the most influential numerical analysis software in geotechnical mechanics and engineering.
This paper takes research on a three-connected-arch front inflow pool of an underground water intake pumping station somewhere in Shenzhen; before construction of the project, the FLAC 3D software [13], with secondary development of the nonlinear creep model, is applied by adopting the method of numerical simulation to survey for a construction method appropriate for the long-span hydraulic underground cavity of this region, and the optimal safety construction method has been proposed through comparative study on numerical simulation response, plastic zone expansion, and so forth of surrounding rock displacement variation of three kinds of construction methods.This research result can provide reference and guidance for the similar projects.

Project Profile
The underground pump station is with floor elevation of the front inflow pool at 17.3 m, while ground elevation of current situation at 55.0 m, with net width of the underground pump station at 26.9 m, net length at 23.7 m, and net height at 15.2 m.It consists of 3 cavities, with span of single cavity exceeding 8.1 m; 12.61 m in the second half of the middle cavity is not equipped with wall support, bearing by cross walls at two sides.The horizontal layout of the pool support structure and the cross-section of the second half of the pool are shown in Figures 1 and 2.
The project is proposed to be constructed among the valleys; the valley bottom is at the ground elevation of 53.1∼ 56.2 m, being relatively plain.The formation lithology of the pump room is mainly distributed with residual soil at the elevation of 55.0∼49.8m, moderately weathered limestone at the elevation of 49.8∼26.0m, and moderately weathered quartz sandstone at the elevation under 26.0 m.

Nonlinear Viscoelastic-Plastic Creep Constitutive Model
The nonlinear viscoelastic-plastic creep model is a tandem compound of a nonlinear viscoelastic-plastic body (the third part in Figure 3) and a Burgers creep model [14], as shown in Figure 3.And see the FLAC 3D secondary development of the model in the document manual [15].Wherein, when  ≤  ∞ (long-term strength or yield strength), the third part does not work, and the model is transformed into Burgers creep model; the creep equation of the model is as follows: When  >  ∞ , the creep equation of the creep model is as follows: Here, (, ) =  −1 / 3 , where  3 is the initial value of (, ).

Numerical Model.
A plane strain model is adopted for calculation; the model consists of moderately weathered quartz sandstone, moderately weathered limestone, and residual soil from the bottom up; the PBA model has 16092 units and 24675 nodes in total, and side-middle cavity method has 15884 units and 24372 nodes in total.The horizontal displacement at left and right boundaries of the whole model is restrained, the vertical displacement of the

The Modeling Details 4.2.1. Parameter Selection.
During the numerical analog calculation process, the elastic constitutive is adopted for initial support and secondary support.The Mohr-Coulomb constitutive is adopted for calculating the initial ground stress, and, according to the geological exploration report and indoor experiment results, the basic mechanical property and the support structure parameters of the surrounding rock at the location of the pump station can be seen in Table 1.
And the mechanical property of initial support anchor rod is shown in Table 2.

The Creep Calculation Details.
The second-phase engineering of the three-connected-arch underground pump station mentioned in this paper is going through feasibility analysis and verification of the design stage, and site displacement deformation monitoring data is not available yet; therefore, only the moderately weathered limestone which is affected much by excavation disturbance is conducted with creep calculation (that was used the nonlinear visco-elasticplastic creep constitutive model, while other rock mass still used Mohr-Coulomb constitutive model), and the creep calculation parameter can be obtained through inversion of the site monitoring displacement data of the first-phase engineering construction; the parameter inversion is realized by adopting quasi-Newton algorithm (BFGS algorithm) Matlab programming as well, as shown in Table 3. Three-step method was used in each cavity excavation and creep calculation age of every step is 15 days.In the process of calculation, the unbalanced force rate is set as 1−6, and the time step is 1 − 4.

Simulation Scheme of Construction Method.
According to the construction experience of long-span underground cavity at home and abroad, and combining with structural features of the underground cavity mentioned in this paper, three excavation construction methods are designed here for numerical simulation optimization calculation.Excavation footage for each construction method is 2 m, and construction among stairs is staggered for 6 m. 30 cm of sprayed concrete and 3 m of anchor rod are adopted for initial support.

ConstructionMethod I. Construction Procedures of
Middle Cavity Method (See Figure 5) Step 1. Excavate the first, second, and third parts of rock mass of middle cavities, hang bar-mat reinforcement at surrounding rock in sequence, blow the anchor rod, and conduct with sprayed concrete.
Step 2. Cast ground beam 4, concrete floor 5, stand wall 6, top beam 7, and second lining 8 of the middle cavity.
Step 3. Excavate the ninth, tenth, and eleventh parts of the rock mass of the left cavity, dismantle the temporary support of corresponding part, and conduct the initial support such as anchor rod, and sprayed concrete.
Step 4. Cast the ground beam 12, floor 13, and left wall 14 and the second lining 15 of the left cavity.
Step 5. Excavate the right cavity with the same method as the left cavity.

Construction Method II. Construction Procedures of Side
Cavity Method (See Figure 6) Step 1. Excavate the left cavities 1, 2, and 3, and perform initial support.
Step 3. Excavate the right cavities 10, 11, and 12 with the same method, and perform the initial support.
Step 5. Excavate the cavities 19, 20, and 21, dismantle the temporary anchor rod, and complete the lining 22 and the floor 23.7) Step 1. Excavate pilot tunnels 1, 2, 3, and 4, hang the bar-mat reinforcement, blow the anchor rod, and spray the concrete.
Step 2. Cast the ground beams 3 and 7, dig holes and cast stand columns 5 and 8, cast the top beams 6 and 9, excavate the rock mass 10, and cast the second lining 11.
Step 3. Symmetrically excavate the side cavity rock masses 12, 13, and 14, dismantle the temporary support, and conduct initial support; cast side ground beam 15, floor 16, side wall 17, and the second lining 18 in sequence.
Step 4. Excavate the bottom rock masses 19 and 20 of the middle cavity, dismantle the temporary support structure, and cast the floor 21 of the middle cavity.

Surrounding Rock Creep Property Analysis.
Figure 8 shows the excavation-completed surrounding rock displacement contour maps of three excavation methods after performing the second support; it can be seen that the maximum range of surrounding rock displacement deformation under   the three excavation methods is focused at the vault part of the three cavities.Figure 9 shows, respectively, cavity vault part surrounding rock displacement monitoring curves of three construction methods.Each curve in the figure reflects the creep condition of the vault at each construction phase.Table 4 shows percentage statistics of vault maximum accumulative creep value and increment at each construction phase; it can     be seen that the first-phase creep value of the side cavity method is relatively lower, being 13.49 mm, while the creep increment of the right cavity at second phase increases to 16.68%; the vault creep value is 16.04 mm by adopting middle cavity method for excavation, which is 0.22 mm lower than that of side cavity method; for PBA construction, the excavation of pilot tunnel releases part of stress in the surrounding rock, and the beam, stand column, and the middle cavity vault second lining and other permanent supports provide well restraining effect for surrounding rock deformation in the subsequent construction, which makes the cavity maximum vault accumulative deformation being merely 14.18 mm.By comparing three construction methods, it can be obtained that the PBA construction is the optimal excavation construction scheme in the point of surrounding rock displacement, and the middle cavity method follows.

Stress Field Distribution
Rule of Surrounding Rock.The surrounding rock maximum and minimum principle stresses variation contour map obtained after excavation completed through three excavation construction methods can be seen in Figures 10,11,and 12.In the FLAC software, it is ruled that tension stress is positive, while pressure stress is negative; therefore, in the figure, SMin actually represents the maximum principle stress, while SMax represents the minimum principle stress.Table 5 is the numerical statistics table of maximum and minimum stresses.
All the three excavation methods enable stresses of the surrounding rock being redistributed and stress concentration appearing at the vault and the bottom part of the three cavities; the middle cavity method and the side cavity method cause the equal maximum pressure stress at 2.04 MPa, while the PBA construction causes the maximum pressure stress Itasca Consulting Group, Inc.

Figure 1 :
Figure 1: Plane figure of the front inflow pool.

Figure 5 :
Figure 5: Construction steps of middle cavity method.

Figure 6 :
Figure 6: Construction steps of side cavity method.

Figure 9 :
Figure 9: Creep curve at vault monitoring point of excavated cavity.

Table 1 :
The rock mass parameters.

Table 2 :
Mechanics parameters of cable and grout.

Table 3 :
The nonlinear creep model parameters.

Table 4 :
Comparative table for maximum settlement value of phased excavation in different methods.