世聯翻譯公司完成土木工程-雙隧道穿越英文翻譯

Abstract: The thesis makes discussion on position selection and optimization of the newly-built single opening and line (left, right) tunnel crossing the existing subway structure vertically. The consideration is made on the influence of the following four factors on the settlement, faulting of slab end and opening of the deformation joint of the existing subway structure: vertical span between the newly-built section tunnel and the existing structure, horizontal span between the left and right line tunnels, position relation between the deformation joint of the existing subway and the newly-built section tunnel and the length of the existing subway structure. The thesis makes the analysis on such factors and determines the primary and secondary factors, thus, discovering the general rule of selecting the crossing position. The results show that the relative relation between the crossing position and the deformation joint of the existing structure is the main factor to affect the deformation of the existing subway structure and that the influence of the vertical span between the newly-built section tunnel and the existing structure is equivalent to that of the horizontal span between the newly-built left and right tunnels.
Key words: Newly-built tunnel, Existing subway structure, Crossing, Position selection, Factor analysis
CLC No. U455         Document Code: A   Article No.:
 

The fast development of the economy leads to the speeding up urbanization, continuously increasing population and crowded life space. The arising traffic jams, environmental pollution and backward infrastructures and weak anti-disaster capacity damage the urban life greatly, which are obstacles for the sustainable development of modern cities.     
The practice of developed countries leading in the modern urban construction has proved that it’s important to solve crisis of urban population, resources and environment by developing and utilizing the underground space resources orderly, reasonably, comprehensively and effectively. The rail transportation (mainly referring to the subway) is playing more and more important part in the daily life for its great transportation capacity, fast speed, safety and punctuality. Especially, the large scale rail transportation network is irreplaceable to relieve the ground transportation pressure for great cities with large populations.
It’s common for the newly-built subway structure to cross the existing subway structure in stations in the construction of the rail transportation network (hereinafter referred to as the crossing construction). The mode of the newly-built single tunnel and line (left and right) section tunnel crossing the existing tunnel is mainly adopted due to the restriction of the underground space and with the purpose of reducing the adverse impact on the existing subway.  The study on the crossing construction is mainly focusing on the following aspects: firstly, professional protective measures along the passing access: study on the construction method of the newly-build subway and supporting measures ^{[1] [2]}; study on reinforcement measures on the stratum between the newly-built line and existing line^[3]; study on safety evaluation and special reinforcement measures on the existing subway structure (including rail structure) ^[4]; secondly, in terms of the position selection, the professional finite element computing software is used at present to make study and analysis on specific engineering, where the complicated model will be established with consideration of the interaction and influence of the existing structure, adjacent soil and the newly-built subway structure ^[5]. However, it's difficult to promote such method in a large range due to shortcomings, including highly professional modeling, high experience requirement in selecting parameters and too complicated software operation. The thesis makes the value solution on the differential equation with the shooting method on the basis of the foundation beam theory^[6]. It makes discussion on the selection and optimization of position of the newly-built single opening and line (left and right) section tunnel crossing existing subway structure vertically. The calculation and study are made on the influence of the four main factors of selecting position,(including vertical span between the newly-built section tunnel and existing structure, horizontal span between the left and right lines tunnels, positional relation between the deformation joint of the existing subway and the newly-built section tunnel and the length of the existing subway structure) on three key factors of the deformation of the existing subway structure, namely structure settlement deformation, faulting of slab end and opening of the deformation joint. The thesis makes the analysis on such factors and determines the importance order of such factors, thus, discovering the general rule of selecting the crossing position and providing the theoretical guidance for the optimization of the crossing position.  
1. Governing differential equation and boundary conditions 
The governing differential equation of the elastic foundation beam can be put into:
     （1）
Where, E--- elastic modulus of the subway structure, Pa; I--- moment of inertia of the subway structure section, m⁴; w(x)--- vertical  displacement of the subway structure, m; S(x)--- vertical  displacement of the soil, m; k--- foundation coefficient, Pa/m; D--- width of the existing subway structure, m.  
Generally, the stratum settlement S(x) can be calculated with Peck Formula:
             （2）
Where, S₁--- (Max.) settlement at x=0, m; i---horizontal distance of the point of contra-flexure of the settlement curve away from x=0, m.
Formula (1) is the four-order nonhomogeneous linear ordinary differential equation. For the infinite long beam, it is general to solve the general solution and a particular solution of the homogeneous equation. However, there are deformation joints in the subway structure and the positions of the deformation joints can be considered to meet the boundary conditions of bending moment and the shearing force are equal to zero. Therefore, the shooting method ^{[9] [10]} is adopted to solve the differential equation in the thesis.
Basic parameters of a certain project are as follows: newly-built left and right line section tunnel is a circular shield tunnel of 6m in the diameter, buried depth at the center of the tunnel of 19m, horizontal span of the left and right line tunnel center of 9m; the existing subway is the section structure with the buried depth of the bottom plate of 12m (net vertical  distance from the newly-built tunnel of 6m), 25m in the length, 5m in the width, elastic modulus of 3´10¹⁰Pa, inertia moment of the section of 25m⁴, stratum foundation coefficient of 4.5´10⁷Pa/m. It's considered to adopt the centrosymmetric crossing method under the existing tunnel. The coordinate of the existing subway is 0-25m and the centers of the left and right tunnel lie at 8m and 17m. 
2. Influence of depth factor 
According to the above mentioned basic equation and related parameters, the net vertical  spans of the existing structure and newly-built tunnel are changed successively into 3m, 6m, 9m and 12m. The settlement of the existing structure, faulting of slab end and the opening of the deformation joint are indicated in Figure 1 and Table 1.
The calculation results in Figure 1 and Table 1 show that:
(1) it is central crossing, so the deformation of the existing subway structure is symmetrical and the faulting of slab end and the opening of the deformation joints on both sides of the center are quite the same;
(2) with the buried depth of the newly-built tunnel increasing, the vertical  span from the existing subway structure is increasing and the maximum settlement deformation of the existing subway is decreasing from 22.59mm to 19.54mm, reduced by 13.5%;
(3) it is similar to the rule of the settlement deformation, with the buried depth of the newly-built tunnel increasing, the faulting of slab end of the deformation joint is decreasing from 21.29mm to 14.03mm, reduced by 34.1% approximately, which shows that the settlement deformation range is expanding and the settlement deformation is becoming more uniform;
(4) it is central crossing, so the structure is horizontal basically with the slight inclination. The openings at the deformation positions can be ignored basically. 

Figure 1 Calculation results of changing vertical distance settlement 
Table 1 Calculation summary of changing vertical distance    (Unit: mm)

No.	Vertical  distance	Max. settlement	Near-end deformation joint		Far-end deformation joint
			Faulting of slab end	Opening	Faulting of slab end	Opening
1	3	22.59	21.29	-0.15	21.29	-0.15
2	6	21.75	19.21	0.14	19.21	0.14
3	9	20.67	16.62	0.46	16.62	0.46
4	12	19.54	14.03	0.73	14.03	0.73

3. Influence of horizontal span 
According to the above mentioned basic equation and related parameters, the central horizontal span of the left and right tunnel are changed successively into 7m, 9m, 11m and 13m. The settlement of the existing structure, faulting of slab end and the opening of the deformation joint are indicated in Figure 2 and Table 2. The calculation results in Figure 2 and Table 2 show that:
(1) with the horizontal span of the newly-built left and right tunnel increasing, the maximum settlement deformation of the existing structure and the faulting of slab end at the deformation joint position are decreasing by about 8.7% and 21.0% respectively;
(2), similarly, it is central crossing, so the structure is horizontal basically with the slight inclination. The openings at the deformation positions can be ignored basically;
(3) compared with Figure 1 and Table 1, increasing buried depth and expanding horizontal span of the newly-built tunnel have the basically same influence on the existing structure with the basically uniform effects, which means the buried depth increased by 1m is equivalent to the horizontal span expanded by 1m basically. 

Figure 2 Calculation results of changing horizontal span settlement  
Table 2 Calculation summary of changing horizontal span 
(Unit: mm)

No.	Horizontal distance	Max. settlement	Near-end deformation joint		Far-end deformation joint
			Faulting of slab end	Opening	Faulting of slab end	Opening
1	7	22.21	20.17	-0.04	21.29	-0.04
2	9	21.75	19.21	0.14	19.21	0.14
3	11	21.11	17.83	0.39	16.62	0.39
4	13	20.28	15.93	0.68	14.03	0.68

4 Influence of crossing position 
According to the above mentioned basic equation and related parameters, the relative position with the deformation joints of the existing subway are changed successively (the coordinate of the existing subway of 0-25m):
(1) centrosymmetric crossing (position I), centers of the newly-built left and right tunnels lie at 8m and 17m;
(2) boundary crossing (position II, a tunnel lies under the deformation joint), centers of the newly-built left and right tunnels lie at 0m and 9m;
(3) crossing at 1/3 position (position III), centers of the newly-built left and right tunnels lie at 4m and 13m;
(4) symmetric crossing under the deformation joint (position IV), centers of the newly-built left and right tunnels lie at -4.5m and 4.5m;
Therefore, the settlement of the existing structure, faulting of slab end and the opening of the deformation joint are indicated in Figure 3 and Table 3.The calculation results in Figure 3 and Table 3 show that:
(1) the changing crossing position affects the structure settlement in a certain degree, of which the settlement deformation is the least in the central crossing (position I) for 21.75mm; that of the symmetric crossing at the deformation joints (Position IV) ranks secondly for 30.70mm and that of the crossing of a tunnel under the deformation joint (position II) is the largest, reaching as much as 36.61mm;
(2) the changing crossing position affects the faulting of slab end at the near-end deformation joint. The calculation results show that in the crossing at the deformation joint (position IV), the structure settlements on both sides of the deformation joint are quite the same due to the symmetry of the left and right tunnels; thus, there is no faulting of slab end at the deformation joints. There are faulting of slab end in other three crossing positions, of which the faulting of slab end in the centrosymmetric crossing (position I) and a tunnel crossing under the deformation joint (position II) are basically equivalent as 19.21mm and 17.77mm. The faulting of slab end is the largest for 25.48mm in the crossing at the 1/3 position (position III);
(3) contrary to the rule of faulting of slab end, in the crossing at the deformation joint (position IV), the opening at the near-end deformation joint is the largest for 9.38mm for the opposite and large intersection angle of the structure on both sides. The openings rank at the second and third places in the crossing at 1/3 position (position III) and a tunnel crossing under the deformation joint (position II). However, in the centrosymmetric crossing (position I), the intersection angle of the structure in the affected range is so small as to be zero nearly. Thus, almost no consideration is made on the opening of the deformation joint for it is also small;
(4) the faulting of slab end at the far-end deformation joint can not be ignored. In the centrosymmetric crossing (position I), there is no near-end and far-end, in which the faulting of slab end reaches 19.21mm; in other conditions, a tunnel crossing under the deformation joint (position II) is the most favorable to control the faulting of slab end at the far-end deformation joint. It is noticeable that in the symmetric crossing at the deformation joint (position IV) there is no faulting of slab end of the deformation joint at the crossing position; however, the faulting of slab end at the far-end deformation joint reaches as much as 7.81mm;
(5) opposite to the opening trend of the near-end deformation joint, that of the far-end deformation joint is negative, which means the top of the deformation expands and the bottom is shrinks. Particular importance should be attached to the waterproof of the top structure in such condition;
(6) in terms of the influence degree, the settlement, near-end faulting of slab end and opening are maximum while the far-end faulting of slab end and opening are less (there is no near-end and far-end in the central crossing. The near-end influence is greater than that of the far-end in the noncentral crossing). Thus, the settlement, near-end faulting of slab end and opening can be considered as main governing index and the far-end faulting of slab end and opening can be considered as supporting index, which is consistent with the perceptual knowledge.
 (7) the above mentioned analysis shows that the crossing position has quite different or even opposite influence on such index. Therefore, it’s difficult to find an absolutely favorable crossing position. The specific crossing position shall be made on the control standards of the actual conditions of the project and relevant index after the comprehensive judgment and analysis.

Figure 3 Calculation results of the changing crossing position settlement 
Table 3 Calculation summary of the changing crossing position 
(Unit: mm)

No.	Crossing position	Max. settlement	Near-end deformation joint		Far-end deformation joint
			Faulting of slab end	Opening	Faulting of slab end	Opening
1	I	21.75	19.21	0.14	19.21	0.14
2	II	36.61	17.77	7.92	3.55	-4.84
3	III	33.41	25.48	4.46	6.22	-3.33
4	IV	30.70	0.00	9.38	7.81	-4.54

5. Influence of the structure length 
According to the above mentioned basic equation and related parameters, the length of the single section of the existing subway structure are changed successively into 20m, 25m, 30m and 35m. The settlement of the existing structure, faulting of slab end and the opening of the deformation joint are indicated in Figure 4 and Table 4. The calculation results in Figure 4 and Table 4 show that:
(1) with the length of the existing subway structure increasing, the maximum settlement deformation of the structure is decreasing from 24.73mm to 17.18mm, reduced by 30.5% approximately, showing remarkable effect;
(2) same with the settlement, with the length of the existing subway structure increasing, the faulting of slab end at the deformation joint is decreasing from 18.62mm to 14.22mm, reduced by 23.6% approximately. The decreasing degree is less than that of the settlement;
(3) the opening of the deformation joint position changes in a certain degree. However, the opening degree remains relatively low basically, which may not be considered as main analysis index in the central crossing;
(4) the comprehensive analysis on the settlement, faulting of slab end and opening of the deformation joint shows that with the length of the existing subway structure increasing, such three index are decreasing. The structure with a larger crossing length is more favorable in conditions with several lengths to choose. 

iii        iv
Figure 4 Calculation results of the changing structure length settlement 
Table 4 Calculation summary of the changing structure length 
(Unit: mm)

No.	Structure length	Max. settlement	Near-end deformation joint		Far-end deformation joint
			Faulting of slab end	Opening	Faulting of slab end	Opening
1	20	24.73	18.62	1.19	18.62	1.19
2	25	21.75	19.21	0.14	19.21	0.14
3	30	19.13	17.15	-0.34	17.15	-0.34
4	35	17.18	14.22	-0.68	14.22	-0.68

 

6. Analysis on primary and secondary factors 
The above mentioned calculation can show that four main factors to the deformation of the existing subway structure are the followings: vertical span from the existing subway structure (hereinafter referred to as vertical span), the horizontal span between the left and right tunnel (hereinafter referred to as horizontal span), position relation with the deformation joint of the existing subway (hereinafter referred to as crossing position) and the length of the existing subway structure (hereinafter referred to as structure length). 
According to the design principle and method of the orthogonal test, the test design on the four factors in the four levels is made to analyze the influence degree of the factors on the structure settlement, faulting of slab end and opening. The test program and the structure deformation calculation results are as indicated in Table 5 and 6. The method of the range analysis is adopted to analyze the primary and secondary relation of the affecting factors, as indicated in Table 7.

 
Table 5 Factor test design program 
 (Unit: mm)

No.	Crossing position	Structure length	Vertical span	Horizontal span
1	I	20	3	7
2	I	25	6	9
3	I	30	9	11
4	I	35	12	13
5	II	20	6	11
6	II	25	3	13
7	II	30	12	7
8	II	35	9	9
9	III	20	9	13
10	III	25	12	11
11	III	30	3	9
12	III	35	6	7
13	IV	20	12	9
14	IV	25	9	7
15	IV	30	6	13
16	IV	35	3	11

Table 6 Calculation summary of changing factors
(Unit: mm)

No.	Max. settlement	Near-end deformation joint		Far-end deformation joint
		Faulting of slab end	Opening	Faulting of slab end	Opening
1	27.38	25.24	0.55	25.24	0.55
2	21.75	19.21	0.31	19.21	0.31
3	11.55	10.66	-0.48	10.66	-0.48
4	15.64	12.38	-0.16	12.38	-0.16
5	30.38	9.62	15.14	9.23	-5.79
6	28.49	9.51	13.04	5.00	-6.35
7	30.59	11.78	13.45	5.28	-7.62
8	30.54	15.11	11.52	6.74	-6.58
9	23.12	5.23	9.58	9.71	0.31
10	25.66	12.81	8.56	6.97	-3.70
11	34.44	32.15	7.40	0.83	-7.81
12	28.62	27.38	4.37	0.58	-6.09
13	28.19	0.00	18.56	1.11	-8.94
14	30.22	0.00	19.85	7.34	-9.58
15	24.78	0.00	13.34	5.70	-6.44
16	25.11	0.00	13.24	7.50	-5.41

Table 7 Analysis on primary and secondary relation of affecting factors 
(Unit: mm)

No.	Max. settlement				Near-end faulting of slab end				Near-end opening				Far-end faulting of slab end				Far-end opening
	Position	Length	Depth	Span	Position	Length	Depth	Span	Position	Length	Depth	Span	Position	Length	Depth	Span	Position	Length	Depth	Span
I	76.32	109.07	115.42	116.81	67.49	40.09	66.90	64.40	0.22	43.83	34.23	38.22	67.49	45.29	38.57	38.44	0.22	-13.87	-19.02	-22.74
II	120.00	106.12	105.53	114.92	46.02	41.53	56.21	66.47	53.15	41.76	33.16	37.79	26.25	38.52	34.72	27.89	-26.34	-19.32	-18.01	-23.02
III	111.84	101.36	95.43	92.70	77.57	54.59	31.00	33.09	29.91	33.71	40.47	36.46	18.09	22.47	34.45	34.36	-17.29	-22.35	-16.33	-15.38
IV	108.30	99.91	100.08	92.03	0.00	54.87	36.97	27.12	64.99	28.97	40.41	35.80	21.65	27.20	25.74	32.79	-30.37	-18.24	-20.42	-12.64
1	19.08	27.27	28.86	29.20	16.87	10.02	16.73	16.10	0.06	10.96	8.56	9.56	16.87	11.32	9.64	9.61	0.06	-3.47	-4.76	-5.69
2	30.00	26.53	26.38	28.73	11.51	10.38	14.05	16.62	13.29	10.44	8.29	9.45	6.56	9.63	8.68	6.97	-6.59	-4.83	-4.50	-5.76
3	27.96	25.34	23.86	23.18	19.39	13.65	7.75	8.27	7.48	8.43	10.12	9.12	4.52	5.62	8.61	8.59	-4.32	-5.59	-4.08	-3.85
4	27.08	24.98	25.02	23.01	0.00	13.72	9.24	6.78	16.25	7.24	10.10	8.95	5.41	6.80	6.44	8.20	-7.59	-4.56	-5.11	-3.16
Range	10.92	2.29	5.00	6.20	19.39	3.70	8.98	9.84	16.19	3.72	1.83	0.61	12.35	5.71	3.21	2.64	7.65	2.12	1.02	2.60
Primary and secondary factor	1	4	3	2	1	4	3	2	1	2	3	4	1	2	3	4	1	3	4	2
Optimum level	A	D	C	D	D	A	C	D	A	D	B	D	C	C	D	B	A	A	C	D

The calculation results in Table 6 and 7 show that:
1. among the four factors, the settlement is mainly affected by the crossing position (44.75%). The vertical span (20.48%) and the horizontal span (25.39%) are basically equivalent in the influence and the structure length has the least influence (9.38%);
2. same to the settlement, the faulting of slab end in the near-end deformation joint is mainly affected by the crossing position (46.28%). The vertical span (21.42%) and the horizontal span (23.48%) are basically equivalent in the influence and the structure length has the least influence (8.82%);
3. the opening of the near-end deformation joint is mainly affected by the crossing position (74.28%), the integrated influence of the vertical span (8.18%) and the horizontal span (2.71%) is about 11%;
4. the faulting of slab end in the far-end deformation joint is the same with that in the near-end deformation joint in that it is also mainly affected by the crossing position (51.67%). However, it is different in that the structure length is the second factor (23.87%). The depth (13.42%) and the horizontal span (11.04%) have the similar least influence basically;
5. the opening of the far-end deformation joint is mainly affected by the crossing position (57.13%). The structure length (15.84%) and the horizontal span (19.39%) have the basically same influence, ranking at the second place together. The depth (7.64%) is the least influential factor;
6. the comprehensive analysis, as indicated in Table 8, shows that the crossing position is the dominating and main factor to affect the settlement, faulting of slab end and opening. The vertical and horizontal spans have the basically equivalent influence. The importance order of these factors is as follows: crossing position, vertical span, horizontal span and structure length. 

 
Table 8 Comprehensive  determination of the primary and secondary relation of affecting factors 

Item	Dominating factor (>50%)	Primary  factor (30-50%)	Secondary factor (10-30%)	Basically irrelevant factor (≤10%)
Max. settlement	/	Position	Depth, span	Length
Near-end faulting of slab end	/	Position	Depth, span	Length
Near-end opening	Position	/	Length	Depth, span
Far-end faulting of slab end	Position	/	Length, depth, span	/
Far-end opening	Position	/	Span, length	Depth

 
Table 9 Calculation summary of changing factors 
(Unit: mm)

No.	Max. settlement	Near-end deformation joint		Far-end deformation joint
		Faulting of slab end	Opening	Faulting of slab end	Opening
1	27.26	25.46	0.84	25.46	0.84
2	21.53	19.61	0.71	19.61	0.71
3	11.26	11.16	0.02	11.16	0.02
4	15.13	13.33	0.46	13.33	0.46
5	30.44	9.75	15.14	9.30	-5.71
6	28.66	9.94	12.89	5.22	-6.09
7	30.51	12.04	13.07	5.40	-7.77
8	30.28	15.52	10.74	7.12	-6.94
9	23.15	5.30	9.57	9.78	0.32
10	25.81	13.06	8.64	7.14	-3.57
11	35.10	32.90	8.00	1.37	-7.32
12	30.00	28.84	5.56	1.64	-5.28
13	28.19	0.00	18.57	1.11	-8.96
14	30.09	0.00	19.54	7.48	-9.76
15	24.70	0.00	13.25	5.86	-6.62
16	24.42	0.00	12.15	8.25	-6.06

The above mentioned calculation and analysis are intended for the condition where the left and right tunnels cross under the existing section structure. In the case of the left and right tunnels crossing under the existing station structure, the section moment of inertia is changing into 2,000 m⁴, as indicated in Table 9. Compared with the calculation results of the existing section structure, the analysis is made on the influence of the existing subway structure type on the structure settlement, faulting of slab and opening of the deformation joint.
Comparing the calculation results of the station in Table 9 and the section in Table 6, we can find that:
1. the station and the section have the same rule and equivalent degree, of which five index including the settlement are basically the same, only with slight differences;
2. the analysis result on the primary and secondary factors of the section applies to the station, with the crossing position as the leading factor;
3. compared with the section, the section moment of inertia of the station increases by 80 times from 25m⁴ to 2,000m⁴. However, the calculation results have slight difference, indicating the station and the section have the adequate rigidity to the stratum. 
7. Position selection and optimization 
There are different control standards for the subway structure and the rail structure at present:
(1) structure internal force control standards: according to related regulations as Code for Design of Metro, the security evaluation is made on the internal force state of the existing subway structure caused by the new construction.  
(2) rail structure control standards: according to work specifications stipulated in various cities, the allowable deviation on the static geometric dimension of the whole line rail bed and rails mainly include: rail span, level, elevation, rail direction and delta warp (twist).  世聯翻譯公司完成土木工程-雙隧道穿越英文翻譯
In terms of influence degree, the settlement, near-end faulting of slab end and opening are largest while the far-end faulting of slab end and opening are less. Thus, the settlement and near-end faulting of slab end are considered as primary control factors.  The settlement deformation curve shows that the station and the section have the less deflection of the structure. Therefore, the absolute settlement has slight influence on the internal force of the structure and the rail geometry. The faulting of slab end and opening at the deformation joint have no influence on the structure safety (except the waterproofing of the structure); however, they determine the internal force and geometry of the rail directly, affecting the operation safety. Thus, the faulting of slab end and opening at the deformation joint are key control factors.  
The following procedures shall be followed to select and optimize the position in the condition where the left and right tunnels cross the existing subway structure:
(1) The crossing position is the dominating and main factor to affect the settlement, the faulting of slab end and opening of the deformation joint. Thus, the calculation analysis shall be made on the crossing position (the relative position relation with the deformation joint) in selecting and analyzing the crossing path of the left and right tunnels.
The crossing position is opposite in the influence on three index: in the central crossing, the maximum settlement is the least, the opening is basically zero while the faulting of slab end is larger; in the crossing at the deformation joint, the faulting of slab end is basically zero while the settlement is larger and the opening is the largest in four conditions; in other crossing positions, the maximum settlement, faulting of slab end and opening of the deformation joint are all larger;
Different cities have various subway control standards. In the example of the thesis, Table 3 shows that if it is controlled with the maximum settlement not more than 30mm, the central crossing (position I) is the only choice; if it is controlled with the faulting of slab end of the deformation joint not more than 20mm, the central crossing (position I), boundary crossing (position II) and crossing under the deformation joint (position IV) are the options; if it is controlled with the opening of the deformation joint not more than 5mm, the central crossing (position I) and 1/3 crossing (position III) are optional. In such example, the central position (position I) is acceptable. Therefore, the crossing position shall be determined according to the control standards.
(2) There is no doubt that increasing the horizontal span and the buried depth of the tunnel can reduce the maximum settlement and the faulting of slab end. However, it has no remarkable influence on the opening of the deformation joint. Compared with increasing the buried depth of the tunnel, expanding horizontal span is more economical. Besides, it has less interaction in the construction of the left and right tunnel. Therefore, it is suggested to expand the horizontal span. However, attention should be paid to that the horizontal span and buried depth of the tunnel are more sensitive and effective at the preliminary stage of the adjustment. When increased to a certain degree, they will have less and less influence on the maximum settlement and the faulting of slab end of the deformation joint. Thus, it is no recommended to expand the horizontal span and increase the buried depth of the tunnel without any limitation.
(3) The structure with larger crossing length is more favorable. However, in terms of the subway structure, the structure lengths are basically the same in the finite path range to choose. Therefore, the structure length is generally ignored in selecting and optimizing the crossing position of the left and right tunnels.