Xiao et al 2023a - Revision history

Rimni: /* References */

2023-10-11T08:12:41Z

‎References

Rimni at 08:12, 11 October 2023

2023-10-11T08:12:15Z

Rimni: /* 6. Conclusion */

2023-10-11T08:04:13Z

‎6. Conclusion

Rimni at 08:00, 11 October 2023

2023-10-11T08:00:19Z

Rimni: /* 5.2 Internal force analysis */

2023-10-11T07:54:26Z

‎5.2 Internal force analysis

Rimni at 07:53, 11 October 2023

2023-10-11T07:53:43Z

Rimni at 14:35, 10 October 2023

2023-10-10T14:35:53Z

Show changes

Rimni at 14:19, 10 October 2023

2023-10-10T14:19:30Z

Rimni at 14:01, 10 October 2023

2023-10-10T14:01:44Z

Rimni: /* 5. Effect of uneven settlement of shield tunnel on the mechanical properties */

2023-10-10T13:47:30Z

‎5. Effect of uneven settlement of shield tunnel on the mechanical properties

@@ Line 489: / Line 489: @@
 ==References==
+<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
 [1] Han B.M., Li Y.W., Lu F., Yang Z.X., Yang R.X., Chen Y.X., Sun Y.J., XI Z., Wang L.Y., Dai Y.J. Statistical analysis of urban rail transit operations in the world in 2021: A Review (in Chinese). Urban Rapid Rail Transit,  35:5-11, 2022.

@@ Line 490: / Line 490: @@
 ==References==
-[1] Han B.M., Li Y.W., Lu F., Yang Z.X., Yang R.X., Chen Y.X., Sun Y.J., XI Z., Wang L.Y., Dai Y.J. Statistical Analysis of Urban Rail Transit Operations in the World in 2021: A Review (in Chinese). Urban Rapid Rail Transit,  35:5-11, 2022.
+[1] Han B.M., Li Y.W., Lu F., Yang Z.X., Yang R.X., Chen Y.X., Sun Y.J., XI Z., Wang L.Y., Dai Y.J. Statistical analysis of urban rail transit operations in the world in 2021: A Review (in Chinese). Urban Rapid Rail Transit,  35:5-11, 2022.
 [2] Lin Y.G., Liao S.M., Lin G.B. A discussion of the factors effecting on longitudinal deformation of subway tunnel. Undergr. Space, 20:264-267, 2000.
-[3] Wei K., Gong Q.M., Zhou S.H. Ant Colony Algorithms of Long-term Uneven Settlement Prediction in Tunne. Journal of Tongji University（Natural Science), 37:993-998, 2009.
+[3] Wei K., Gong Q.M., Zhou S.H. Ant colony algorithms of long-term uneven settlement prediction in tunne. Journal of Tongji University（Natural Science), 37:993-998, 2009.
 [4] Tan W.L., Pathegama R.G. Parameters and considerations in soft ground tunneling. Electronic Journal of Geotechnical Engineering, 8:1-17, 2003.
-[5] Zheng Y.L., Han W.X., Tong Q.H., Yang L.F., Pan J. Study on longitudinal crack of shield tunnel segment joint due to asymmetric settlement in soft soil (in Chinese). Chinese journal of rock mechanics and engineering, 24(24): 4552-4558, 2005.
+[5] Zheng Y.L., Han W.X., Tong Q.H., Yang L.F., Pan J. Study on longitudinal crack of shield tunnel segment joint due to asymmetric settlement in soft soil (in Chinese). Chinese Journal of Rock Mechanics and Engineering, 24(24):4552-4558, 2005.
-[6]Ye Y.D., Zhu H.H., Wang R.L. Analysis on the current status of metro operating tunnel damage in soft ground and its causes (in Chinese). Chinese journal of underground space and engineering, 3:157-160, 2007.
+[6]Ye Y.D., Zhu H.H., Wang R.L. Analysis on the current status of metro operating tunnel damage in soft ground and its causes (in Chinese). Chinese Journal of Underground Space and Engineering, 3:157-160, 2007.
-[7] Wang R.L. Factors influencing deformation of Shanghai soft soil metro tunnel and deformation analysis (in Chinese). Underground engineering and tunnels, 1: 1-6, 2009.
+[7] Wang R.L. Factors influencing deformation of Shanghai soft soil metro tunnel and deformation analysis (in Chinese). Underground Engineering and Tunnels, 1:1-6, 2009.
 [8] Liu X., Dong Z.B., Bai Y., Zhu Y.H. Investigation of the structural effect induced by stagger joints in segmental tunnel linings: First results from full-scale ring tests. Tunn. Undergr. Space Tech., 66:1-18, 2017.
-[9] Xiao Z.R., Wang J.C. A Three-Dimensional Model of Shield Tunnel considering Interaction of Soil and Lining. Math. Probl. Eng., 4245384, 2022.
+[9] Xiao Z.R., Wang J.C. A three-dimensional model of shield tunnel considering tnteraction of soil and lining. Math. Probl. Eng., 2022, 4245384, 2022.
 [10] Liao S.M., Peng F.L., Shen S.L. Analysis of shearing effect on tunnel induced by load transfer along longitudinal direction. Tunn. Undergr. Space Tech., 23:421-430, 2008,

@@ Line 473: / Line 473: @@
 The uneven settlement coefficient ∆/L under five different transverse convergence rates of 0‰D, 1‰D, 2‰D, 3‰D and 4‰D are 0.3542,0.3333,0.3125,0.2708 and 0.1875, respectively. According to [[#tab-9|Table 9]], the damage to the tunnel lining can be preliminarily judged or the spacing of monitoring points can be reasonably arranged according to recommended value [<math display="inline">  \Delta /L</math>].
-==6. Conclusion ==
+==6. Conclusions ==
-A three-dimensional numerical model is established to study the mechanical behavior of tunnel lining when uneven settlement occurs under different transverse deformations of lining. The uneven settlement coefficient ∆/L is proposed as an index to reflect the mechanical properties of the tunnel. Based on the analysis, the following conclusions are drawn :
+A three-dimensional numerical model is established to study the mechanical behavior of tunnel lining when uneven settlement occurs under different transverse deformations of lining. The uneven settlement coefficient ∆/L is proposed as an index to reflect the mechanical properties of the tunnel. Based on the analysis, the following conclusions are drawn:
 (1) The transverse and longitudinal deformation of the shield tunnel are coupled. The uneven settlement displacement of the tunnel will cause the transverse deformation of the lining ring to a certain extent. The transverse deformation of the lining has little effect on the force characteristics of the tunnel, and the settlement is the main factor affecting the force characteristics of the tunnel.

@@ Line 443: / Line 443: @@
 |-style="text-align:center"
 ! Transverse convergence rate !! Settlement value  <math display="inline">  \Delta</math> (mm) !! Settlement control range <math display="inline">L</math> (m) !! Uneven settlement coefficient [<math display="inline">  \Delta /L</math>]
-|-
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0‰D</span>
+|  0‰D
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">8.5</span>
+|  8.5
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.3542</span>
+|  0.3542
-|-
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">1‰D</span>
+|  1‰D
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">8.0</span>
+|  8.0
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.3333</span>
+|  0.3333
-|-
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;"> 2‰D</span>
+|   2‰D
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">7.5</span>
+|  7.5
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.3125</span>
+|  0.3125
-|-
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">3‰D</span>
+|  3‰D
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">6.5</span>
+|  6.5
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.2708</span>
+|  0.2708
-|-
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">4‰D</span>
+|  4‰D
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">4.5</span>
+|  4.5
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.1875</span>
+|  0.1875
 |}
-The uneven settlement coefficient ∆/L under five different transverse convergence rates of 0‰D, 1‰D, 2‰D, 3‰D and 4‰D are 0.3542,0.3333,0.3125,0.2708 and 0.1875, respectively. According to Table 9, the damage to the tunnel lining can be preliminarily judged or the spacing of monitoring points can be reasonably arranged according to recommended value '''[∆/'''L''']'''.
+The uneven settlement coefficient ∆/L under five different transverse convergence rates of 0‰D, 1‰D, 2‰D, 3‰D and 4‰D are 0.3542,0.3333,0.3125,0.2708 and 0.1875, respectively. According to [[#tab-9|Table 9]], the damage to the tunnel lining can be preliminarily judged or the spacing of monitoring points can be reasonably arranged according to recommended value [<math display="inline">  \Delta /L</math>].
 ==6. Conclusion ==

@@ Line 425: / Line 425: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image18.png|300px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image18.png|400px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 6'''. Relationship between uneven settlement coefficient <math display="inline">  \Delta /L</math> and bending moment

@@ Line 374: / Line 374: @@
 |+
 |-
-|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image15.png|288px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image15.png|308px]]
-|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image16.png|center|282px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image16.png|center|302px]]
 |-
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(a) Axial force
 |style="text-align: center;font-size: 75%;padding-bottom:10px;"|(b) Shear force
 |-
-| colspan='2' style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image17-c.png|306px]]
+| colspan='2' style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image17-c.png|326px]]
 |-
 |colspan='2' style="text-align: center;font-size: 75%;padding-bottom:10px;"|(c) Bending moment
@@ Line 399: / Line 399: @@
 |-style="text-align:center"
 ! Working condition !! Uneven settlement coefficient <math display="inline">  \Delta /L</math> !! Bending moment（kN·m）
-|-
+|-style="text-align:center"
 |  Condition 1
 |  0.9804
 |  -36400
-|-
+|-style="text-align:center"
 |  Condition 2
 |  0.8333
 |  -30800
-|-
+|-style="text-align:center"
 |  Condition 3
 |  0.7246
 |  -28000
-|-
+|-style="text-align:center"
 |  Condition 4
 |  1.0417
 |  -37000
-|-
+|-style="text-align:center"
 |  Condition 5
 |  0.6250
@@ Line 425: / Line 425: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image18.png|270px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_847150402842-image18.png|300px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 6'''. Relationship between uneven settlement coefficient <math display="inline">  \Delta /L</math> and bending moment

@@ Line 321: / Line 321: @@
 <div class="center" style="font-size: 75%;">'''Table 7'''. Condition information</div>
-{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
+<div id='tab-7'></div>
-|-
+{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">'''working condition'''</span>
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">'''transverse convergence rate'''</span>
+! Working condition !! Transverse convergence rate !! Number of lining rings !! Settlement control range L (m) !! Settlement value <math display="inline">  \Delta</math> (mm) !! Uneven settlement coefficient <math display="inline">  \Delta /L</math>
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">'''Number of lining rings'''</span>
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">'''Settlement control range L（m）'''</span>
+|  Condition 1
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">'''Settlement value ∆(mm)'''</span>
+|  1‰
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">'''Uneven settlement coefficient ∆/L'''</span>
+|  36
-|-
+|  20.4
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Condition 1</span>
+|  20
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">1‰</span>
+|  0.9804
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">36</span>
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">20.4</span>
+|  Condition 2
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">20</span>
+|  1‰
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.9804</span>
+|  42
-|-
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Condition 2</span>
+|  20
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">1‰</span>
+|  0.8333
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">42</span>
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
+|  Condition 3
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">20</span>
+|  1‰
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.8333</span>
+|  48
-|-
+|  27.6
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Condition 3</span>
+|  20
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">1‰</span>
+|  0.7246
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">48</span>
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">27.6</span>
+|  Condition 4
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">20</span>
+|  1‰
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.7246</span>
+|  42
-|-
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Condition 4</span>
+|  25
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">1‰</span>
+| 1.0417
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">42</span>
+|-style="text-align:center"
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
+|  Condition 5
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">25</span>
+| 1‰
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">1.0417</span>
+|  42
-|-
+|  24
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">Condition 5</span>
+|  15
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">1‰</span>
+|  0.6250
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">42</span>
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">24</span>
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">15</span>
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|<span style="text-align: center; font-size: 75%;">0.6250</span>
 |}
@@ Line 369: / Line 365: @@
 ===5.2 Internal force analysis ===
-The axial force, shear force and bending moment of the five working conditions are shown in Figure 5. Obviously, the axial forces are very different for the five conditions. The axial forces are smallest in condition 5, whose uneven settlement coefficient ∆/L is 0.6250. The largest axial forces are in condition 4, whose uneven settlement coefficient ∆/L is 1.0417. The axial forces increase with the increase of uneven settlement coefficient ∆/L. It can be seen from Figure 5(b) (c) that the varying of shear force and bending moment with ∆/L is similar to that of axial force.
+The axial force, shear force and bending moment of the five working conditions are shown in [[#img-5|Figure 5]]. Obviously, the axial forces are very different for the five conditions. The axial forces are smallest in condition 5, whose uneven settlement coefficient <math display="inline">  \Delta /L</math> is 0.6250. The largest axial forces are in condition 4, whose uneven settlement coefficient <math display="inline">  \Delta /L</math> is 1.0417. The axial forces increase with the increase of uneven settlement coefficient <math display="inline">  \Delta /L</math>. It can be seen from [[#img-5|Figure 5]](b)-(c) that the varying of shear force and bending moment with <math display="inline">  \Delta /L</math> is similar to that of axial force.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

@@ Line 7: / Line 7: @@
 ==Abstract==
-The transverse deformation of the tunnel under various loads is unavoidable with the long-term operation of the subway, and the problem of uneven settlement is gradually highlighted. A three-dimensional of tunnel lining model is established in ABAQUS to simulate the uneven settlement and transverse deformation on the safety performance, in which the deformation, internal force, and damage are further analyzed. Based on the simulation, safe settlement values for the shield tunnel with different level of existing transverse deformations (L) are suggested. Because the internal force and damage are not only related to the settlement value (∆) but also to the length of the tunnel where the settlement occurs, the ratio of the settlement value (∆) to the corresponding length (L) of the shield tunnel ∆/L which is called the uneven settlement coefficient is proposed as an index. The uneven settlement coefficient ∆/L is given for different transverse deformations to extend the applicability of the safe settlement values, which provides theoretical support for on-site monitoring and tunnel maintenance to some extent.
+The transverse deformation of the tunnel under various loads is unavoidable with the long-term operation of the subway, and the problem of uneven settlement is gradually highlighted. A three-dimensional of tunnel lining model is established in ABAQUS to simulate the uneven settlement and transverse deformation on the safety performance, in which the deformation, internal force, and damage are further analyzed. Based on the simulation, safe settlement values for the shield tunnel with different level of existing transverse deformations (<math display="inline">L</math>) are suggested. Because the internal force and damage are not only related to the settlement value (<math display="inline">  \Delta</math>) but also to the length of the tunnel where the settlement occurs, the ratio of the settlement value (<math display="inline">  \Delta</math>) to the corresponding length (<math display="inline">L</math>) of the shield tunnel <math display="inline">  \Delta /L</math> which is called the uneven settlement coefficient is proposed as an index. The uneven settlement coefficient <math display="inline">  \Delta /L</math> is given for different transverse deformations to extend the applicability of the safe settlement values, which provides theoretical support for on-site monitoring and tunnel maintenance to some extent.
 '''Keywords''': Shield tunnelling, uneven settlement, transverse deformation, recommended value of safe settlement
@@ Line 25: / Line 25: @@
 According to the study by Liu et al. [8] a three-dimensional model is built in ABAQUS. The parameters of lining are shown in [[#tab-1|Table 1]]. The parameters of concrete utilized to construct the lining are shown in [[#tab-2|Table 2]]. 42 rings are built with staggered -180°assembly. In order to simplify the calculation, the joint weakening model is used, the joint width is taken as 6mm, the transverse effective rigidity ratio is taken as 0.75, so the joint elastic modulus E is 176Mpa [9]. The tunnel model is shown in [[#img-1|Figure 1]].
-<div class="center" style="font-size: 75%;">'''Table 1.''' Parameters of lining </div>
+<div class="center" style="font-size: 75%;">'''Table 1'''. Parameters of lining </div>
 <div id='tab-1'></div>
@@ Line 39: / Line 39: @@
-<div class="center" style="font-size: 75%;">'''Table 2.''' Parameters of concrete</div>
+<div class="center" style="font-size: 75%;">'''Table 2'''. Parameters of concrete</div>
 <div id='tab-2'></div>
@@ Line 88: / Line 88: @@
 Multiple working conditions are considered show in [[#tab-3|Table 3]] in order to analyze the internal force and deformation of shield tunnel with different transverse deformations under the influence of uneven settlement. The transverse convergence rate of the lining is the ratio of lateral convergence value to tunnel diameter, which is altered by changing the value of water and soil pressure (not exceeding the control value of the transverse convergence rate of 5‰).The transverse convergence rate of condition 1 is 0‰, which represents the new built tunnel. The transverse convergence rates of condition 2 to condition 5 are 1‰, 2‰, 3‰ and 4‰ respectively, representing the tunnel conditions in different periods.
-<div class="center" style="font-size: 75%;">'''Table 3.''' Condition information</div>
+<div class="center" style="font-size: 75%;">'''Table 3'''. Condition information</div>
 <div id='tab-1'></div>
@@ Line 171: / Line 171: @@
-<div class="center" style="font-size: 75%;">'''Table 4.''' Tunnel key ring internal force value</div>
+<div class="center" style="font-size: 75%;">'''Table 4'''. Tunnel key ring internal force value</div>
 <div id='tab-4'></div>
@@ Line 277: / Line 277: @@
-The settlement of tunnel damage caused by uneven settlement under different working conditions is different. The settlement corresponding to the damage in conditions 1-5 is 8.56mm, 7.84mm, 7.61mm, 6.39mm and 4.58mm, respectively. With the increase in the transverse convergence rate, the settlement value corresponding to the damage occurring decreases.
+The settlement of tunnel damage caused by uneven settlement under different working conditions is different. The settlement corresponding to the damage in conditions 1-5 is 8.56 mm, 7.84 mm, 7.61 mm, 6.39 mm and 4.58 mm, respectively. With the increase in the transverse convergence rate, the settlement value corresponding to the damage occurring decreases.
 Based on the above analysis, under the action of uneven settlement displacement load, the greater the transverse convergence rate of the shield tunnel, the smaller the settlement corresponding to the tensile damage of lining, the slower the development of damage, but the more lining rings damaged due to settlement.
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 Combined with the analysis of the damage in the shield tunnel under the action of uneven settlement, the settlement corresponding to the damage of the center ring is approximated as the recommended value of the safety settlement of the tunnel. For shield tunnels with different transverse deformations during operation, the recommended safe settlement value of the tunnel when the monitoring distance is 24 m is given, as shown in [[#tab-6|Table 6]].
-<div class="center" style="font-size: 75%;">'''Table 6.''' Recommended settlement safety values for different transverse deformation</div>
+<div class="center" style="font-size: 75%;">'''Table 6'''. Recommended settlement safety values for different transverse deformation</div>
 <div id='tab-6'></div>
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-<span style="text-align: center; font-size: 75%;">'''Table 8.''' Central ring bending moment information</span></div>
+<span style="text-align: center; font-size: 75%;">'''Table 8'''. Central ring bending moment information</span></div>
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-<span style="text-align: center; font-size: 75%;">'''Table 9.''' Recommended value of uneven settlement coefficient</span></div>
+<span style="text-align: center; font-size: 75%;">'''Table 9'''. Recommended value of uneven settlement coefficient</span></div>
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 ==5. Effect of uneven settlement of shield tunnel on the mechanical properties ==
-The settlement is a key factor affecting the mechanical behavior of the tunnel. The ratio of the maximum settlement value (∆) to the length of the shield tunnel (L) where the settlement occurs ∆/L is used to express the non-uniformity of the settlement. The degree of tunnel settlement non-uniformity varies with the value of ∆/L. By changing ∆/L, the influence of uneven settlement on the safety performance of shield tunnel is analyzed, and further, the safety settlement values corresponding to different monitoring distance are given.
+The settlement is a key factor affecting the mechanical behavior of the tunnel. The ratio of the maximum settlement value (<math display="inline">  \Delta</math>) to the length of the shield tunnel (<math display="inline">L</math>) where the settlement occurs <math display="inline">  \Delta /L</math> is used to express the non-uniformity of the settlement. The degree of tunnel settlement non-uniformity varies with the value of <math display="inline">  \Delta /L</math>. By changing <math display="inline">  \Delta /L</math>, the influence of uneven settlement on the safety performance of shield tunnel is analyzed, and further, the safety settlement values corresponding to different monitoring distance are given.
 ===5.1 Condition information===
-Taking the transverse convergence rate of 1‰ as an example, the maximum settlement of conditions 1, 2 and 3 is 20 mm when the number of lining rings is 36, 42 and 48 respectively, and the maximum settlement of conditions 4 and 5 is 25 and 15 mm when the number of lining rings is 42. The settlement control range L is the tunnel length corresponding to the settlement difference ∆. The specific working condition information is shown in Table 7, and other parameters are the same as before.
+Taking the transverse convergence rate of 1‰ as an example, the maximum settlement of conditions 1, 2 and 3 is 20 mm when the number of lining rings is 36, 42 and 48 respectively, and the maximum settlement of conditions 4 and 5 is 25 and 15 mm when the number of lining rings is 42. The settlement control range <math display="inline">L</math> is the tunnel length corresponding to the settlement difference <math display="inline">  \Delta</math>. The specific working condition information is shown in [[#tab-7|Table 7]], and other parameters are the same as before.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div class="center" style="font-size: 75%;">'''Table 7'''. Condition information</div>
-<span style="text-align: center; font-size: 75%;">'''Table 7.''' Condition information</span></div>
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