Based on the field investigation and analysis, the mechanical characteristics of segment structure in shield tunnels are compared and analyzed under the circumstances of different concrete spalling region by the method of similarity model experiment. Through data analysis of acoustic emission, the results for displacement and internal force of shield tunnel segments are clarified on the segment lining, the influential rule of load bearing capacity is also determined, and the deformation and stress for the different concrete spalling region are described as well. The corresponding research results indicate that range for elastic bearing stage is enlarged while it is narrowed for plastic bearing stage, the convergence and deformation and the accumulated event numbers for acoustic emission on critical instability point are obviously increasing, and the process of damage and failure tends to be sudden for segment lining structure. The ultimate bearing capacity of the damaged segment lining obviously decreases due to regional concrete spalling; to be more specific, the reduction rate for ultimate bearing capacity becomes 6%, 6%, and 13%, respectively, when the range of concrete spalling reaches 45°, 60°, and 75°.

In the process of shield tunnel construction, because of the influential factors such as the geological condition, the construction design, and the bias load, it is unavoidable during tunnel construction for the occurrence of segment cracking, damage, and regional concrete spalling [

At present, various degrees of damage problems have been observed during construction and service period for a large number of shield tunnels. Combined with the specific projects, scholars have conducted a large amount of researches on the influential factors of structural damage for segment lining and the corresponding controlling measures are proposed in the perspective of stratum condition, stratum defects, and unfavorable load condition during construction. Li et al. have collected a mass of disease specimens for shield tunnels and have established TSI comprehensive tunnel service index for the evaluation of disease condition in shield tunnel by the regression formula of least square method [

Most of the existing research achievements are focusing on the crack generation and expansion in the process of segment failure; so far, relevant reports are not displayed aiming at the effect of regional concrete spalling in the aspect of structural bearing capacity and mechanical behavior. In this paper, a subway project is taken as the background, based on the field investigation and analysis for the situation of regional concrete spalling and the mechanical characteristics of segment lining structure under the circumstances with different concrete spalling region by similarity test, and the conclusion can be provided as the theoretical proof for the design optimization, disease analysis, and shield tunnel evaluation.

The stratum is complicated and flexible in the crossing range of the metro tunnel, and the soil property is cross distributed from north to south, which is specifically presented in sequence as hard-soft-hard-soft-hard-soft-hard-soft-hard, and the proportion of crossed soft soil for the whole section accounts for 56.4%. The soil layer property is defined as compound stratum with a relatively large proportion of soft soil, and the tunnel construction underneath passes across multiple surface water. The section profile of the damaged segment lining is shown in Figure

Cross section formation condition.

The outer and inner diameters of the cross-river tunnel for the metro project are 6.2 m and 5.5 m, respectively. The segment thickness is 0.35 m, and the width is 1.2 m. “3 + 2 + 1” blocked mode is adopted for the segment lining, of which standard block accounts for 67.5°, adjacent block accounts for 68.75°, and the key block accounts for 20°; staggered assembly is applied for the segment, and for each ring, 16 longitudinal bolts are distributed and arranged with equal angle. As presented in Figure

Sketch of tenon between segment rings (unit: mm).

The overall length of this investigated tunnel section is 3.61 km, totally 3008 rings are observed in the investigated area, and up to 443 damaged places are recorded. According to the characteristics of geometrical form, the damage form for the disease of shield tunnel segment can be divided into 3 categories which are, respectively, corner damage, longitudinal cracks, and regional concrete spalling, and the greatest value for the numbers of each individual disease among them is summarized for regional concrete spalling which amounts to 203 and accounts for 45.8% of all the diseases observed in tunnel; undoubtfully, the severity for concrete spalling is the most.

In this metro project, all of the regional concrete spalling takes place around the circumferential joints between segment rings, mostly occurred in the posterior part of segments along excavation direction, and distributed symmetrically on the vault along circumferential direction. Besides, as presented in Figure

The investigated picture for the disease of concrete spalling on the scene. (a) Multiple successive ring spalling on the vault. (b) Regional concrete spalling.

Distribution of spallings in the circumferential region along segment ring.

The statistical result is presented in Table

Statistical results of the length, width, and depth of spallings.

Characteristic value | Length (mm) | Spalling angle (°) | Width (mm) | Depth (mm) |
---|---|---|---|---|

Maximum value | 3190 | 66.46 | 230 | 118 |

Minimum value | 60 | 1.25 | 50 | 12 |

Average value | 1443 | 30.06 | 183 | 94 |

Length, width, and depth for the regional concrete spalling of segments.

11/12 geometrical similarity ratio and 1/1 unit weight similarity ratio are taken as the basic similarity ratios, _{u} = _{g} = _{φ} = 1 is used for Poisson’s ratio, stress and frictional angle are deduced according to similarity theory, and _{R} = _{σ} = _{c} = _{E} = 12 is applied for similarity ratio of strength, stress, cohesive force, and elasticity modulus.

The cross-river shield tunnel excavation has encountered various stratums with different buried depth, water pressure, and the degree of softness and hardness. The effect due to construction is not taken into consideration for the test while the test is mainly focusing on the mechanical characteristics after the damage of the segments; therefore, the most undesirable soil body towards the stability of the structure is selected as the prototype soil which is specified as silty clay, eluvial silty clay, eluvial sandy clay, and the primary controlling parameters such as unit weight, elasticity modulus, and cohesive force are confirmed. Mainly, fly ash and river sand are taken as the similarity materials, and certain proportional hot-melt mixture is used, which is consisted of crystal powder, coarse quartz sand, fine quartz sand, petroleum jelly, rosin, and engine oil. The mix proportion is maintained being adjusted until the parameters of physical mechanics reach the expectation value for the material of soil model. The mix proportion and the parameters of physical mechanics for the material of soil model are indicated in Tables

Mix proportion of model soil.

Crystal powder | Fine quartz sand | Coarse quartz sand | Engine oil | Fly ash | River sand | Petroleum jelly | Rosin |
---|---|---|---|---|---|---|---|

1 | 0.35 | 0.35 | 0.15 | 0.35 | 0.65 | 0 | 0.06 |

Physical and mechanical parameters of soil.

Parameter | c (MPa) | Φ (°) | E (MPa) |
^{−3)} |
---|---|---|---|---|

Prototype material | 18.1∼21.9 | 7.9∼11.3 | 4.6∼6.1 | 17.2∼19.0 |

Model material | 1.67 | 9 | 0.42 | 18 |

Corresponding prototype value | 20 | 9 | 5 | 18 |

The strength grade for the segmental concrete is C50. In the model test, plaster is chosen as the basic material for the segment model, and certain proportional diatomite is mixed. The proportion of the materials is trial-produced by the adjustment of ratio between water and plaster, and the proportion is evaluated by the data of uniaxial compressive strength test. Finally, the ratio between water, plaster, and diatomite will be determined as 1 : 1.38 : 0.1, and these materials will be applied for the segment lining structure. The parameters of physical mechanics for segment concrete are shown in Table

Physical and mechanical parameters of segment concrete.

Parameters of physical mechanics | Prototype value | Model value | Corresponding prototype value |
---|---|---|---|

Elasticity modulus (GPa) | 34.5 | 2.875 | 34.4 |

Standard value for uniaxial compressive strength (MPa) | 32.4 | 2.7 | 32.0 |

Equivalent compressional stiffness for the circumferential main reinforcement (N) | 2.434e9 | 1.803e5 | 2.817e9 |

The diameter of the mesh reinforcement is chosen as 1.3 mm for the circumferential main reinforcement, and the simulation is conducted according to the principle of equivalent bending stiffness. For the intermediate ring of the model, respectively, 4 iron wires are applied for the main reinforcement simulation on both inner side and outer side of the segment. The main reinforcement for the circumferential segment is shown in Table

The simulation of segmental joint can be divided into circumferential joint simulation and longitudinal joint simulation, of which the weakening effect of bending stiffness for the joint is simulated by the incision on the place of circumferential joint along depth direction. The groove depth of incision is determined by the principle of equivalent bending resistance of prototype joint [

Gap depth of segment transverse joints.

Bending stiffness (N·m·rad^{−1}) |
Groove depth for entity (m) | Groove depth for model (m) | |
---|---|---|---|

Positive bending | 2.44 × 10^{8} |
0.14 | 0.023 |

Negative bending | 1.46 × 10^{8} |
0.16 | 0.026 |

Groove of partition for segment joint.

Considering the longitudinal assembly effect, the model is assembled by 3 rings which are consisted of one integral segment ring and two half-width segment rings along longitudinal direction. As shown in Figure

Fabrication and installment for the segment model of regional concrete spalling. (a) Model fabrication. (b) Arrangement for regional spalling. (c) Model installment.

According to the distribution results of the spalling angle corresponding to spalling length in the process of field investigation, the location of regional concrete spalling is arranged at the vault position and symmetrically distributed along ring direction relative to the axis of vault in the experiment. Four cases with different spalling ranges are arranged, and the ranges are set to 0°, 45°, 60°, and 75°, respectively. The statistical average values are selected for the spalling width and depth, namely, 183 mm and 94 mm; the grouping situation of the test is shown in Figure

Groups of test schemes.

Grouping number | Assembly method | Center point for the target block “F” | Range of regional spalling | Spalling length (mm) | Spalling width (mm) | Spalling depth (mm) |
---|---|---|---|---|---|---|

1 | Relatively rotate 180°between segment rings | 45°left to the bottom of the arc | None | 0 | 0 | 0 |

2 | 45° at vault | 2159.8 | 15.5 | 8.0 | ||

3 | 60° at vault | 2879.8 | 15.5 | 8.0 | ||

4 | 75° at vault | 3599.7 | 15.5 | 8.0 |

The model test is carried out by “Combined tunnel-stratum loading test system.” As presented in Figure

Loading device. (a) Vertical view of the loading device. (b) Lateral view of the loading device. ①Jack of direction I. ②Jack of direction II. ③Jack of direction III. ④Plate of direction I. ⑤Plate of direction II. ⑥Plate of direction III. ⑦Loading plate. ⑧Surrounding soil. ⑨Model segment.

Test load applying scheme.

Loading step | Jack pressure of direction III (MPa) | Load of direction I | ||
---|---|---|---|---|

Jack pressure (MPa) | Formation pressure of the model vault (kPa) | Formation pressure of the prototype vault (kPa) | ||

0 | 0 | 0 | 0 | 0 |

1 | 4 | 2 | 2.7 | 32.4 |

2 | 6 | 4 | 6.5 | 78.0 |

3 | 8 | 6 | 10.4 | 124.8 |

4 | 10 | 8 | 13.9 | 166.8 |

5 | 12 | 10 | 17.3 | 207.6 |

6 | 14 | 12 | 20.9 | 250.8 |

7 | 16 | 14 | 24.2 | 290.4 |

8 | 17 | 16 | 28.3 | 339.6 |

9 | 18 | 18 | 31.6 | 379.2 |

10 | 18 | 19 | 35.3 | 423.6 |

11 | 18 | 20 | 38.7 | 464.4 |

12 | 18 | 21 | 42.2 | 506.4 |

13 | 18 | 22 | 45.8 | 549.6 |

14 | 18 | 23 | 49.6 | 595.2 |

15 | 18 | 24 | 53.5 | 642.0 |

16 | 18 | 25 | 56.9 | 682.8 |

17 | 18 | 26 | 60.6 | 727.2 |

18 | 18 | 27 | 64.8 | 777.6 |

It is shown in Figure

Segment AE test results. (a) Variation curve of acoustic emission for group 1. (b) Variation curve of acoustic emission for group 2. (c) Variation curve of acoustic emission for group 3. (d) Variation curve of acoustic emission for group 4.

The integral stiffness of the structure is reduced due to the existence of regional concrete spalling compared with undamaged segment rings. According to the comparison analysis for the test segments with different range of concrete spalling from group 1 to group 4, while the flexibility of segment lining is increased, the corresponding range of elasticity capacity is augmented as well. The numbers for the gradually formed step shape are reduced for the accumulated event numbers of acoustic emission with the increase of load step and the stage height also gradually increases, indicating a sudden change for the process of damage and failure of segments.

According to the displacement value of the vault, bottom of the arch, and the left and right haunches for different groups of segment lining, the variation curve of lateral and vertical convergence value is obtained for different groups of segment lining by statistical method, which is shown in Figure

Convergence value of horizontal and vertical directions of segment lining.

As shown in Figure

Elliptical aspect ratio for groups of test segment.

To have a better description of the change law, for the different groups of segment rings, it is summarized in Table

Deformation of each group of segment.

Group number | Range of regional spalling | Elastic-plastic demarcation point | Critical point for loss of stability | ||||||
---|---|---|---|---|---|---|---|---|---|

Corresponding loading step | Vertical convergence (cm) | Lateral convergence (cm) | Elliptical aspect ratio (%) | Corresponding loading step | Vertical convergence (cm) | Lateral convergence (cm) | Elliptical aspect ratio (%) | ||

1 | 无 | 5 | 1.75 | 3.83 | 0.90 | 16 | 12.12 | 13.58 | 4.15 |

2 | 45° | 6 | 4.26 | 3.98 | 1.33 | 15 | 22.20 | 21.58 | 7.06 |

3 | 60° | 6 | 5.23 | 4.10 | 1.50 | 15 | 23.20 | 22.70 | 7.40 |

4 | 75° | 6 | 5.40 | 4.45 | 1.59 | 14 | 25.67 | 26.59 | 8.43 |

According to Figures

As shown in Figure

Segment circumferential internal force diagram at elastic-plastic demarcation. (a) Segment circumferential axial force diagram. (b) Segment circumferential bending moment diagram.

As shown in Figures

Load-axial force curves at key points of lining. Variation curve of axial force for (a) group 1, (b) group 2, (c) group 3, and (d) group 4.

Load-bending moment curves at key points of lining. Variation curve of bending moment for (a) group 1, (b) group 2, (c) group 3, and (d) group 4.

Because the regional concrete spalling is located on the vault, and on the one hand, the cross-sectional area is reduced by concrete spalling, and consequently, the transmission of axial force between adjacent segments will be affected; on the other hand, the longitudinal joint tends to be damaged due to concrete spalling, and then the interaction between segment rings will be affected as well, and consequently, additional stress due to the stagger-jointed assembly will be reduced. Therefore, the magnitude for the value of structural axial force on the vault is relatively smaller compared with that on other parts.

For further research on the change of internal force for different groups of the experiment in both elastic stage and plastic stage, the characteristics of internal force in the demarcation point between elasticity and plasticity are summarized in Table

Statistics of the internal force features in elastic-plastic demarcation point.

Group number | Range of regional spalling | Loading step at elastic-plastic demarcation point | Internal force in the spalling region | Maximum axial force (kN) | Maximum positive bending moment (kN·m) | Maximum negative bending moment (kN·m) | |||
---|---|---|---|---|---|---|---|---|---|

Axial force (kN) | Bending moment (kN·m) | Value | Location | Value | Location | ||||

1 | None | 5 | 3128 | 306.5 | 4250 | 306.5 | Vault | −220.2 | Right haunch |

2 | 45° | 6 | 2714 | 277.4 | 4292 | 309.6 | Invert | −200.8 | Right haunch |

3 | 60° | 6 | 2386 | 259.1 | 4033 | 304.4 | Invert | −191.3 | Right haunch |

4 | 75° | 6 | 2082 | 231.6 | 4012 | 291.5 | Invert | −200.2 | Left haunch |

Generally speaking, on the one hand, the effective cross-sectional area for segment structure will be reduced by regional concrete spalling, of which the bending stiffness of the segment is reduced as well, and furthermore, the magnitude of the bending moment for the structure will also be decreased; on the other hand, the transmission of internal force between adjacent segments is affected by regional concrete spalling, and the damage on longitudinal joint will be more likely caused under the action of external load, which affects the interaction between adjacent segment rings, and as a result, the additional stress is reduced as well due to stagger-jointed assembly; finally, the magnitude of axial force will be significantly reduced. It is relatively limited for the influential range of regional concrete spalling on the whole internal force of the structure, most of the distinctions are within 10%, but the variation in axial force and bending moment for the damaged part is prominent due to regional concrete spalling, and the effect on axial force is more obvious than that on bending moment, which could be terrifically undesirable on the structural mechanical behavior; therefore, it has to be necessarily attached importance for this kind of disease.

This thesis is based on some metro project, according to the field investigation of regional concrete spalling for the segments, and the mechanical characteristics of segment lining structure in shield tunnel were analyzed and compared by similarity model test under different concrete spalling ranges. The main conclusions can be summarized as follows:

Compared with undamaged segment rings, the integral structure stiffness is reduced by regional concrete spalling, while the flexibility of segment rings is increased. The corresponding range of elastic bearing stage is slightly amplified with the expansion of segmental concrete spalling range while the range of plastic bearing stage is drastically decreased. Sudden changes have been discovered in the process of the damage and failure of segment lining structure.

The numbers of steps are obviously decreased for the accumulated event numbers of acoustic emission with the increase of load step as the range of concrete spalling continues to expand, and the step height is gradually increased, when the ranges of concrete spalling reach 45°, 60°, and 75°. The accumulated event numbers of acoustic emission increase by 34.9%, 45.8%, and 112.3% on the critical collapsing point.

Compared with undamaged segment rings, the magnitude for deformation is significantly increased for damaged segment due to regional concrete spalling under the action of identical external load, when the range of concrete spalling reaches 45°, 60°, and 75°. The vertical convergence value will increase by 143.43%, 198.86%, and 208.57% on the plastic-elastic demarcation point, respectively, the lateral convergence value increases by 3.92%, 7.04%, and 16.2%, and the elliptical aspect ratio increases, respectively, by 47.78%, 66.67%, and 76.67%; meanwhile, the vertical convergence value increases by 83.17%, 91.42%, and 95.30% on the critical collapsing point, the lateral convergence value increases by 58.91%, 67.16%, and 95.80%, and the elliptical aspect ratio increases by 70.12%, 78.31%, and 103.13%.

Compared with undamaged segment lining structure, after the emergence of the disease due to regional concrete spalling, the ultimate bearing capacity is prominently decreased for the segment lining structure, when the range of concrete spalling reaches 45°, 60°, and 75°, and the corresponding reduction rate for ultimate bearing capacity reaches 6%, 6%, and 13%.

The distribution law of axial force and bending moment for segment lining is not changed under the effect of regional concrete spalling, under identical load level, the value magnitude of axial force and bending moment for damaged segment due to concrete spalling is comparatively smaller than that for undamaged segment rings, and the difference value is increased with the increase of concrete spalling range.

The effect of regional concrete spalling is limited on the range of the global internal force, mostly within 10%, while the variation of axial force and bending moment is significantly great due to regional concrete spalling, when the corresponding range of concrete spalling becomes 45°, 60°, and 75°. Respectively, the axial force decreases by 13.2%, 23.7%, and 33.4% in the damaged area of segment rings, while the corresponding bending moment decreases by 9.5%, 15.5%, and 24.4%, and the effect on axial force is much more conspicuous than that on bending moment, which could be extraordinarily unfavorable on the structural mechanical behavior.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (grant no. 51578461) and the National Key Research and Development Program of China (grant no. 2016YFC0802202).