Case Study on Influence of Step Blast-Excavation on Support Systems of Existing Service Tunnel with Small Interval

Abstract

During the construction of newly built tunnel (NBT) adjacent to the existing service tunnel (EST), stability of the EST with small interval is affected by vibration waves which are caused by blasting load. The support structures of the EST will be cracked and damaged, while the unreasonable blast-excavation methods are adopted. Presently, the studies on behavior of support structure in the EST under blasting load are not totally clear, especially for the bolts system. Besides, the responses of support structure on blasting load are lacking comprehensive research. In this paper, New Zuofang tunnel is taken as a study case to study the influence of step blast-excavation in NBT on support structures of the EST through field experiment and numerical simulation. Some data, such as blasting vibration velocity (BVV) and frequency of support structures, are obtained through field measurement. Based on these data, the formula of BVVs is obtained. Research on stability of tunnel support structures affected by step blast-excavation is conducted using numerical simulation method. The dynamic-plastic constitutive model is adopted in the software ABAQUS to assess safety of support structures. The range and degree of damage for the support structures are obtained. In addition, change laws of axial force and stress with time for the bolts are analyzed.

1. Introduction

The structural types of tunnel with small interval (less than 1.5 times of tunnel width) exist widely in the tunnelling projects. The major risks resulted from vibration failure induced by blasting load in NBT when they are excavated by the drill and blast method. The blasting load in NBT will be easy to cause the adverse influence of blast-induced vibrations in the EST lining. How to protect the support structures of the EST during blast-excavation in NBT has become to a significant and valuable research work. It is necessary to carry out both experiments and numerical analysis to research the impact of BVVs on the support structures of the EST.

The damage of concrete lining in the EST under blasting load has been studied by lots of researchers. For example, Hisatake et al. [1] have researched a dynamic method with respect to effects of adjacent blast operation on vibration behavior of the EST. Krajeinovie [2] has introduced the damage acoustic wave of surrounding rock and obtained an important result that damage cracking of surrounding rock can be expressed by change rate of acoustic wave in rock masses. Kuszmaul [3] has obtained the “KUS damage” constitutive model for fragmentation of rock under the dynamic loading. Oriard [4] and Law et al. [5] have researched the accumulative damage of surrounding rock due to multitimes repetitive blasting loads by monitoring changes of peak BVVs and velocity of acoustic wave. Preece and Thlone [6] have studied the detonation time and fragmentation using PRONTO-3D dynamic finite-element program and obtained a modified “KUS damage” constitutive model. Doucet et al. [7], Villaescusa et al. [8], and Ramulu et al. [9] have studied the damage degree and damage range of surrounding rock under multi-times blasting by use of sliding micrometer and imaging well log technique. Singh [10] has introduced the blasting vibration damage to underground coal mines from adjacent to open-pit blasting. Toraño et al. [11] have researched FEM models including randomness and its application to the blasting vibrations prediction. Nateghi et al. [12] have researched a negative effects method of blasting waves on concrete by analyzing parameters of underground vibration. The control method of blasting waves has been proposed based on the peak BVVs of underground structure. From the aforementioned research results, it can be seen that most works on blasting vibration response focus on the theoretical study which is very little combined with engineering cases, especially for the research on the blast-excavation effect on the EST. The vibration wave gathering method is mostly realized through the natural vibration method. However, there are usually many differences between vibration waves caused by natural earthquake and those caused by blasting vibration. So it is important to adopt a reasonablility natural earthquake analysis theory. Generally, the numerical simulation methods are used to analyze damage cracking of support structures in the EST, although the results based on different calculation methods might vary greatly. Currently, the wave function expansion method is a main way to analyze BVVs of the EST. However, the surrounding rock is regarded as a homogeneous elastic medium in this method. In addition, the shape of tunnel and structure of rock masses are complicated actually, and the discontinuities exist widely in surrounding rock. Therefore, only some conventional views can be obtained in the past researches.

About the damage of the EST lining under dynamic load, the analysis on field experimental data and numerical simulation have been focused on in the recent decades. For instance, Wang et al. [13] have found that the BVVs and tensile stress of side-walls are bigger than the sections of the EST. The most dangerous part in the EST is the side-walls. Li et al. [14] and Xia et al. [15] have researched the damage properties of rock masses under blasting load in nuclear power station project. Feng and Wen [16] have simulated the dynamic response process of the EST under blasting load and found that blasting in adjacent distance is a key factor for the safety of concrete lining. Zhang et al. [17] have researched the vibration properties and change laws of middle wall and tunnel face in tunnel with small interval by vibration effect experiment of surrounding rock under blasting load. Shen et al. [18] have found that the attenuation of BVV is very obvious and amplitude of particles will likewise decrease with the distance increasing between monitoring point and blasting center. Chen [19] has studied the vibration response and accumulative damage of rock pillar in the EST with small interval. The attenuation formula of blasting wave in the rock pillar under blasting load has been obtained. Yang et al. [20] have researched the degree and range of rock masses damage in the EST under blast-excavation by using of two-side-wall pilot tunnel method. Although there are many successful cases in which the adverse influences of blast-induced vibrations on EST lining have been avoided or minimized, the studies on response of support structures of the EST under the blast-excavation are mostly only to analyze the damage cracking of concrete lining, while ignoring the influences on other support structures, such as bolts system and shotcrete. Therefore, it is important to study the vibration response of bolts support system placed in the surrounding rock of arch section and shotcrete support placed between the secondary lining and surrounding rock. At present, it is not clear that the deformation and failure laws of shotcrete and bolts under blasting loads are consistent with secondary lining. In addition, the dynamic response laws of bolts installed in surrounding rock at the arch section under dynamic loads are not understood uniformly. In this paper, the field experiment and numerical simulation are used to study the response laws of support structures in the EST under blasting load. The responses of blasting load on bolts and shotcrete support are analyzed based on stress wave theories and vibration mechanics theories.

2. Site Description and Experimental Methods

2.1. General and Geological Information

New Zuofang Tunnel in Lanzhou-Chongqing railway is located in Hechuan District of Chongqing, next to Fu River, China. As shown in Figure 1, the NBT (New Zuofang Tunnel) is located on the left side of the EST (Old Zuofang Tunnel) with length of 487 m (DK888+156−DK888+643). The minimum distance between the two side-walls is less than 10 m (less than 1.5 times tunnel width with 33 m). The NBT built three railway lines is approximately parallel to the EST, where the Suining-Chongqing railway is a single railway line and Lanzhou-Chongqing railway is double lines. The tunnel becomes double-arch tunnel from single-arch tunnel at DK888+600. The largest span of single-arch tunnel is 22 m, and the maximum burial depth is 75 m. There is a single railway line in the EST built in 2005 and used for eight years on this unique single railway line. The support system of EST is consisted of bolts in surrounding rock, shotcrete support (its thickness is 25 cm) and secondary lining (its thickness is 80 cm). The arch section of the EST is supported by the grouted rockbolt each 1.0 m. The elevation of NBT's bottom boundary is higher than that of the EST (see Figure 2), which will seriously affect the stability of the support structure of arch section in the EST.

Figure 1:

Location and layout of New Zuofang Tunnel.

Figure 2:

Excavation steps and monitoring points.

The NBT and the EST are located in a region of the denuded hills, where the lithology is Jurassic fine sandstone and mudstone with weak strength. The thickness of mudstone intercalations is about 1.0-2.0 m. It tends to mud and is easy to expand when it is mixed with water. The occurrence of whole strata varies little with small dip angle. Some intercalary strata of impurities develops little in surrounding rock with grade IV and V. The rock masses classified based on Chinese Code for Design of Railway Tunnel (TB10003-2005) which considers many influence factors, such as strength of intactness rock, geometrical characteristics and mechanical properties of discontinuity, intactness of rock mass, groundwater, ground stress, and so forth. The properties of different surrounding rocks are shown in Table 1.

Table 1:

Properties of surrounding rock with different grades.

Milepost	DK888+177–250	DK888+250–290	DK888+290–510	DK888+510–550	DK888+550–626

Grade	V	IV	III	IV	V

Properties	Mudstone intercalation (horizontal bedding) and fragment rock	Mudstone intercalation (horizontal bedding)	Intact sandstone	Mudstone intercalation (horizontal bedding)	Fragment rock (fracture development)

2.2. Field Experimental Method

(1) Method of Blast-Excavation. The NBT is step-excavated by use the two side-wall pilot tunnel method, which is a kind of drill and blast method, and the sequence of excavation is shown in Figure 2. The parallel excavation is applied to side-wall pilot tunnel on both sides, and the distance of excavation face is more than 100 m to decrease influence on each other. The measures of smooth blasting and microdifference blasting in deep borehole are applied to decrease the influence on the surrounding rock and the EST lining, and the depth in horizontal direction of each round excavation is about 2.0 m. The method of the decoupling charge with 2# rock emulsion explosive is applied in blasting of periphery borehole. The depth of blast boreholes is about 2.0 m and is divided into 9–11 segments to be filled with emulsion explosive. The excavation cross-section of NBT is divided into seven steps (see Figure 2). Because of the minor effects on the fifth step and the sixth step of the EST, the stress and deformation of the EST affected by these two steps would not be considered in this paper.

(2) Measure Method. The vibration transducers are fixed on the side-wall of the EST to obtain BVVs under blasting load at the same position (see Figure 3). There are 4 monitoring points numbered one, two, three, and four on the side-walls. Two vibration transducers with horizontal (along tunnel axis) and vertical directions are fixed one very monitoring point. After blasting occurred, the vibration signal of particles at the concrete lining subsurface caused by the blasting vibration waves is transformed as the electrical signal and inputted into memory instrument through the vibration transducer, the memory instrument connected with PC. The vibration signal is transferred into BVVs and frequency to analyze the response spectrum. This vibration experiment is carried out for every excavation step to obtain corresponding data.

Figure 3:

Setup and installation of monitoring instruments.

3. Field Experimental Results and Analysis

3.1. Statistical Analysis of Field Experimental Data

The variation of peak BVVs with distance to the blasting center is shown in Figure 4. As seen, the vertical BVVs of particles caused by longitudinal and Rayleigh waves are different from the horizontal BVVs caused by shear and Love waves. Most of the BVV values are small. The maximum vertical BVV is 8.668 cm/s which is close to critical safety state of concrete lining. The maximum horizontal BVV is 3.788 cm/s, which is less than vertical BVV. The energy increases with the increasing of BVV, and the BVV of vertical is usually larger than the one of the horizontal, so the vertical BVV is often taken as a safety control indicator of concrete lining. The maximum BVV value occurs at the 4th step for the same monitoring point and then reduces from the 7th step, the 3rd step, and the 2nd step to the 1st step. The maximum BVV is at the monitoring point 1 for the same blast-excavation step. The monitoring numbers of vertical BVV from the maximum value to the minimum value are point 1, point 2, point 3, and point 4. Therefore, the BVVs attenuate rapidly with the increasing of distance to the blasting center. The energy density and strength decrease rapidly with the expansion of spread range of vibration waves and influence of rock fracture during the spread process of stress wave. The pre-reinforcement distance of NBT is designed to be 20.0 m because of the very small value of BVV at point 4.

Figure 4:

Relationship between horizontal and vertical peak BVVs and distance to the blasting center.

Presently, based on the principle of dimensional analysis, the attenuation formula (1) of BVV put forward by Sadov (1978) is widely used:

V = k {(\frac{Q^{1 / 3}}{R})}^{α},

(1)

where R is the distance from monitoring point to blasting center (m); V is BVV of particle at the monitoring point (cm/s); Q is a single-stage initiation charge weight (kg) and Q is equal to 3 in here; and k and α are the coefficients related to media properties, blasting method, and spread path.

Based on the measurement data from field experiment, the coefficients of k and α of BVVs by fitting Sadov's formula are 1.185 and 3.544 for the vertical BVV and 2.443 and 2.427 for the horizontal BVV, respectively.

3.2. Application of Sadov's Formula

The BVVs of concrete lining at different positions and excavation steps are predicted by using Sadov's formula and shown in Figure 5. As seen, the BVV values of the 4th and 7th steps are bigger at point 1, and these values are close to the limited safety velocity controlled by “Blasting Safety Code” published by Chinese State Administration of Work Safety. In addition, the cracks occur at the hance of the EST at the 4th step and the 7th step; this phenomenon is consistent with the observation in the field.

Figure 5:

Vertical and horizontal BVVs forecasted by Sadov's formula.

3.3. Analysis on Dominant Vibration Frequency

The dominant vibration frequency distribution of BVVs measured at the different monitoring points is shown in Figure 6. As seen, BVVs less than 5 cm/s have a high frequency and their dominant vibration frequencies are distributed at the range of 50–150 Hz. This indicates that the vibration waves caused by blasting load are low-frequency waves, and its frequency is much larger than the natural frequency of concrete lining. The dominant vibration frequency is less than 50 Hz when the BVV is more than 6 cm/s. The vibration frequency at the position of the greater BVV is mostly low frequency. In general, the frequency decreases with distance increasing in the inhomogeneous rock masses. The existing joints and fractures in intermediate strata have a great effect on the stress wave spread. High BVV and low frequency intensify the damage of concrete lining, because the low vibration frequency is close to the natural frequency of the EST lining (about 10–15 Hz) and causes resonance of concrete lining. Therefore, the concrete lining is not safe at the position with the maximum BVV. The high BVV occurs mostly at the 4th step, which leads to the greater possibility of damage at the position of hance and spandrel facing the blasting side.

Figure 6:

Distribution of dominant vibration frequency.

3.4. Time-Domain Analysis of BVV

The attenuation laws of particle BVV are obtained by the time-domain analysis of BVV. The curve of BVV of point 2 at the 4th step is shown in Figure 7. As seen, the time-dominant curve has lots of wave peaks and troughs with continuous intervals. This is caused by the millisecond blasting in each borehole and vibration reflection at the interface. Meanwhile, there exist certain time intervals among periphery boreholes, satellite boreholes, cutting boreholes, and so on during blast-excavation. Due to the adoption of presplitting blasting, the first maximum BVV peaks and troughs are caused by the blasting in periphery boreholes. The blasting in periphery holeh as the greatest impact on the support structures of the EST. The serious oscillation stage and stationary oscillation stage are shown on the BVV curve. The serious oscillation stage is the main phase caused by superposition of body wave (longitudinal wave on the vertical BVV curve and transverse wave on the horizontal BVV curve) and surface wave. The stationary oscillation stage is called after shock phase caused by complementary waves from surface wave.

Figure 7:

Time-history of horizontal and vertical BVV for the point 2.

The complex vibration process will be arised at the measured point, and every round blasting corresponds to a peak BVV, which lasts for 0.55 s. The massive stress waves generate in the process of blasting, and the properties of stress waves analyzed by the principle of superposition are the same except for amplitude. The damage possibility of concrete lining is caused by the longer duration of vibration. The vibrations processes of particles at point 3 and point 4 are quicker finished than those at point 1 and point 2, because the spread of vibration waves attenuates before arriving at measured points due to far spread path. The blasting vibration wave is triangle waveform along with severe vibration which is different from the natural vibration wave. The total time of blasting is 0.55 s when BVV reduces to zero. After blasting, there are still small amplitude oscillations, and the horizontal residual vibration lasts a little longer. This is because the spread direction of transverse wave is horizontal and the decay speed is less than that of longitudinal wave. The discontinuous BVV shown in Figure 7 can be divided into several different regions with interval every 0.1 s by means of millisecond delay blasting. The vibration superposition can be avoided by using interval blasting in different position and stage blasting at the same position.

4. Theoretical Verifications of Field Experimental Results

In order to understand the response on tunnel support structures under blast-excavation load specifically, the numerical simulation method is used to analyze the surrounding rock with grade III (DK888+290−DK888+510). Firstly, the calculation results of vertical peak BVVs are compared with the field monitoring results to validate the reasonable of numerical simulation. Secondly, the variation laws of stress and displacement in the support structures are analyzed under the different blast-excavation steps. Finally, the plastic damage in the concrete lining and the laws of response on bolts are studied by introducing dynamic-plastic constitutive model of concrete.

4.1. Physical-Mechanical Parameters of Rock Masses and Concrete

(1) Physical-Mechanical Parameters of Surrounding Rock. The plastic state under blasting load might appear in the surrounding rock, so the Drucker-Prager model is used to simulate damage of concrete lining, and the elastic model is used to simulate bolts. According to the reports of engineering geological investigation and the results of laboratorial experiments, the physical-mechanical parameters are listed as Table 2.

Table 2:

Physical-mechanical parameters of surrounding rock and bolts.

Materials	Weight/kN/m³	Elastic modulus/GPa	Poisson's ratio	Internal friction angle/°	Dilation angle/°	Cohesion/kPa

Surrounding rock	25.50	2.06	0.3	30.6	30.6	20
Bolts	78.50	210	0.2	/	/	/

(2) Physical-Mechanical Parameters of Concrete Lining. Damage-plastic constitutive model is defined as the constitutive model of shotcrete and secondary lining. The physical-mechanical parameters of concrete lining are shown in Table 3.

Table 3:

Physical-mechanical parameters of concrete lining.

Concrete lining	γ/kN/m³	E₀/GPa	μ	Ψ/°	ξ	σ_{b ₀}/σ_{c ₀}	K	ω_t	ω_c

Secondary lining	25	30	0.2	15	0.1	1.16	0.6667	0	1
Shotcrete	24	23	0.2	/	0.1	1.16	0.6667	0	1

Notes: γ is weight; E₀ is initial elastic modulus; μ is Poisson's ratio; Ψ is dilation angle; ξ is eccentricity ratio; σ_{b
₀} is initial yield compressive stress of equal axial; σ_{c
₀} is initial yield compressive stress of unequal axial; K is yield constant; ω_t is tensile restore factor; ω_c is compressive restore factor.

4.2. Rational Verification of Numerical Calculation

The average values of vertical BVVs at point 1 by the numerical simulation based on the software ABAQUS and the field experiment are shown in Table 4. The BVVs obtained by numerical simulation are larger than those of field experiment. This is because there are a large number of discontinuities in rock masses in field experiment to make the stress waves decay faster than those in the rock masses regarded as a homogeneous material in numerical simulation. In addition, the calculation formula of blasting-borehole pressure is set up in an ideal condition. The blasting energy is totally translated into the force to throw the rock into the air. The allowed error range of BVVs larger than actual values is about 10%, so the calculation results obtained by numerical calculation are reliable to analyze the law of stress and strain of support structures under different blasting excavation steps.

Table 4:

Comparison between vertical BVVs of field experiment and that of numerical calculation.

Excavation steps	The 1st step	The 2nd step	The 3rd step	The 4th step	The 7th step

Field experiment/cm/s	2.642	3.622	4.740	8.616	8.668
Numerical simulation/cm/s	3.123	4.342	6.346	10.125	10.084
Error	18.2%	19.9%	33.9%	17.5%	16.3%

4.3. Analysis on Damage Degree of the EST Lining

4.3.1. Damage Mechanism of Concrete Lining under Cyclic Load

The representation of damage variable proposed by Kachanov is widely used to describe the damage variable. The formula is listed as follows:

D = 1 - \frac{A^{*}}{A} = \frac{A - A^{*}}{A} = \frac{Δ A}{A},

(2)

where D is the damage variable value, 0 ≤ D ≤ 1. It indicates no damage when D is equal to zero. It indicates complete damage when D is equal to 1.0; A is initial sectional area of damage zone; A^* is the effective bearing area after the structure is damaged.

The process of damage in the concrete lining can be regarded as a cyclic loading process with high loading rate, because of the influence of repeated vibration caused by multi-times blast-excavation and a high loading rate being 5 m/s with a longer time of blasting vibration. This process is also regarded as an accumulative process of multi-times dynamic damages. The distribution of damage in the concrete lining and degree of damage in different points can be obtained by the damage-plastic constitutive model of concrete in the process of numerical analysis.

4.3.2. Comparison Analysis on Damage under Different Blast-Excavation Steps

The damage process of the EST lining is irreversible because of the sublevel millisecond blasting. The fatigue damages of concrete lining occur on the support structures of the EST under a longtime dynamic load. The damage process of concrete lining caused by blasting load at different excavation steps is shown in Figure 8.

Figure 8:

Damage of concrete lining under different excavation steps (C: compression; T: tensile).

As seen in Figure 8, there is no damage appearing in concrete lining at the 1st step and the 2nd step, which means that the stress wave is not strong enough to produce damage because the wave intensity attenuates while spreading to the concrete lining. Damage of concrete lining begins at the 3rd step. The range and area of damaged zone of secondary lining are almost the same to those of shotcrete. The compressive damage zone focuses on secondary lining and arch foot facing the blasting side. The cyclic-dynamic stress concentration takes place in the aforementioned positions due to their acute angle types. This position can be damaged easily under compressive stress. The maximum damage value less than 1.0 under the compressive stress is smaller than the limited value, so only a few of microcracks appear on the subsurface of concrete lining. The buckling failure of concrete lining and shotcrete is not produced at the 3rd step. The macrocracks begin to emerge when the maximum damage value caused by tensile stress in the concrete lining is 0.8213. However, these cracks without connection fail to result in the failure of concrete lining. The maximum damage value in the shotcrete is 0.6974. The damage degree of shotcrete is smaller than that of secondary lining, but the damage range of shotcrete is greater than that of secondary lining. The minor damage at the back facing the blasting side of concrete lining can be seen from the damage graph. This phenomenon shows that the intensity diffracted here is still very strong when the stress waves spread to this position. At the 4th step, the minor compressed damage in shotcrete and small range of compressive damage in secondary lining appear at the same position with the 3rd step. The maximum damage value is 0.6123, and the degree of damage is larger than that at the 3rd step. The maximum damage value in tensile stress zone is 0.8720, and the macrocracks begin to emerge but not posing failure of concrete lining. Larger damage zone exists at arch foot, which is similar to the 3rd step, and the maximum damage value is 0.8882. Comparing with the 3rd step, there is no damage emergeing at the back facing the blasting side of concrete lining. Damage generation concentrates mainly on the inside of invert at the 7th step. The range and degree of damage are small under the compressive stress and become bigger under the tensile stress. The punctuate distribution of damage zones appears in the concrete lining at the 7th step, and the damage degree in shotcrete is far less than that in secondary lining under the tensile stress.

According to the aforementioned analysis, the distance from blasting center to monitoring point has great impact on the range and degree of damage. Damage appears at the 3rd step, the 4th step and the 7th step, and the largest one is at the 4th step. Therefore, the blasting parameters should be controlled mainly at the 4th step and the fifth step. The maximum damage value is between 0.8 and 0.9 with some microcracks appearing at the damage zone. The total damage in the concrete lining after every round blast-excavation is shown in Figure 9. As seen, the macrocracks appear at the hance facing the blasting side of concrete lining, arch foot, and arch spandrels, and at spandrel back facing the blasting side of concrete lining.

Figure 9:

Damage range and zone under different excavation steps.

It can be seen from Figure 9(b) that the damage degree of concrete lining at back facing the blasting side is higher than that of facing the blasting side. This phenomenon is consistent with the distribution of peak principle stress. The simulation results can be proved by field observation. Some reinforcement measures of concrete lining are taken by railway administrative department. Two main reasons lead to the cracks in the concrete lining. Firstly, because of the closeness of EST to NBT, the charge is too excessive to produce a large blasting load. Secondly, lots of initial defects exist in the concrete lining because of concrete aging. Comparing Figure 9(a) with Figure 9(b), it can be found that the range and degree of damage due to tensile stress are larger than those of damage due to compressive stress. This is because the cyclic principle tensile stress in the concrete lining is big and it is close to tensile strength of concrete. Besides, the duration of blasting load with 65 ms promotes the development of damage zone.

4.3.3. Development Process of Damage in the Concrete Lining

The expansion of damage range and deepening of damage degree at the 4th step are taken as example to analyze the development of damage in the concrete lining under the successive blasting load.

(1) Expansion Process of Damage Zone. The range of damage zone in the concrete lining becomes larger with the excavation steps firstly and then tends to be stable. The distribution range of damage at different time is shown in Figure 10. As seen, the damage caused by tensile stress occurs firstly near subsurface facing the blasting side at 0.012 s, and the damage value is 0.01463. The damage zone enlarges to two sides with the lasting function of stress wave, and the degree of damage deepens continually. The damage zone of hance facing the blasting side enlarges obviously at 0.057 s, and the maximum value is up to 0.1480. The damage zone emerges at arch foot facing the blasting side, and two aforementioned sections are damaged seriously at 0.077 s. The maximum value reaches 0.8313 at 0.207 s. Macrocracks begin to generate here, and cracks extend with the deepening of damage zone. Damaged zone begins to expand to the side near shotcrete along the deepening direction, and the range of damaged zone reaches the maximum value at 0.293 s. Damage value of outside (near subsurface) is larger than that of inside. This phenomenon shows that the macrocracks do not enlarge to inside of concrete lining (there are microcracks at inside) and just extend along profile of concrete lining at outside. Therefore, the fracture of concrete lining along the deepening direction is avoided.

Figure 10:

Damage of concrete lining at different time.

(2) Deepening Process of Damage Degree. The damage emergence of concrete lining in the EST is caused by the blast-excavation. Under the cyclic loading, the mechanical parameters of concrete lining began to decrease, and damage degree enlarged gradually. Meanwhile, the damage value D began to increase from zero to a stable value.

The damage process of concrete lining with time at the 4th step is shown in Figure 11. As seen, the damage of concrete lining does not appear immediately but later after blast-excavation. This may be caused by two main reasons. Firstly, it requires enough time to make stress wave spread from blasting center to the concrete lining. Secondly, the concrete lining has inertia effect under the dynamic cyclic loading. The increase of strain and displacement does not coincide with stress under high strain rate load. This means that it does not have enough time to make deformation increase with increase of stress under the inertia function. This is the theory of damage effect lag that the cracks lag to appear in the concrete lining. The theory based on the deformation of concrete lining is the direct reason of damage generation.

Figure 11:

Development process of damage value at the 4th step.

It needs some time to make the damage of concrete lining reach the maximum value once the concrete lining emerges damage. According to the time-history curve of stress, the stress superposition is in the form of triangle. Stress will decrease and cracks will stop extending when stress value reaches the critical value of producing cracks. Subsequently, stress will accumulate continuously, and cracks will continue to extend. Damage of concrete liningwill stop developmentwhen stress wave doesn't make cracks further extend. As seen in Figure 11, the increase tendency of damage value is coincident with logarithm curve. So the express formula is listed as follows:

D_{t} = {\begin{cases} 0, & t < t_{0}, \\ A \ln t + B, & t_{0} \leq t \leq t_{1}, \\ D_{\max}, & t > t_{1}, \end{cases}

(3)

where D_t is damage value and A and B are two coefficients which are related to materials of concrete lining and can be fitted with least square method. It is noticed that A and B are different under compressive damage and tensile damage even under the same engineering condition. D_max is a final damage value; t₀ is the initial time of damage; t₁ is the final time of damage; t is one time of damage.

According to (3), the damage development speed of concrete lining will become slower with time lasting. This is because the reflection and diffraction of stress wave occur at the position of concrete cracks to make the stress and energy releases. The development speed of damage in the concrete lining decreases gradually with strength decrease of stress wave.

4.4. Dynamic Response of Bolts on Blasting Load under Different Steps

4.4.1. Support Effect of Bolts under Blasting Load

In order to understand the dynamic response of bolts on blasting load in the surrounding rock at the arch section of the EST under blasting load, the 3rd step is taken as an example to analyze the distribution of stress and displacement along the arch section of tunnel. The arch section of the EST and the arrangement of bolts at the arch section are shown in Figures 12 and 13, respectively.

Figure 12:

The arch section of the EST.

Figure 13:

Arrangement of bolts at the arch section.

The distribution laws of stress and displacement of different arch section are shown in Figure 14. As seen, the horizontal stress at the arch section is negative at the 3rd step. This proves that the stress in surrounding rock at the arch section is a compressive one along horizontal direction. From the distribution of horizontal stress, it can be found that the pressure at the arch section facing the blasting side is larger than that of other parts, and the stress distribution of surrounding rock with bolts is similar to that without bolts. The stress of spandrel facing the blasting side with bolts is smaller than that without bolts, while it is the opposite at other sections. The maximum vertical stress happens at the spandrel facing the blasting side. The stress decreases rapidly firstly and then increases from the spandrel to the center of arch section. After entering into the side-wall back facing the blasting side, it decreases gradually and even becomes negative so that the rock mass here is subjected to compressive stress. Comparing the stress with bolts and that without bolts is shown in Figure 14. It can be found that the stress with bolts is generally larger than that without bolts in the arch section. The maximum compressive stress being 0.222 MPa appears at the arch section where it is smaller than that of other sections. Horizontal displacement is smaller, and the displacement direction of particle moves from right to left at the side-walls facing the blasting side. The displacement increases at first and then decreases from the side-walls facing the blasting side, the arch section, to the side-walls back facing the blasting side. The maximum displacement being 23.0 mm happens at the arch section of the EST. It can be found that the displacements with bolts are similar to those without bolts. The vertical displacement at the 3rd step follows the similar change law with horizontal displacement. The maximum value of vertical displacement at the arch section is 16.0 mm without bolts and 2.3 mm with bolts.

Figure 14:

Stress and displacement at the arch section (H: horizontal direction; V: vertical direction; NA: no bolt; A: bolt).

It can be seen from Figure 14 that the displacement of surrounding rock without bolts is much larger than that with bolts at the arch section. The difference at the center of arch section is larger than that at two sides of arch section. The largest difference of displacement between them is 14.0 mm. The dynamic stress in the surrounding rock with bolts is larger than that without bolts. Simultaneously, the displacement of the former is smaller than that of the latter. The reason is that the reinforcement role of bolts at the arch section makes the rock masses close to each other. The attenuation speed of stress wave decreases in rock masses. The stress wave in the surrounding rock with bolts is stronger than that without bolts at the same section. The displacement of rock masses reinforced by bolts becomes smaller than that of without bolts. The arrangement of bolts enhances equivalently the stiffness of surrounding rock at the arch section. Comparing with surrounding rock without bolts, the capacity of bearing dynamic load of surrounding rock with bolts is enhanced obviously.

4.4.2. Axial Force Analysis of Bolts at the Arch Section under Different Steps

It can be seen from Figure 13 the bolts under different blasting loads. They also suffer different axial forces with different angles even at the same excavation step. The peak axial force on the middle of No. 1, No. 3, No. 5, No. 8, and No. 10 bolt is shown in Table 5.

Table 5:

Peak axial forces on the middle of bolts under different excavation steps (units: kN).

No. of bolts	No. 1	No. 3	No. 5	No. 8	No. 10

The 1st step	4.134	6.35	2.459	1.775	1.235
The 2nd step	1.523	2.432	1.166	0.809	0.809
The 3rd step	5.814	8.384	7.053	4.773	3.591
The 4th step	35.553	45.904	28.033	8.432	6.483
The 7th step	9.606	22.017	6.365	2.409	3.804

As seen in Table 5, the peak axial forces of bolts at the arch section facing the blasting side are generally larger than those of bolts at other section. This is because the bolts in this position are influenced by stress waves firstly, and the stress waves attenuate when they spread to the other side. About the axial forces of bolts at the same step, the sequence from big to small is No. 3, No. 1, No. 5, No. 8, and No. 10 bolts, respectively. It indicates that the angle of bolts has great effect on the axial force of bolts. Dynamic load has the greatest impact on inclined bolts, horizontal bolts secondly, and vertical bolts at last. About the axial force of the same bolt, the sequence from big to small is the 4th step, the 7th step, the 3rd step, the 1st step, and the 2nd step, respectively. Stress waves generating at the 4th step have greatest impact on bolts, and the smallest influence appears at the 2nd step. This is because the small distance between monitoring point and blasting center has great effect on axial forces of bolts and the change of blasting center and angles of bolts have significant impact on axial forces of bolts.

4.4.3. Time-History Analysis on Axial Stress of Bolts

The strength of bolts is enhanced obviously after lasting stress waves from surrounding rock. The axial stress of bolts vibrates intensely with time. The time-history analysis on axial stress on the middle of No. 3, No. 5, and No. 8 bolts is shown in Figure 15.

Figure 15:

Time-history analysis on different bolts.

As seen in Figure 15, bolts with different angles have different change trends of axial stress. It indicates that the stress waves with different angles have the different spread laws. Just as the time-history of axial stress in the concrete lining, the stresses in bolts vibrate intensely and last for 0.1 s, which is almost consistent with the function time of blasting load, and then concuss slightly because of inertia function. They do not decrease to zero during the calculation time while vibrating appreciably around a certain value. The permanent compressive stress and tensile stress in bolts caused by the vibration function of blasting load, rotation, or extrusion of rocks in the arch section. The tensile stress or compressive stress of bolts prevents the rotation or extrusion of rock masses. These stresses are put together with static stress of bolts caused by ground stress. Bolts force will increase if two kinds of stress are in the same direction. On the contrary, bolts force will decrease. The concussion process of stress in bolts with different angles exists significant differences, for example, the superposition phenomenon of axial stress appears in bolts (as No. 3 bolt) facing the blasting side under blasting load. However, it does not appear in bolts back facing the blasting side (as No. 5 and No. 8 bolts), which are vibrated by tensile stress and compressive stress circularly. As a result, the yield strength of bolts decreases obviously under cyclic load.

5. Conclusions

At the same monitoring point, BVVs caused by different blast-excavation steps decrease with the distance to blasting center increasing. After analysis on particle BVVs from different positions to blasting center, Sodev's formula which is suitable for similar projects is obtained. The particle BVVs in the concrete lining subsurface are forecasted by this formula.

Under different blast-excavation steps, the peak principle stress appears at spandrel at the 1st step and the 3rd step and appears at hance at the 2nd step and the 4th step. Because the largest peak principle stress appears at the 4th step and the 7th step, the damage zones of the concrete lining are mainly concentrated in hance and arch foot facing the blasting side. Stress in support structures concusses with many peak values. The concussion lasts for very long time which is far longer than that of stress in borehole. It is shown on the stress wave curve that the first peak of stress is the largest one, and then peaks attenuate gradually. Stress waves which spread in the concrete lining present superposition phenomenon at the 1st step and the 2nd step.

Damage of support structures happens at the 3rd step, the 4th step, and the 7th step. It is mainly concentrated on the concrete lining facing the blasting side. The most serious damage happens at the 4th step. This shows that the damage degree is related to the distance from blasting center in terms of the same charge. The cracks at hance and spandrel facing the blasting side are caused by the cumulative damage of these three steps. The area of damage zone, as well as distribution law of peak damage value, begins to extend from one point on the subsurface of concrete lining to any direction. At the same monitoring point, damage does not happen immediately after blast-excavation occurs, but it experiences a delay time before enlarging rapidly.

It can be seen from the distribution of damage zone that the range and degree of damage in the surrounding rock at the arch section are very small. This proves that bolts improve the capacity of bearing dynamic load for the surrounding rock efficiently. In addition, bolts with different angles suffer different stresses. The inclined bolts suffer larger stress than that of horizontal bolts and vertical bolts. This shows that stress wave with oblique incident is stronger than that with forward incident. After blast-excavation is finished, the fact that the residual stress is left in bolts proves that the interaction dislocation happens in the surrounding rocks at the arch section.

Footnotes

Acknowledgments

This paper is financially supported by the National Natural Science Foundation of China (Grants nos. 41002089 and 41102162) and Jiangsu Overseas Research & Training Program for University Prominent Young and Middle-Aged Teachers and Presidents. The authors gratefully acknowledge M. S. Chuanlei Zhang at the School of Earth Sciences and Engineering, Hohai University, China, for his contribution to the field experiment. The authors would also like to acknowledge the editors and reviewers of this paper for their very helpful comments and valuable remarks.

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