Stability analysis of surrounding rock mass in underground powerhouse considering damage effect of microfractures

Peiwei Xio, Hoyu Mo, Bo Qin, Bio Li, Xingguo Yng, Nuwen Xu,**

a State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China

b Guodian Jinshajiang Xulong Hydropower Development Co., Ltd, Chengdu, 610041, China

c School of Geoscience and Technology, Southwest Petroleum University, Chengdu, 610500, China

Keywords:Underground powerhouse Microseismic (MS) monitoring Numerical modeling Microfracture damage Constitutive relation

ABSTRACT A high-precision microseismic (MS) monitoring system was built to monitor surrounding rock microfractures in the underground powerhouse on the left bank of Shuangjiangkou Hydropower Station. The surrounding rock damage area with spatiotemporal clustering of MS activities was studied for qualitative analysis of the damage mechanism of surrounding rock microfractures,based on the source parameters of MS events. The surrounding rock microfracture scale characterized by the source radius of MS events was considered to establish the constitutive relation. MS information was imported into the model for numerical analysis using fast Lagrangian analysis of continuain 3 dimensions (FLAC3D). The results indicated that the numerical simulation results considering MS damage can better reflect the actual situation of the field. The surrounding rock microfractures mainly showed mixed failure characteristics.Shear failures appeared in localized areas while the fracture scale of sections from K0-33 m to K0-15 m on the vault was large. The deformation increment caused by microfracture damage in the shallow surrounding rock of the top arch accounted for 10%-13%, and the stress decrement in the surrounding rock caused by microfracture damage accounted for about 10%.

1. Introduction

With the rapid socio-economic development and the increasing demand for clean energy, a great number of hydropower projects have been constructed in Southwest China. To meet the requirements for hub layout and construction in a deep-incised valley,most of these hydropower projects adopt underground powerhouses,such as Jinping-I(Qian and Zhou,2018),Houziyan(Xu et al.,2017), and Baihetan (Xiao et al., 2016). Southwest China, located in the high mountain and canyon area of the transverse ranges at the eastern edge of the Qinghai-Tibet Plateau,has a complex geological environment with high in situ stress that is unevenly distributed,and the ratio of rock mass strength to the in situ stress is low (Ma et al., 2021). Moreover, the large-scale excavation and unloading of underground caverns have led to a series of serious problems,including the deformation and failure of surrounding rock mass(Zhu et al., 2008; Xu et al., 2015; Feng et al., 2017). Many scholars have carried out extensive research on the stability of underground caverns (Hoek and Brown, 1980; Kwon and Wilson, 1999;Manouchehrian and Cai, 2018), mainly using numerical simulation and conventional monitoring data for stability analysis.

The microseismic(MS)monitoring technology,asa high-precision and reliable method,has been adopted to monitor the fractures and deformation of rock mass in recent years.A MS monitoring system is able to monitor the rock mass in three dimensions(3D)and collect elastic waves emitted from microfractures inside the rock mass in real-time using pre-installed MSsensors around the target area.Then,through a quantitative inverse calculation of seismological parameters,the potential high-risk areas in host rock can be delineated and themacroscopicdeformationfailureof therockmasscanbepredicted in advance(Dai et al.,2017).Ma et al.(2020)studied the deformation and instability of the right bank slope at Dagangshan Hydropower Station by combining the 3D discontinuous deformation analysis(DDA) method with MS monitoring data, and described its failure mechanism.Young et al.(2004)elaborated the meanings of various MS parameters and their applications in mine MS monitoring. At present, there are two kinds of fracture prediction methods using seismic data (Al-Dossary and Marfurt, 2006; Chopra and Marfurt,2007; Gray and Head, 2009). One method is to extract geophysical fracture attributes based on post-stack seismic data,such as coherent,curvature and ant body properties.Coherent property is suitable for large-scale fractures or faults and curvature property often represents meso-scale fracture information. Ant body property, derived from coherent or curvature property,is equivalent to a more refined curvature or coherent property.Another method is on the basis of prestack data and a typical method is the fracture prediction technique based on longitudinal wave azimuth-anisotropy.Compared with the coherent,curvature and ant body properties,the fracture prediction technology based on P-wave anisotropy can predict small-scale fracture information, including fracture intensity and direction.However,this technology based on P-wave anisotropy uses different seismic azimuth information, and thus the azimuth information should be as wide as possible to ensure the reliability of fracture prediction. Xu et al.(2011)developed an MS monitoring system for the rocky slope on the left bank of the Jinping-I Hydropower Station,and identified the damage areas induced byconstruction according to the spatiotemporal distribution of MS signals. Yu et al. (2015)analyzed the characteristics of MS signal changes before rockbursts from the #3 diversion tunnel of the Jinping-II Hydropower Station,which proved the feasibility of using MS monitoring for real-time rockburst forecast.Tang et al.(2018)studied MS data collected from the Duoxiongla tunnel in Tibet,China,and concluded the connection between the number and energy of MS events and TBM activities.Li et al. (2020a, 2022) deployed the MS monitoring system in the deep-buried underground powerhouse of the Wudongde Hydropower Station, the MS b-values associated with rock mass large deformation and their temporal variation are analysed, and delineated the potential destabilized area of the underground cavern under the effect of excavation and unloading. Previous scholars have established the relationship between the spatiotemporal evolution of MS activities and construction state based on seismic data analysis and revealed the main potential high-risk areas in the rock mass.

As MS signals contain a large amount of fracture information,studies on MS signals from the microscopic aspect can facilitate the qualitative assessment on the macro-stability of the rock mass (Dai et al., 2017; Li et al.,2019). As a research method in signal processing,waveform analysis has been introduced into the engineering field in recent years.Lu et al.(2012)applied time-frequency analysis to the MS waveforms and revealed the signal frequency shift before rockbursts.Liang et al.(2020)analyzed the amplitude-frequency spectra of signal waveforms to recognize MS signals.Then they determined therockburstsequencetypeinthetunnelasforeshock-mainshockaftershock,based on MS event frequency and released energy timeseries curves. The development of rock damage in underground caverns from destabilization,macroscopic deformation to failure is a result of many complex factors,among which geographical and human factors are dominant.Specifically,geographic factors refer to the natural geological conditions including formation lithology and poor geological structures, while human factors mainly refer to the dynamic disturbance induced by construction and unloading. The development of surrounding rock damage in underground caverns into macroscopic failure is progressive,which is closely related to the geographicaland humanfactorsinthetime domainand isanintuitive manifestation of the transition from quantity to quality. However,preceding waveform studies mainly focused on time-frequency characteristics but did not combine source parameters with timefrequency characteristics.The damaging effect of microfractures has rarely been quantitatively researched.

This paper focused on the excavation of an underground powerhouse with high ground stress in the Shuangjiangkou Hydropower Station. The surrounding rock damage area with the spatiotemporal clustering of MS activities was studied to qualitatively analyze the damage mechanism of microfractures, based on the source parameters and time-frequency waveform characteristics of MS events. Then, the size of microfractures in the surrounding rock characterized by the source radius was considered to establish the constitutive relation.The MS information was imported into the model for analysis using the numerical modeling software fast Lagrangian analysis of continuain 3 dimensions(FLAC3D).Compared with the calculation results without considering the fracture scale in the host rock, more accurate stress and deformation values were obtained when fracture damage was considered.

2. Project background

2.1. Project overview

The Shuangjiangkou Hydropower Station, located in Tibetan Qiang Autonomous Prefecture of Ngawa,Sichuan Province,is at the fifth level of the cascade development plan of hydropower stations in the Dadu River Basin.This project consists of the water diversion and power generation system, spillway system and dam system. The water-retaining structure is a rockfill dam with a solid earth wall.The dam crest has a height of 312 m, making it the highest dam in the world.The underground powerhouse is equipped with four 500 MW generator sets with a total installed capacity of 2000 MW. Three main caverns including the main and auxiliary powerhouses, main transformer room and tailrace surge chamber, with the horizontal burial depth of 400-640 m and vertical burial depth of 320-500 m,were arranged parallelly. Fig.1 shows the overall layout of the underground powerhouse caverns on the left bank of the Shuangjiangkou Hydropower Station(Li et al.,2020b).

2.2. Project geology

The bedrock on both sides of the powerhouse is exposed,which contains mainly porphyraceous biotite moyite. The longitudinal wave velocity of the drilling sound wave in the rock mass is about 5500 m/s,and the surrounding rock type is mainly IIIa according to the national code of China(GB 50487-2008,2008).The powerhouse has a simple geological structure with intact rock mass, joints and fissures undeveloped, no regional fault cuts, some low-order and low-level small faults,and compresso-crushed zones.There are two small faults, SPD9-f1 and SPD9-f2, affecting the underground powerhouse. Five groups of fractures (J1-J5) develop in the predominant direction, among which two or three groups are in the same place with the extension length of 2-3 m and the spacing is more than 1 m.The characteristics of all weak structural planes are listed in Table 1.The maximum stress detected at each measurement point of the powerhouse is 37.82 MPa and the maximum principal stress ranges from 15.98 MPa to 37.82 MPa.The azimuth of σ1at each measurement point ranges from 310.4°to 357°and the dip angle is mostly less than 30°. In this high-stress area, the tectonic stress is dominant, and the direction of the maximum principal stress intersects the axial direction of the powerhouse at a small angle.

3. Construction of the MS monitoring system

3.1. Composition of the MS monitoring system

Fig.1. Overall layout of the underground powerhouse caverns on the left bank of the Shuangjiangkou Hydropower Station (Li et al., 2020b).

In this project, the high-precision ESG MS monitoring system produced by The Engineering Seismology Group (ESG) in Canada was introduced to monitor the deformation and failure of the Shuangjiangkou underground powerhouse,and its installation was completed on July 19,2018.The system is composed of the Paladin data acquisition substation, the Hyperion data processing system,and the uniaxial acceleration sensors. A total of 10 uniaxial acceleration sensors were used to pick up signals, with a sensitivity of 25 V/g, a frequency response range of 50-5 kHz, and a dynamic range of 100 dB. Two Paladin data acquisition substations were used for signal acquisition: one was connected to six uniaxial acceleration sensors while the other one was connected to the rest four.The Hyperion data processing system consists of the Hyperion network acquisition system (HNAS) software for real-time signal acquisition and recording, WaveVis for waveform processing and analysis, and SeisVis for 3D visualization and interpretation of detected MS events.

3.2. Spatial topology of the MS monitoring system

As for MS monitoring of the underground caverns, the spatial arrangementof sensorsisdirectly relatedtothemonitoring result and will affect the reliability and validity of the MS monitoring data.With the consideration of abovementioned factors,the main underground powerhouse of the Shuangjiangkou Hydropower Station was monitored.Considering the disturbance degree of the construction site,the difficulty of instrument installation, and the later maintenance and transfer of instruments,ten uniaxial acceleration sensors were finally deployed,numbered S1-S10.Fig.2 shows the spatial arrangement of the sensors.The spatial topology of the MS monitoring system consists of two Paladin data acquisition substations connected in parallel and 10 sensors for real-time continuous monitoring of rock fractures in the main powerhouse.Specifically,upon receiving MS signals,the sensor converts the elastic wave signals into electrical signals that are transferred to the connected Paladin data acquisition substation through the cable. In the Paladin data acquisition substation, the electrical signals are converted to digital signals. As the fiber optic connection between the Paladin data acquisition substation and the Hyperion signal processing host ensures the integrity and stability of the digital signal transmission, the converted digital signals are transferred to the Hyperion signalprocessing host via fiber optics.The two Paladin data acquisition substations are synchronized through automaticpulsepersecond(PPS)timesynchronizationtoensuretime consistency and the synchronization of signal transmission through 10 channels.

Multiple blasting tests were conducted on the construction site to determine the rock wave velocity in the underground powerhouse of the Shuangjiangkou Hydropower Station. When the rock wave velocity was set to 5800 m/s,the smallest positioning error of 5.79 m was achieved,which met the accuracy requirement for the positioning error to be less than 10 m. Thus, the final input rock wave velocity of the MS monitoring system was set to 5800 m/s.

4. Microseismicity characteristics of the main powerhouse

The MS monitoring system for the underground powerhouse of the Shuangjiangkou Hydropower Station has been in operation since July 19, 2018, to real-time monitor excavation unloading induced rock fracture activities. The coverage area of MS sensors includes the main and auxiliary powerhouses, installation room,and the upper and middle drainage galleries.Until October 3,2018,278 MS events were located in the monitoring area after signal acquisition, screening and identification.

In combination with the results of routine monitoring and site surveys,the spatial distribution and spatiotemporal evolution characteristics of the preceding MS events were studied to reveal the macroscopic fracture state of the rock mass under different construction conditions.In addition,the surrounding rock damage area was delineated according to the energy loss and concentration rules in rock fractures,which laid the foundation for the further analysis of the fracture damage mechanism of the surrounding rock.

4.1. Characteristics of the spatial distribution of MS activities

Fig.3 shows the spatial distribution pattern of MS events during the monitoring period from July 19 to October 3, 2018, with the color of the filled circle representing the moment magnitude of the MS event and the size representing the energy value of the MS event. It can be seen from Fig. 3a that MS events are mainly distributed on the vault and downstream spandrel at elevations of 2275-2298 m. It can be found from Fig. 3b that there are two concentration zones of MS events: sections from K0-57 m to K0-43 m on the downstream spandrel of the installation room (MS activity concentration zone I) and sections from K0-29 m to K0-13 m on the vault and downstream spandrel in the connection section between the installation room and main powerhouse (MS activity concentration zone II).Fig.4a shows the density of the MS events.It can be seen that the concentration zones of MS events are located in sections from K0-51 m to K0-20 m in the powerhouse,which are almost the same as the two zones shown in Fig.3.As MSevents represent the fracture activities in host rock, the spatial distribution of MS events actually reveals the distribution of fracture activities within the rock mass.The fracture density is high and the integrity of the rock mass reduces significantly in the two concentration zones of MS events.

Table 1 Characteristics of the weak structural plane.

The released energy is one of the most important basic parameters of MS activities and is an important measure of the extent of the damage to the surrounding rock (Lu et al., 2015). A rock microfracture event is a manifestation of rock damage, and the occurrence of an MS event is accompanied by a continuous release of energy within the surrounding rock, which will reduce the mechanical strength of the surrounding rock and increase its damage. Fig. 4b shows the energy loss density of the rock mass during the blasting and excavation of the Layer I of the main powerhouse. The energy loss density of the rock mass is large on the vault of the connection section between the main powerhouse and the installation room and on the downstream spandrel of the middle section of the installation room, which is caused by the fracture evolution of the rock mass in concentration zones I and II of MS activities.

4.2. Spatiotemporal evolution characteristics and construction response of MS activities

Fig. 2. Network topology of the MS monitoring system.

Fig. 3. Spatial distribution of MS events: (a) Front view and (b) Top view (Qian et al., 2019).

The middle pilot tunnel in the main and auxiliary powerhouses of the Shuangjiangkou Hydropower Station was excavated successfully in June 2018.After applying the bolt-shotcrete support and other preliminary construction preparations in the next two months,the rock stress was basically released and the surrounding rock of the tunnel was stable after stress adjustment until August 10, 2018. The middle drainage gallery was excavated and constructed during the period.Fig.5 shows the number of MS events as well as routine monitoring results during the construction period.

It can be seen from Fig. 5 that the average daily number of MS events between July 19 and August 10 stays below seven and MS activities are mainly distributed in the rock mass of the mid-partition between the downstream pilot tunnel and #1 branch tunnel of the upper drainage gallery.The bolt-shotcrete support of the middle pilot tunnel and the#1 branch tunnel of the upper drainage gallery have been completed before the construction of the middle drainage gallery from the perspective of construction nodes.Affected by excavation disturbance, the internal fractures initially developed and expanded in the mid-partition areawith lower intactness and a larger degree of fragmentation than the original rock, and deteriorated strength and rigidity of the surrounding rock. The construction disturbance of the middle drainage gallery induced the stress adjustment and increased the extent of the damage to the rock mass in the mid-partition area.

On August 11, 2018, blasting and excavation construction continued on both the upstream and downstream sides of the top arch(Layer I)of the main and auxiliary powerhouses.The upstream sidehadbeen excavatedto sectionK0+10mandthedownstreamside to section K0+20 m on October 3.On August 29,both the upstream and downstream sides of the powerhouse were excavated successfully.To speed up the construction progress,drilling and blasting on the tunnel face were implemented twice a day,with an average daily footageof5-6m and amaximumnumberofMS events reaching 19in one day. A large number of MS events accumulated in the midpartition area and distributed in a strip shape between the spandrelsonthedownstreamsideof thepilottunneland#1branchtunnel of the upper drainage gallery. The monitoring results of the anchor stressometer R1-5CF-01 buried on the downstream spandrel in section K0-53 m showed that stress concentration appeared on the shallow rock mass and tended to shift to the vault area. The monitoring results of the multipoint displacement meter M5CF-034 on the downstream spandrel of this section showed that the cumulative absolute displacement of the rock mass at the orifice increased sharply and that the routine monitoring data significantly lagged behind the MS monitoring data.According to the site surveys,block falls occurred near the top arch in section K0-21 m after the excavation completed,and there were large fissures unidentified during the geological exploration stage in the rock mass near section K0-53 m, which matched well with the concentration zones of MS activities in Section 4.1(see Fig.6).It can be concluded from the analysis of construction conditions,routine monitoring results and site survey results that blasting and excavation construction broke the stress balance inside the rock mass of the downstream spandrel in the installation room with stress adjustment,and that a banding microfracture zone running through the rock mass formed in the stress concentration area.As a result,the energy loss of the rock mass was deepened and the damage to the rock mass was intensified,resulting in the macroscopic deformation.For safe construction,the contractor reduced the frequency of blasting and excavation to once a day on September 18, with an average daily footage within 3 m. After the adjustmentof the constructionplan,the number of MSevents per day was maintained at 0-5 from September 18 to October 3, 2018,showing the M-shaped distribution along the time axis.The MS activity entered a quiet period,with rock mass fractures undeveloped,little energy loss induced,and reduced risk of potential deformation instability of the surrounding rock.

In summary, the frequency of blasting, excavation and unloading is closely related to the extent of construction disturbance.High blasting frequency caused a large degree of construction disturbance, which accelerated the development of fractures inside the rock mass, increased energy loss of the rock mass, deepened the damage and deterioration, and ultimately increased the risk of deformation and destabilization. Deformation is a macroscopic manifestation of the development of surrounding rock damage to a certain extent. The main reason for the sudden increase in deformation during the monitoring period is the intensified damage to the surrounding rock on the downstream spandrel in section K0-53 m.

5. Analysis of the microfracture damage mechanism of the surrounding rock

5.1. Analysis of microfracture damage of the surrounding rock

5.1.1. Delineation of the surrounding rock damage area

Fig. 4. Density contours: (a) Density of MS events and (b) Energy loss density of the rock mass (Qian et al., 2019).

Fig.5. MS events and displacement and stress monitoring results:(a)Distribution of MS monitoring;(b)The position of conventional monitoring instrument;and(c)Number of MS events and displacement and stress monitoring results during the construction period.

From July 19 to October 3, 2018, a large number of MS events accumulated in the downstream spandrel of the main powerhouse,during the excavation of sections from K0+00 m to K0-20 m on the downstream top arch of the main powerhouse. The surrounding rock damage area with spatiotemporal clustering of MS activities was studied.Specifically,the MS events in the spandrel area of the top arch and the mid-partition area between the downstream sidewall and the middle drainage gallery in sections from K0-70 m to K0+27 m (North: 70-27 m, East: 5-57 m, Depth (Elevation):2250-2318 m were analyzed. A total of 261 MS events were detected in this area. Fig. 7 shows the spatial distribution of these MS events.

5.1.2. Types of surrounding rock microfractures

According to the seismological theory,the energy ratio between the S- and P-waves (Es/Ep) is directly related to the type of rock fractures. In the field of MS monitoring, Es/Epis often used as the main reference indicator to determine the type of rock microfractures characterized by MS signals. Both Esand Epcan be calculated (Gibowicz and Kijko,1994):

Fig. 6. MS activity concentration zones and site damage photos.

where ρ is the rock density (kg/m3), r is the distance between the sensorandthelocation of theMSsource(m),c isthewavevelocity(m/s), Jcis the integral of the particle velocity, and Fcrepresents the empirical coefficient for the type of seismic wave radiation.When the seismic source mechanism isunknown,the average root mean square of the radiation coefficient on the seismic source is usually set as follows: Fα= 0.52 (P-wave) and Fβ= 0.63 (S-wave) (Boore and Boatwright,1984).

Scholars have carried out extensive research on the Es/Epof MS signals.Accordingto BoatwrightandFletcher(1984),theenergy value of the S-wave in fault slip or shear failure mode and that of the P-wave were quite different in macroseismicactivities,and usually Es/Ep≥10;Es/Ep≤3 in non-shear failure modes including tensile failure and volumetric stress changes; when 3 < Es/Ep< 10, the rock showed characteristics of mixed failure. Cai et al. (2001) conducted experimental studies on the underground engineering library (URL),analyzed the Es/Epvalues of 804 MS events in the specific tunnel,and found that the proportion of MS events with Es/Ep≤10 reached 78%.The failure mode revealed by the Es/Epvalues was basically consistent with field stress test results and failure phenomena. The results indicate that the Es/Epvalue of rock microfractures is closely related to the type of rock fractures.

Based on the above analysis, Es/Epwas studied in this paper to qualitatively analyze the microfracture type in the surrounding rock damage area. The parameters of 261 MS events in the surrounding rock damage area were substituted into Eq.(1)for calculation.Fig.8 shows the Es/Epdistribution of MS events in the surrounding rock damage area.It can be seen from the figure that MS events with Es/Ep≤10 account for 79%,those with Es/Ep≤3 account for only 12%,and those with Es/Ep≥10 account for 21%,which indicates that the MS damage of the surrounding rock is mainly mixed failure and that a small number of areas show shear damage characteristics.

From the perspective of the surrounding rock stress environment,after the excavation of the pilot tunnel in the main powerhouse was completed, a free face appeared on the downstream sidewall. The disturbance from the unloading of the blasting excavation induced the self-adjustment of the stress field in the surrounding rock and made the primary microfractures develop for the first time and expand to the deep surrounding rock. When the expansion of the downstream sidewall was completed,the spandrel rock mass on the downstream top arch lost the supporting layer, with the 3D stress state degrading to the two-dimensional (2D) stress state, and the tangential stress increased and became dominant.As the excavation unloading of the pilot tunnel has caused the initial expansion of microfractures of the spandrel surrounding rock, affected again by the unloading of the blasting excavation of the downstream sidewall,the primary and secondary microfractures expanded along the principal stress path. That is, non-shear failure occurred in the tangential stress direction, such as tensile failure. According to the geological survey results, there was a weak structural plane in the spandrel position with the degraded rock mass and a relatively loose mineral particle structure. Affected by the stress adjustment, the friction between mineral particles was intensified and the area showed the dislocation or slip and shear failure characteristics.This is the evolution mechanism of microscopic fractures in the surrounding rock damage area.

Fig. 7. Spatial distribution of MS events in the surrounding rock damage area: (a) Top view and (b) Front view.

Fig. 8. ES/EP distribution of MS events in the surrounding rock damage area.

5.2. Evolution of the surrounding rock microfracture scale

The fracture scale is an important dynamic indicator of the microfracture damage state of the surrounding rock, which can qualitatively reveal the progressive damage state of surrounding rock microfractures. The analysis mode of MS signals can be classified into parametric analysis and waveform analysis according to the main research object. Compared with the traditional parametric analysis, the waveform analysis has the signal theory introduced and the mathematical method used to process the rock mass microfracture signal waveform, which can more accurately and deeply explore the source information. Based on the above understanding, the S-transform time-frequency analysis method was introduced in this paper.More details about this method can be found in Xu et al. (2016).

Ohnaka and Mogi (1982) conducted statistical analysis of the frequency characteristics of the acoustic emission signals generated during the uniaxial compression of the rock sample and found that when the rock was approaching failure, the proportion of the detected low-frequency acoustic emission signals increased significantly.Xiao et al.(2018)collected statistics on the frequency characteristics of MS signals and the fracture scale of rock mass in several large hydropower projects and studied their relationships.The results indicated that when the fracture scale increased, the center frequency of MS signals showed low-frequency characteristics and the fracture scale was negatively correlated with the frequency of MS signals.All of the preceding results demonstrated that the microfracture scale of the surrounding rock was closely related to MS signals. Therefore, the S-transform time-frequency analysis method was used in this paper to extract the center frequency of the MS signal waveform for the qualitative analysis of the microfracture scale in the surrounding rock damage area.The highamplitude frequency in the signal time-frequency spectrum is the dominant frequency, and the center frequency is the central value of the dominant frequency.

Qian et al.(2019)calculated the center frequency of MS events in surrounding rock damage areas, and analyzed the trend of center frequency, as shown in the Fig. 9. The overall trend of the center frequency of MS signals in the surrounding rock damage area first went downward and then upward. During the time period from July 19 to August 14, 2018, the center frequency of MS signals was composed of both high and low frequencies, without obvious features. As the fracture scale was negatively correlated with the MS signal frequency, fractures of the surrounding rock in this stage were evenly distributed with no obvious expansion or development trend. After August 14, 2018, the number of MS signals was relatively small, but the center frequency remained between 200 Hz and 500 Hz,which was at a low level.Therefore,the fracture had a large scale but small number. Around August 22, the center frequency of the MS signal began to shift significantly to the low frequency, with the high frequency decreasing and the center frequency dropping to 50-400 Hz. Over this time, fractures showed obvious development and expansion.As the center frequency of the MS signal gradually shifted to the low frequency,the fracture scale increased. Around September 26, the center frequency of the MS signal began to rise with high frequency signals appearing,and the fracture scale decreased.

Fig.10 shows the distribution of the center frequency and source radius of the MS signals from July 19 to August 14,2018.The source radius of low-frequency signals is mainly between 3 m and 5 m while that of high-frequency signals is mainly between 1 m and 3 m.The relationship between the source radius and the center frequency is similar to that between the fracture scale and the center frequency of MS signals. Therefore, the source radius can approximately characterize the microfracture scale of the surrounding rock.

Fig. 9. Center frequency evolution diagram of MS events.

According to the analysis of the microscopic damage of the surrounding rock,the blasting of the downstream top arch severely disturbs the rock mass and causes microfractures to develop and expand. The disturbance is transmitted to the internal of the rock structure in the form of kinetic energy, and the mineral particles and the cement between them inside rock are energized. Then,violent friction is generated between them, accompanied by the release of high-frequency elastic wave signals.Under the weakened surrounding rock disturbance, the energy input and friction between the mineral particles and the cement are weakened,and the number of high-frequency elastic wave signals is reduced. As the gap between the mineral particles and the cement increases due to the initial friction, the friction frequency will decrease, and lowfrequency signals will be released under the action of severe disturbance and energy input again. Therefore,large gaps induced obvious low-frequency characteristics of elastic waves.

6. Numerical modeling of surrounding rock damage in underground powerhouse

6.1. Constitutive model considering microfracture damage

Generally speaking,poor geological structures such as joints and faults have a great impact on the physical and mechanical properties of rock mass.Compared with the intact rock mass without joints or faults,the rock with fracture has deteriorated strength and stiffness properties, making it more prone to deformation instability. Therefore, in this paper, the microfractures inside the rock mass were studied and the MS monitoring technology was used to locate and deduce the seismic source information, including the number of microfractures, density, apparent volume, apparent stress, and spatial orientation. In addition, the evaluation and calculation methods of the rock mass flexibility matrix with fracture damage considered were proposed based on the seismic source information.

In the study of the rock mass with fracture surface development,rock of a certain size was selected as the representative elementary volume(REV)to define its average stress as follows(Cai et al.,2001):

Fig.10. Distribution of the center frequency and source radius of MS events.

The fractured surrounding rock of the underground caverns will go into the unloading state in most cases.Assuming that the rock is holistically elastic with a determined damage state,the constitutive relation in Eq. (4) can be simplified, which is indicated by the flexible tensor Cijkl.The simplified average strain can be expressed as follows:

In addition, the interaction between fractures within the rock mass is also considered,which is critical in determining the overall response of the fractured rock mass. In this regard, Cai and Horii(1992) proposed an effective method to calculate the strain increment due to fractures based on the analysis of fractured materials with and without consideration of the interaction between the fractures, and the effective modulus calculated was consistent with the experimental results. The constitutive relation can be simplified as follows:

Substituting the fracture damage variable a0of the rock mass into Eq. (8), the flexibility matrix of the fractured rock mass is obtained as follows:

In this paper, since the length in the axial direction of the underground powerhouse of the Shuangjiangkou Hydropower Station is much longer than the length or width of the tunnel section, a cross-sectional numerical model is developed to study the stressstrain state in the tunnel section.Therefore,it can be simplified as a plane strain problem in elastic mechanics,and the displacement in the out-of-plane direction can be ignored.The elastic modulus E of intact rock is transformed to E/(1-ν2) and the Poisson’s ratio ν is transformed to ν/(1-ν).

According to the theory of elasticity, the stress-strain constitutive equation for an isotropic body is expressed as

Table 2 Source radius and spatial location of typical MS events in the surrounding rock damage area.

Based on the results of Cai and Horii(1992),the flexibility matrix of the fractured rock mass in the plane strain case can be obtained by transforming Eq. (11) as follows:

6.2. Model development

The constitutive model proposed in Section 6.1 was used to conduct quantitative analysis of the microfracture damage of the surrounding rock in this paper.Fig. 7 shows the study area, where 261 MS events were recorded and for which a quasi-3D numerical model was established.

According to Section 6.1, selection of the rock fracture scale is the key to model establishment and the source radius in seismology is often used as a reference indicator for the rock fracture scale. There are two popular models for source calculations,namely, the Brune’s kinematic model and Madariaga’s quasidynamic model. As studies have shown that Madariaga’s quasidynamic model reflects a more realistic source radius, it has been chosen in this paper to calculate the source radius with a circular fault using the following expression:

where r0is the source radius; Kcis the reference constant of the seismic source model that is usually set to the average value of the fracture velocity of 0.9c in the case of unknown fault surface;Kc = 2.01 for P-wave, Kc = 1.32 for S-wave; fcis the angular frequency of P-or S-waves,which can be calculated by referring to the low-frequency amplitude Ω0of the teleseismic displacement spectrum and the velocity integral Jcof the particle.

The Madariaga’s quasi-dynamic model is used to calculate the source radius of 261 MS events in the surrounding rock damage area.Table 2 lists the source radius calculation results of typical MS events. It can be seen that the source radius of MS events in the study area is mainly between 2.2 m and 4.8 m.

Based on the preceding results, the finite difference numerical calculation software FLAC3Dwas used in this paper. The microfracture scale was characterized by the source radius. The constitutive model considering the surrounding rock fracture damage was applied to establish the numerical calculation model and perform a quantitative analysis of the damage state of the surrounding rock. Fig.11 shows the specific flowchart.

6.2.1. Construction and geological conditions

The quantitative numerical analysis of the surrounding rock damage was carried out in sections from K0-70 m to K0+27 m.The category of the regional surrounding rock is class IIIa. Table 3 illustrates the mechanical parameters of the surrounding rock.Fig.12 shows the support scheme of the top arch in the installation room, with the long blue line indicating the pre-stressed bolt and short black line indicating the common mortar bolt. They are alternately deployed. The pre-stressed bolt has the pre-tensional force of 120 kN, a diameter of 36 mm, and the length of 9 m. The common mortar bolt has the length of 7 m and a diameter of 32 mm, with the grouting material of common mortar and the bolting material of screw-thread steel. The spacing between the two bolts is 1.5 m × 1.5 m. The top arch of this section is not equipped with pre-stressed bolts.

Table 3 Mechanical parameters of the regional surrounding rock.

Fig.12. Support scheme of the top arch in the installation room.

Fig.13. Quasi-3D numerical model.

6.2.2. Numerical model

A quasi-3D numerical model shown in Fig.13 was established based on sections from K0-70 m to K0+27 m of the top arch in the main powerhouse, with reference to the layout of caverns and geological prospecting data.The model size is 400 m×160 m×5 m(width×height×thickness).The Rhino software is used for model geometry and grid discretization, and the grids can be directly converted into files that can be loaded by FLAC3Dover the programmed conversion interface. The distance between the upper and lower boundaries of the carven is 32 m,and that between the left and right boundaries of the carven is about 100 m. Therefore,the height of the model is 5 times the distance between the upper and lower boundaries of the carven,and the width of the model is 4 times the distance between the left and right boundaries of the carven. In addition, the model is divided into a total of 89,828 tetrahedral grid units and 21,165 nodes. The size of the REV is determined according to the source radius,which is between 2.2 m and 4.8 m for MS events in this area, thus the selected size of the REV is 5 m × 5 m × 5 m. The divided REVs are represented by colored boxes, as shown in Fig.13. The constitutive model considering the surrounding rock fracture damage proposed in Section 6.1 was introduced. The Visual Studio 2010 was used to compile the dynamically linked database in the C programming language,which can be directly used by FLAC3Dfor constitutive model calculation. The model is a quasi-3D model, whose main disadvantage is damage homogenization and simplification in a certain profile area, and this may have some differences with the actual state. In this paper, the main purpose is to study the influence of damage and non-damage on the stability of surrounding rock,which is a qualitative judgment.It was assumed that the quasi-3D model could meet the requirement.In addition,it is convenient to improve the calculation efficiency.

6.2.3. Boundary and in situ stress conditions

The actual burial depth of the numerical model is more than 320 m.According to the geological prospecting results,this area is dominated by tectonic stress. Based on the in situ stress field and the measured ground stress data, the research team led by Zhang et al. (2015) from the Geotechnical and Structural Engineering Research Center, Shandong University, China, used numerical simulation and multiple linear regression method to deduce the 3D initial ground stress in the underground powerhouse of the Shuangjiangkou Hydropower Station. The standard error of the mean between the initial and measured ground stresses is 3.14 MPa,with a small residual error,and in general the two results are in good agreement.In this paper,based on the 3D initial stress field obtained by back analysis, the ground stress is calculated as

where σX, σYand σZare the stresses in the X-, Y- and Z-directions(MPa),respectively;H is the burial depth of the measurement point(m), i.e. the vertical distance from the measurement point to the surface; and Z represents the corresponding surface elevation of the measurement point (m).

The normal displacement constraint in the X-direction is applied to the left and right sides of the model. The normal displacement constraint in the Y-direction is applied to the front and rear sides of the model.The normal displacement constraint in the Z-direction is applied to the top and bottom sides of the model, and a uniform load of 10 MPa in the Z-direction is applied to the upper surface of the model.

6.3. Analysis of modeling results

6.3.1. Comparative analysis of routine monitoring data

To verify the numerical calculation results,the surrounding rock displacement data monitored by the multipoint displacement meter M45CF-03 on the downstream spandrel of section K0-53 m of the main powerhouse were selected for comparative analysis.As the displacement meter M45CF-03 was installed and buried after the upper drainage gallery was excavated, the data pertaining to surrounding rock deformation caused by the early excavation of the pilot tunnel were missing, and the cumulative absolute displacement of the surrounding rock finally measured was low. Fig. 14 shows the cumulative absolute displacement of the surrounding rock recorded by the multipoint displacement meter M45CF-03 and the displacement data calculated by the numerical model.The cumulative absolute displacement recorded by the multipoint displacement meter reached 3.21 mm after the excavation of sections from K0-70 m to K0+27 m on the downstream side was completed on October 3, 2018. Thus, the displacement recorded after the whole downstream side was completed should be greater than 3.21 mm. In the case where the microfracture damage of the surrounding rock is not considered,the final displacement obtained by the numerical model is 2.95 mm at the measurement point.While the value is 4.08 mm when the microfracture damage of the surrounding rock is considered, which is close to the measured results.

Fig. 14. Comparison of monitoring data of the multipoint displacement meter and displacement data at the model measurement point: (a) Numerical results, and (b)Monitoring data of the multipoint displacement meter.

Fig.15. Displacement distribution before the excavation of the downstream top arch.

6.3.2. Displacement characteristics

Fig.15 shows the displacement distribution before the excavation of the downstream top arch. It can be seen that the absolute displacement of the surrounding rock on the downstream sidewall is about 15 mm before excavation,and the absolute displacement of the floor is about 10-15 mm.The absolute displacement of the rock mass on the shallow surface of the downstream sidewall near the top arch is about 13 mm.It decreases abruptly and remains within 7 mm in the deep surrounding rock,and it is about 2-6 mm in the mid-partition area between the middle pilot tunnel and the middle drainage gallery.

Fig.16 shows the displacement distribution after the excavation of the downstream top arch with the microfracture damage of the surrounding rock being considered or not. It can be seen that the large deformation appeared in the area between the footwall of the weak structural plane and the free face after the excavation of the surrounding rock of the downstream sidewall, when the microfracture damage of the surrounding rock is not considered. In addition,the absolute displacement reached 23 mm,and that of the rock mass on the hanging wall of the weak structural plane was about 18 mm.When the microfracture damage of the surrounding rock is considered,MS events at this stage are mainly concentrated in the area near the weak structural plane of the spandrel. The constitutive model considering the microfracture damage of the surrounding rock was used to import MS information into the REVs and obtain the displacement distribution of the damaged surrounding rock.It can be seen that the absolute displacement of the surrounding rock on the hanging wall of the weak structural plane has increased, with the deformation increment caused by the microfracture damage accounting for 10%-13%. At this stage, the rock mass on the sidewall was removed. Over this time, the surrounding rock on the downstream top arch of the main powerhouse lacked an effective supporting layer, and the microfractures within the rock mass between the weak structural plane and the free face expanded and penetrated again, thus intensifying the microfracture damage and causing macroscopic relaxation and deformation.

Fig. 17. Distribution of the maximum principal stress before the excavation of the downstream top arch.

6.3.3. Stress distribution characteristics

Fig.17 shows the distribution of the maximum principal stress before the excavation of the downstream top arch. It can be seen that the stress release of the surrounding rock occurs around the middle pilot tunnel before the excavation of the surrounding rock on the downstream sidewall. Specifically, the maximum principal stress is reduced to 3 MPa, and it is 8 MPa on the weak structural plane and about 16-18 MPa in the mid-partition area between the middle pilot tunnel and the middle drainage gallery is.

Fig.18a and b shows the distribution of the maximum principal stress after the excavation of the downstream top arch with and without consideration of the microfracture damage of the surrounding rock, respectively. It can be seen that the distribution of the maximum principal stress changes dramatically after the excavation of the surrounding rock on the downstream sidewall with the microfracture damage of the surrounding rock being considered.The maximum principal stress of the surrounding rock in the middle area between the footwall of the weak structural plane and the free face decreases.This is because after the removal of the rock mass on the downstream sidewall, the initial microfractures expanded to the free face and stress release was simultaneously induced.In addition,the stress relaxation areas appeared on the shallow surface. The maximum principal stress in the shallow surrounding rock of the spandrel was reduced from 2 MPa to 1.8 MPa, and the proportion of the stress decrement of the surrounding rock caused by the microfracture damage was about 10%. The maximum principal stress on the weak structural plane was reduced from 5.7 MPa to 3.5 MPa,and the stress decrement of the surrounding rock caused by microfracture damage was up to 2.2 MPa, which accounted for about 38.6%.

Fig. 18. Distribution of the maximum principal stress after the excavation of the downstream top arch: (a) Fracture damage is not considered; and (b) Fracture damage is considered.

7. Conclusions

An MS monitoring system was applied in the main powerhouse of the Shuangjiangkou Hydropower Station. The surrounding rock damage area with spatiotemporal clustering of MS activities was studied to qualitatively analyze the damage mechanism of surrounding rock microfracture, based on the source parameters and signal waveform time-frequency characteristics of MS events.Then,the surrounding rock microfracture scale characterized by the source radius was considered to establish the constitutive relation.Moreover, MS information was imported into the model for analysis by using the numerical modeling software FLAC3D. Compared with the calculation results that do not consider the fracture scale of the rock, more accurate stress and deformation values were obtained when the fracture damage was considered. Main conclusions are as follows:

(1) MS activities are closely related to construction and geological conditions. The accumulation of MS events on the downstream spandrel in sections from K0-57 m to K0-43 m in the installation room is controlled by the strength of blasting excavation and the large fractures in the rock mass.The spatiotemporal evolution of MS activities reveals the progressive fracture damage process of the rock mass. This can help to identify potentially poor geological structures,provide a basis for encrypted routine stress and deformation monitoring,act as a reference for the subsequent adjustment of the excavation plan and other construction organization,and guide the construction site to take grouting and reinforcement(e.g.bolt-shotcrete support)measures in a timely manner for the damaged surrounding rock.

(2) The Es/Epratio was used to conduct qualitative analysis of the microfracture type in the damaged surrounding rock,and the calculation results show that the microfracture damage of the surrounding rock mainly shows characteristics of mixed failure, and a small number of areas show shear damage characteristics.

(3) The S-transform time-frequency analysis method was adopted to extract the center frequency of the MS signal waveform and analyze the evolution of the microfracture scale in the damaged surrounding rock. The calculation results show that the fracture scale was large from around August 22 to September 26, 2018, with the reduced center frequency of 50-400 Hz. The relationship between the source radius and the center frequency of MS signals was studied, and the results showed that the relationship is similar with that between the center frequency of MS signals and the fracture scale, thus the source radius can approximately characterize the microfracture scale of the surrounding rock. According to the expansion of the fracture scale of the surrounding rock characterized by the fracture energy loss,it is show that the fracture scale on the vault in sections from K0-33 m to K0-15 m is large.

(4) Comparison between the numerical modeling results and the monitoring data of the multipoint displacement meter showed that the ultimate displacement at the measurement point calculated by the numerical model is close to the measurement results when the microfracture damage of the surrounding rock was considered.After the excavation of the surrounding rock on the downstream sidewall, the deformation increment due to microfracture damage in the shallow surrounding rock of the top arch accounted for 10%-13%,and the stress decrement in the surrounding rock due to microfracture damage accounted for about 10%. The stress decrement due to microfracture damage on the weak structural plane accounted for about 38.6%.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors are grateful for the financial support from the National Key R&D Program of China(Grant No.2017YFC1501100),the Science Foundation for Distinguished Young Scholars of Sichuan Province (Grant No. 2020JDJQ0011), and the National Natural Science Foundation of China (Grant No.42177143).