Study on Damage Evolution Mechanism of Rock-Soil Mass of Accumulation Slope Based on Shaking Table Test

To investigate the seismic dynamic characteristics of the accumulation slope, a slope of the Zheduo Mountain tunnel along the Sichuan-Tibet Railway in China was selected 17 as the prototype, based on dimensional analysis and similarity principle, two groups of model 18 tests were carried out at 50° accumulation slope and 60° accumulation slope to obtain the 19 dynamic response influenced by different amplitude of seismic wave. A transfer function 20 analysis method suitable for shaking table test is proposed. Based on the data pretreatment 21 method of eliminating trend terms and digital filter, the frequency response function was 22 calculated by method of average periodic chart. And the variation of frequency response 23 function was analyzed by Pearson correlation coefficient. At last, the least square iteration 24 method was used for modal analysis. It is found that the transfer function changes obviously 25 when both the slopes are destroyed, the weak interlayer has a significant influence on seismic 26 wave transmission. The modal analysis results show that with the increase of the excitation 27 intensity, the natural frequency decreases and the damping ratio increases.


Introduction 31
The high hill-river valleys in the southwest mountainous area of China are characterized by 32 strenuous cutting, fractured rock mass, bad stability and even loose accumulation bodies are 33 In the Wenchuan earthquake that occurred in China, a large number of slope landslide 57 damage occurred. As is shown in Fig.1, the slope angles of these slopes are different, resulting 58 7 In equation (1), 1 , 2 , … … , are the elementary quantity, and +1 , +2 , … … , are the 124 derived quantity. In equation (2), 1 , 2 , … … , − Dimensionless constant. The matrix 125 method can be used to derive the similarity criterion of the physical model, is shown in Table  126 1. Among them, Geometric scale is L; gravitational acceleration is g; cohesion is c; dynamic 127 elastic modulus is E; internal friction angle is φ; dynamic Poisson's ratio is μ; gravity is γ; shear 128 wave velocity is υs; input acceleration is A; duration is Td; frequency is ω; angular displacement 129 is θ; linear displacement is s; response speed is V; response acceleration is a; stress is σ; strain 130 is ε. 131 In the case that phenomena and similar phenomena can be expressed as same functions. 132 Those which can be regarded as similar if they have similar individual parameters and equal 133 similarity criteria. According to the above criteria, the similarity relationship of the main 134 physical quantities in the model adopted in this paper, as is shown in Table 2. 135

Test device and model 136
This experiment adopted large one-way seismic simulation shaking table to simulate, the 137 model box floor and skeleton material is mainly composed of steel plate, gradient steel, iron 138 channel, to facilitate the observation and record in the test process of the model of slope 139 deformation and failure phenomena, and the model box is visualized with 12mm optical 140 plastics on both sides. Apply vaseline evenly between optical plastics and model to reduce 141 friction. Using a 10 cm thick foamed polyethylene to reduce boundary effect between model 142 and boundary. The bottom board of the model box is adhesive stone columns with epoxy resin 143 to make it a rough surface to reduce the relative displacement between the model box and the 8 To satisfy the needs of the experiment, taking the slope relying on engineering drilling data 146 as the background, this paper adopted two kinds of gradients natural slope model, 50° and 60° 147 respectively. And the model of total 1.5 m high, 1.2 m high of side slope. To adapt the 148 characteristics of side slope, the side slope model is 2.21 m at the bottom, the vertical section 149 of the model is consistent with a width of 2m, the bedrock is 0.25m high. The weak interlayer 150 is covered on the bedrock with a thickness of 5 cm, and the accumulation mass is covered on 151 the weak interlayer. The basic physical parameters of the test model material can be obtained 152 through laboratory tests, as is shown in Table 3. 153 The test model was made on site. In the process of filling the model, it was filled layer by 154 layer and bottom-up, with one density test for each fill of 20 cm. And compaction was carried 155 out by artificial vibration, that is, the central part and boundary of the model were compacted 156 by artificial compaction to ensure the compaction quality, as shown in Fig.4.The overall model 157 is shown in Fig.5, the gradient is the angle between the overlying accumulation body and the 158 level surface. The layout of the measuring point adopted in this paper is shown in Fig.6, as it 159 shows, it mainly divided into two categories, the acceleration sensor distribution in free field, 160 central slope surface, the interface between bedrock and weak interlayer, the interface from 161 weak interlayer to accumulation body as well as the free field. And displacement sensors are 162 mainly distributed at the top, middle and bottom slope surface, sensor sampling frequency is 163 1000 Hz. 164 Loading cases and measuring points layout 165 9 the input for the two groups of shaking table tests includes the following working conditions, 168 as shown in Table 4. In the table, white noise comes from measured data, as shown as Fig.7, 169 the first loading of white noise was mainly to reduce the random disturber and transient effect. After loading was to scan the slope as a whole by loading white noise while reducing the 171 transient effect, so as to analyze the structural characteristics by using the transfer function 172 method, the seismic wave contains: Wenchuan wave, Kobe wave and EL Centro wave. The 173 amplitude normalization of the earthquake waveform loaded in this paper is shown in Fig.8~10. 174

Slope failure phenomenon 175
In the seismic wave loading process of the two groups of shaking table tests, the HD camera 176 system was used to shoot the phenomenon. The test results showed that the 50° slope had 177 obvious failure when the input Wenchuan wave peak acceleration was 0.6g, while the 60° slope 178 had the relatively similar phenomenon when it was 0.5g. The test phenomenon was shown in 179 surface was partially deformed. The slope was greatly deformed and a large amount of debris 182 flow was generated when the 60° slope is destroyed. The slope surface was deformed a lot, 183 generating a lot of debris flow. Obvious back edge expansion crack appeared at the top of the 184 accumulation mass of the two groups of slopes. According to the monitoring data of 185 displacement sensors, as Fig.13 shows, the top displacement of the 60° slope is larger, and the 186 bottom displacement of the 50° slope is larger, but its displacement change trend is similar. It 187 means that slope failure mainly occurs along the weak interlayer plane in the overall collapse. 188 In addition, the displacement monitoring data of the slopes shows that the slopes of the two 189 slopes have a "step-off" change curve, which is consistent with the two energy fluctuations in 190 the Wenchuan earthquake waveform. According to the video and sensor monitoring data, the 191 failure stages of the slope under both working conditions are as follows: first, the slope surface 192 appeared cracks and deforms, the accumulation body squeezed the weak interlayer and 193 develops downward, and cracks may appear between the accumulation mass and the weak 194 interlayer. Subsequently, the movement of superstructure (accumulation mass) and 195 substructure (weak interlayer and bedrock) were gradually inconsistent during the earthquake. Transfer function is the main methods to study control theory, which embodies the 202 transformation relationship between input signal and output signal, and theoretically is 203 irrelevant with input parameters. In structural dynamics, the transfer function can describe the 204 motion law of the structure and analyze the dynamic characteristics and stability of the system. 205

Structural seismic frequency response function 206
In a single-degree-of-freedom linear structure, its non-time-dependent vibration motion 207 equation is written as Equation Where, is a complex variable, above equations are equivalent to the Fourier transform 214 when ( ) = 0, and 0 is the inherent circular frequency of the structure. 215 Let ( ) and ( ) be the displacement and displacement exerted on the structure 216 respectively, then the Laplace-transforms of the two are Equations (5) and (6) respectively: 217 After dividing the above equations, the displacement transfer function of the structure can 220 be obtained as Equation (7): 221 In the above Equation (7), is the damping ratio. Similarly, velocity transfer function 223 Equation (8) and acceleration transfer function Equation (9) can be obtained: 224 From the above formula, the transfer function is a complex-valued function, which is 227 represented as a curved surface in the Laplace Domain. Therefore, frequency response analysis 228 and root locus method are often used to describe the transfer function in practical applications, 229 among which the former is the main approach. Due to space limitation, taking the displacement 230 frequency response function as an example, Equation (7) can be written in the frequency Considering that the initial state of the structure is stationary under the action of earthquake, 234 the real part is 0, and the imaginary part is angular frequency. The frequency domain response 235 of the structure under the action of earthquake is shown in Equation (11): 236 Where, is the angular frequency variable, ( ) is the complex function of , ( ) is 238 the vibration signal, is the imaginary number. Taking frequency as independent variable, the 239 real part of can be expressed as the real frequency curve of the signal, and the imaginary part According to the above theory, the transfer function method represents the ratio of input and 258 output. And the frequency response function method is a subset of the transfer function method 259 and is the ratio of response to incentive. Therefore, it is suitable for the analysis of nonlinear 260 random vibration signals represented by earthquakes. 261

Data pre-processing 262
In the shaking table test, due to the existence of various kinds of interference, it is often 263 necessary to pre-process the vibration signal to make the sampling frequency as close to the 264 true value as possible. In this paper, the eliminating trend term and digital filter are used to pre-265 process the collected data. 266 The polynomial least-squares is commonly used to eliminate the trend term, and the order 267 of eliminating trend term adopted in this paper is order 5. 268 In the model test, as the collected disperse cosine signals contain a variety of sources, digital 269 filter is needed to filter out the noise or false components in the test signals. In this paper, taking 270 that is Equation (17) : 284 Where, ( ) and ( ) are defined as Equations (18) and (19) respectively: 286 In the above formula, ( ) and ( ) are the Fourier transform of the th data segment 289 of one or two random vibration signals. * ( ) and * ( ) are the conjugate complex 290 numbers of ( ) and ( ) respectively. And is the average degree. 291 In this paper, the sampling frequency was taken as 1000Hz, the fast Fourier transformation 292 (FFT) length was set as 2048. The excitation signal was the acceleration signal collected by the 293 measuring point A0, and the results were analyzed according to the distribution of measuring 294 points at different positions. It can be seen from Equations (11) that the frequency response 295 function can be represented by real frequency and imaginary frequency or amplitude versus frequency and phase. The former is more often used in use. The data frequency collected in 297 this paper is 1000Hz, and high-frequency sampling leads to a wide frequency range of random 298 interfering signals, which accounts for a large proportion. Therefore, there are many glitches 299 after the collected data are plotted, which are not smooth, data smoothing can eliminate burrs 300 and the influence of higher-order trend terms can also be eliminated. The data smoothing 301 method selected in this paper is the five-spot triple smoothing method, because it can smooth 302 the signal in both time domain and frequency domain, effectively reduce the high-frequency 303 random noise. When analyzing the frequency response function, the intersection of the real 304 frequency characteristic curve and the frequency axis of the multi-degree of freedom system is 305 prone to horizontal movement. Under the influence of near modes, the imaginary frequency is 306 usually used for analysis. Pearson correlation coefficient can be used to analyze the variation 307 of frequency response function, currently, the commonly used judgment criteria in the 308 engineering field were shown in Table 5. were shown in Fig.15 and Fig.16. It can be clearly observed from Fig.15 that, when the 50° 315 slope is loaded, the real frequency and imaginary frequency parts of the frequency response 316 function of A1 measuring point are relatively similar before the excitation intensity is 0.5g.
While the real frequency and imaginary frequency parts of the loaded seismic wave change 318 obviously after the excitation intensity is 0.5g, both the real frequency and the imaginary 319 frequency parts of the first-order natural frequency become smaller. The increase of the 320 amplitude of the signal fluctuation indicates that the structure appears damage deformation in 321 the signal transmission from measure point A0 to measure point A1. The Fig.16 shows that as 322 the excitation intensity increases, frequency response function of the measured points A1 of 60° 323 slope has changed, real frequency and the imaginary frequency part of the first order natural 324 frequency and the corresponding amplitudes were gradually reduced. Before the excitation 325 intensity was 0.4g, the variation rules of the real frequency and the imaginary frequency parts 326 were similar of 60° slope, and the frequency response function changed significantly when the 327 excitation intensity was 0.4g and 0.5g. 328 Taking the frequency response function of the point A1 on the slope surface when the 329 excitation intensity is 0.1g as the reference. With the excitation intensity increases, the variation 330 law of the correlation coefficient of the frequency response function shown in Fig.17. 331 According to the definition of correlation coefficient, both the real frequency and the imaginary 332 frequency of a 50° slope are greater than 0.8 before the excitation intensity is 0.6g, which 333 indicates a high correlation. Thereafter, the correlation coefficient decreased significantly and 334 was less than 0.8. Similarly, the real frequency and imaginary frequency parts of 60° slope are 335 highly correlated before the excitation intensity is 0.4g, when the excitation intensity is 0.4g, 336 the correlation coefficient of 60° slope will be severely reduced, however, the slope surface 337 will not be damaged until the excitation intensity is 0.5g. This indicates that cracks may have that the frequency response function of the 60° slope decreases more sharply than that of the 340 50° slope, which is consistency with the failure phenomenon of the slope. 341

Effects of the weak interlayer 342
Similarly, the frequency response functions of the accelerations at points A2 to A5 on both 343 sides of the weak interlayer of the slope were calculated based on the accelerations at points 344 A0. The correlation coefficient of the frequency response function of the above measurement 345 points for 50°slope and 60°slope can be calculated based on the excitation intensity is 0.1g, as 346 shown in Fig.18 and Fig.19. In Fig.18 Fig.19 shows that the variation trend of the correlation of the frequency response 356 function of the 60° slope is similar to that of the 50° slope. The real frequency part changes 357 little and the law is not obvious, so it should be affected by the near modes. The change of 358 imaginary frequency is more obvious, in which the correlation coefficient of point A2 point is 359 less than that of point A4. It indicates that the crack in the slope body evolves from the lower 360 part to the upper part and is still a traction landslide, which is inconsistent with the surface 361 displacement of the slope and may be due to the movement form of the accumulation body. 362 The correlation coefficient of point A3 is lower than that of point point A2, which may be due 363 to the large own weight of the deposited mass at point A2, structure center is at the front, the 364 seismic wave transmission first arrives at point A2 and then arrives at point A3. In addition, the 365 correlation coefficient is less than 0.4 when the excitation intensity is 0.5g, it should be caused 366 by the signal fluctuation after the structure is damaged and cracks appear. 367 It can be seen from the above phenomena that the sliding of the experimental slope is mainly 368 due to the occurrence of cracks between the accumulation mass and the weak interlayer caused 369 by the earthquake. The obvious movement of the bedrock and the accumulation mass is 370 inconsistent. Under the horizontal force of the earthquake and the gravity along the weak 371 interlayer zone, the cracks between the soil are constantly expanding, the of the "anchor section" 372 shear surface is broken, the cracks gradually develop and extend, and finally the penetration 373 cracks appear, and the slope collapses. It can be expressed as shear-slide-fall type, which 374 belongs to traction landslide. 375

Modal analysis 376
The frequency response function can also be used for modal analysis of vibration signals. 377 The white noise input in this test can be regarded as the environmental excitation, therefore, 378 white noise can be used to identify the modal parameters of the vibration signal. The lowed 379 recognition accuracy can be avoided by avoiding the signal side-lope and low resolution in the 380 ground motion response signal, currently, the methods commonly used in modal analysis 381 include the half-power bandwidth method, the admittance circle method, etc, the former is based on the single-degree-of-freedom structure, the latter only uses the least square rationale 383 to estimate the radius or mode shape of conductance circle (Nyquist plot). The least-square 384 iteration method is a classical solution method based on analytic expressions to numerically fit 385 the real frequency response function data, it can obtain the best fitting between the test data can be seen from the Fig.21 that the vector of the first vibration mode of the two groups of 399 slopes is significantly larger than that of the second and the third. This indicates that the slope 400 vibration is mainly controlled by the first mode of vibration. However, the magnitude of the 401 second mode vector of the in some cases under excitation intensity is large, and it means that 402 the seismic mode of the slope under this gradient is relatively complex and can be regarded as 403 having two degrees of freedom. Represented by two groups of measuring points on the slope 404 surface, the natural frequency and damping ratio of the first mode (main mode) of the slope in 405 the measured group were calculated and observed. It is worth mentioning that, empirically, 406 some scholars believe that it is spurious mode when the damping ratio>20%. However, due to 407 the large discreteness of soil and the wide frequency band of white noise, the calculated 408 damping ratio will be larger, therefore, this paper believes that the calculated results are reliable 409 in trend. It can be seen from Fig.22 that, with the increase of the excitation intensity, the natural 410 frequency of the slope was decreases in trend. Assume that the weight of the test model will 411 not change when the damping ratio is not taken into account, the reduction of the natural 412 frequency indicates that the lateral stiffness of the structure decreases. The increase in the 413 damping ratio indicates that cracks and expansion occurred in the test model, resulting in 414 increase of friction between soils and enhanced energy absorbing action, therefore, the damping 415 ratio increases. Meanwhile, under the same intensity seismic wave, the comparison shows that 416 the damping ratio of a 60° slope is higher than that of a 50° slope, the 60° slope natural 417 frequency is less than that of the 50°slope, indicating that the higher the gradient is, the less the 418 anti-lateral stiffness will be, while the internal friction of soil mass will be more obvious. 419

Conclusions 420
This paper is based on a typical accumulation slope at the entrance of Zheduo Mountain 421 tunnel, shaking table model tests of the 50° accumulation slope and 60° accumulation slope 422 respectively were carried out. The displacement and acceleration of the slope were tested, the 423 dynamic characteristics of the measuring point were analyzed using the transfer function, and 424 the modal analysis was carried out. The main conclusions are as follows: (1) Under the action of earthquake, the failure of the overlying slope is mainly the overall 426 collapse along the weak interlayer zone, the slope displacement of the slope is relatively 427 consistent. At the same time, debris flow was generated on the slope surface. The 50° slope 428 was destroyed when the peak acceleration of Wenchuan earthquake wave was 0.6g, the 60° 429 slope was destroyed when the peak acceleration of Wenchuan earthquake wave was 0.5g. At 430 the top of the accumulation mass, there were obvious expanding cracks at the back edge. 431 (2) Based on the data pre-processing and average periodic diagrams method, the transfer 432 function can be calculated and reflecting the vibration characteristics of the accumulation slope. 433 Pearson correlation coefficient and modal analysis can be used to analyze the structural 434 characteristics reflected by the transfer function. The analysis method can be well applied to 435 the slope shaking table test. 436 (3) The frequency response function of accumulation slope can be analyzed from two aspects: 437 slope surface and slope interior. Based on the frequency response function by white noise 438 scanned after the excitation intensity is 0.1g, on the slope surface, the correlation coefficient 439 50° slope significantly decreased and was destroyed after the excitation intensity is 0.6g, while 440 the correlation coefficient of 60°slope significantly decreased after the excitation intensity is 441 0.4g, failure will not occur until the excitation intensity is 0.5g. With the increase of the 442 excitation intensity, the correlation coefficient of the 60°slope is lower than that of 50° slope       Step 1    50° slope self-shaking frequency 50° slope damping ratio 60° slope self-shaking frequency 60° slope damping ratio