JP6033635B2 - Evaluation method of rock fall risk of rocks on slopes based on vibration measurement - Google Patents

Description

  The present invention relates to a rock fall risk evaluation method for rocks on slopes based on vibration measurement.

  The methods for evaluating the risk of falling rocks at the source have been studied and improved by organizations and business operators that manage slopes. However, the occurrence mechanism of falling rocks is not fully elucidated, and empirical evaluation methods based on statistical analysis of past falling rock cases are still the mainstream.

  A rockfall is an event that is caused by various intricately intertwined factors, and is a disaster that is difficult to predict and predict (see Non-Patent Documents 1 and 2 below). Therefore, railway operators regularly inspect rockfall caution areas and strive to minimize the damage caused by rockfall disasters by taking necessary measures according to the inspection results.

  It is important to evaluate the risk of falling rocks by comprehensively evaluating the occurrence risk at the source and whether the fallen rock mass reaches the railroad.

  Regarding the evaluation of the degree of impact on the track, which is the latter risk level, the inventors of the present application conducted slope classification of slopes using a numerical terrain model, and provided information and information such as existing slope inspection records and rockfall disaster histories. In order to effectively and efficiently extract rockfall caution points from a wide range of railway slopes, they are organized (see Non-Patent Documents 3 and 4 below). In addition, if an unstable rock block falls at the extracted cautionary point, the impact on whether or not it reaches the track is quantitatively evaluated by the probability of arrival by rockfall simulation, and the slope gradient, rockfall diameter, presence of steep cliff A simple determination chart of arrival probability categorized based on the slope parameters such as the number and position was created (see Non-Patent Documents 4, 5, and 6 below).

  On the other hand, the evaluation of the risk of falling rocks at the former source is based on the scoring method by referring to existing manuals and standards (see Non-Patent Documents 7 and 8 below) at sites where slope management along railways is practiced. Evaluation / judgment by Although this scoring method is a merit in that the risk assessment can be easily performed, there are many qualitative evaluation items, and field engineers cannot fully understand the evaluation criteria. There are cases in which there are things, and variations in judgments may occur due to the experience of engineers.

  Therefore, we want to inspect a large number of unstable rock masses at the point of caution with a rational and efficient method.In other words, we want to have an objective risk assessment method based on quantitative indicators. The current situation is not meeting the demands of

  Therefore, first, we review that the research on the risk assessment of rockfall so far is a scoring method mainly based on statistical analysis of past rockfall cases, and is still the mainstream of evaluation methods. Next, in the research and examination of such rock fall risk assessment methods, it is necessary to consider the mechanism of rock fall occurrence in order to establish a quantitative risk assessment method. We will explain the fact that it was important to pay attention to the rooted state for the degree evaluation. We also mention the recent rock fall risk assessment method using vibration.

  Then, as a subject of the present invention, the instability depth estimation method using vibration proposed by the inventors of the present application (see Non-Patent Document 9 below) is used to directly calculate the mechanical stability of the rock on the slope. Consider a new rock fall risk assessment method.

  Of the 113 rockfall disasters that could be identified from 2005 to 2009 in the West Japan Railway Company jurisdiction (Western Japan area, 2 prefectures, 16 prefectures, 51 line, approximately 5000 km of track length), As shown in Fig. 16, 99 rockfalls occurred. Since the ratio accounts for as much as about 88%, in the present invention, a risk evaluation method mainly for boulder-type rockfalls is examined.

  Next, the previous research on the rock fall risk assessment method is explained.

(1) Statistical method (scoring method)
Falling rocks are complicated by a number of predisposing factors (for example, topographical and geological conditions) and incentives (for example, erosion by surface water, freezing and thawing, snow accumulation, effects of trees and vegetation, earthquake motion, and weathering of rocks and sediments) It is a phenomenon that occurs entangled and occurs naturally. For this reason, as for the occurrence mechanism of falling rocks, many of them have not been elucidated yet (see Non-Patent Documents 1 and 2 below).

  Against this background, the statistical evaluation method based on the analysis of disaster cases is the starting point for research on the risk assessment of rockfall at the source. In the wake of a serious rockfall disaster related to human life, each organization, such as roads and railways, has developed technical standards for risk assessment against rockfall through repeated examinations by experts in the form of committees (the following non-patents) References 10 and 11).

  Specifically, evaluation criteria based on the so-called scoring method, which set points for evaluation items such as topography and geology, the status of springs and water collection, regionality of rainfall and climate, and land cover conditions such as standing trees and vegetation ( For example, the following non-patent documents 12, 13, 14, 15, 16) have been formulated. Thereafter, methods based on quantification theory (for example, see Non-Patent Documents 17, 18, and 19 below) have been energetically studied for the purpose of optimizing scoring standards and incorporating judgment standards of professional engineers. And, the rock fall risk assessment method currently used on roads and railways (falling stone countermeasure manual (refer to the following non-patent document 20), road disaster prevention inspection guide (refer to the following non-patent document 21), falling rock countermeasure technical manual (the following non-patent document) (See Patent Document 7), Maintenance Standards for Railway Structures, etc. (see Non-Patent Document 8 below)], the concept of this statistical method (scoring method) is inherited and has become the mainstream in practice.

  However, the statistical method is effective as a simple risk assessment method, but the relationship between rockfalls and their predispositions and incentives is complicated, and Japan has a regional characteristic in terms of topography and geological conditions. Because it is difficult to determine the evaluation criteria, it is difficult to say that the on-site engineer fully understands the evaluation criteria and wants to perform a reasonable risk assessment. .

(2) Research on Murakami and Sakaiuchi focusing on the mechanism of rockfall occurrence Murakami and Sakaiuchi et al. Conducted research on statistical methods for risk assessment (see Non-Patent Documents 17 and 18 below), but the possibility of rockfall occurrence from an early stage It is pointed out that an index that quantifies the above is practically necessary (see Non-Patent Documents 22 and 23 below).

  Therefore, as a first step in investigating the mechanism of rock fall, a simplified two-dimensional model experiment was conducted, and factors such as slope gradient, slope soil quality, depth of tumbled rocks, rainwater, and ground motion were found. The effect on tumbling type rockfall (synonymous with “rolling stone type rockfall”, hereinafter the same) was examined.

According to this, using the rooting angle θ = cos ⁻¹ [(r−h) / r] (the radius r of the boulder, the rooting depth h), the critical inclination angle of rockfall occurrence is stably calculated against sliding and falling. Each was obtained from the above, and this was compared and verified with the experimental results. As a result, the fall type rock fall is predisposed to the frictional force and adhesive force between the ground and the rock, the slope inclination angle, and the depth of the inset of the roll. It is pointed out that the movement form at the time is mainly a tipping movement, but it is a complex thing in which the sliding movement is intricately intertwined, and the development of the separation part from the ground at the upper part of the rolling stone and the intrusion of rainwater there It was considered that the decrease of the contact area between the rock and the ground due to erosion and slope erosion increases the risk of falling rocks.

In other words, the occurrence of tumbling type rocks (rolling type rocks) is the slope inclination angle around the rocks, the frictional force and adhesive force acting between the rocks and the ground, the radius representing the size of the rocks, the unit volume weight of the rocks, It indicates that it is governed by mechanical factors such as the penetration angle, and the rock penetration depth z and critical penetration depth z ₀ = r (1-cos θ ₀ ) (θ ₀ : critical penetration angle for rockfall occurrence ) = Z / z ₀ determined from (1) suggests that it is effective as an index representing the stability of rockfall, that is, the degree of danger.

  In this way, the pioneering research of Murakami and Sakaiuchi refers to the mechanical stability considering the mechanism of rock fall in addition to the analysis by the quantification method incorporating the topographical, geological and mechanical factors so far. However, it is important to understand the depth of the inset of the boulder as a method for quantitative evaluation of rock fall risk.

(3) Rock fall risk assessment using vibration In the 1980s, technical research institutes in roads and railways began to examine the relationship between rock vibration characteristics and stability (see Non-Patent Documents 24 and 25 below). )

  The Japan Highway Public Examination Research Institute (current Highway Technical Research Institute) installs velocity vibrometers on unstable rock masses on the slope and the foundation ground, respectively, and rock masses using noise from automobiles as a vibration source. And measure the two tremors of the ground and calculate the RMS velocity amplitude ratio, the dominant frequency, and the damping constant, and the RMS velocity amplitude ratio is 2 or more and the dominant frequency is less than 30 Hz or the damping constant is less than 0.2. We have developed a method (see Non-Patent Document 26 below) for determining an object as an unstable rock mass.

  In addition, the National Institute of Civil Engineers measures the vibration velocity waveform of the rock mass and basement rock on the rock slope, evaluates the stability based on the dominant frequency, velocity amplitude ratio, vibration locus, etc. A method of extracting block blocks (see Non-Patent Document 27 below) is proposed.

  These methods have been put into practical use as rock fall risk vibration investigation methods and rock slope unstable block extraction methods, and are currently being improved (see Non-Patent Document 28 below), but measurement and analysis by specialist engineers are still possible. There are not many reports of implementation examples.

Kazuhiko Ikeda, Seiji Kobashi, “Trends and Occurrence Prediction of Falling Rocks from the Topography and Geology”, Construction Technology, Vol.6, No.8, pp. 17-21, 1982. Kanji Kajiuchi, “Investigation and Countermeasures for Rock Falling, Geology and Investigation”, No. 3, pp. 38-45, 1987.3. Takahiro Fukada, Yasuki Mori, Hiroshi Sugano, "Trial of rock fall warning point extraction on railway slopes using 10m-DEM", 46th Geotechnical Engineering Conference (Matsuyama), 2011.8. Takahiro Fukada, Yasuki Mori, Hiroshi Sugaya, “Method for creating a rockfall risk map based on the impact assessment on railroads”, JSCE C (Geosphere Engineering), Vol. 68, No. 1, pp. 199-212, 2012.2.3. Takahiro Fukada, Yasuki Mori, Hiroshi Kanno, Koji Fujita, "Prototype of Ochiishi Hazard Map along Railway Line", 66th Annual Conference of Japan Society of Civil Engineers (Matsuyama), 2011. Takahiro Fukada, Tatsuhiko Taniguchi, Kei Sugaya, “Study on the Influence of Ochiishi on Tracks”, 67th Annual Conference of Japan Society of Civil Engineers (Nagoya), 2012.2. Railway Technical Research Institute, “Oppishi countermeasure manual”, 1999.3. Ministry of Land, Infrastructure, Transport and Tourism, “Maintenance standards for railway structures, etc., explanation (structure embankment / cutting)”, 2007.1. Takahiro Fukada, Hironori Hashimoto, Hiroshi Kajitani, “Method of Estimating Intrusion Depth by Vibration Characteristics of Rigid Body Simulating Rolls”, JSCE Proceedings A2 (Applied Mechanics), Vol. 68, no. 2 (Applied Mechanics Vol.15), pp. I-337-I-344, 20122.9. Tatsuo Noguchi, “A Study on Stability Evaluation of Rock Slopes along Railways”, Railway Research Institute Report, Special 51, pp. 7-9, 2002.2.3. Yuzo Onishi and Satoshi Nishiyama, “Current Situation and Issues on Rock Mass Collapse and Rock Fall Problems”, Journal of the Japan Landslide Society, Vol. 39, no. 1, pp. 1-2, 2002.6. Seiji Kobashi, “Reexamination of cut slope scoring table and concept of rock fall management”, Railway Civil Engineering, Vol. 15, no. 6, pp. 39-43, 19733.6. Japan Railway Facility Association, “Concept of Civil Engineering Building Replacement (Japan National Railway Facility Bureau Civil Engineering Division), 1974. Japan Railway Facility Association, “Guide to Ochiishi Countermeasures (Japan National Railway Facility Bureau, Civil Engineering Division), pp. 16-28, 198.3. Highway Survey Committee, “Survey Report on the Installation of Rockfall Protection Facilities”, pp. 61-70, 1974.2. Japan Road Association, “Opposhi Handbook”, pp. 57-75, 1983. 7. Yukito Murakami, Kanji Kajiuchi, “Risk evaluation of falling rocks by quantification method”, Proceedings of Japan Society of Civil Engineers, No. 406 / III-11, pp. 223-231, 1989.6. Yukito Murakami, Kanji Kajiuchi, “Risk Evaluation Standards for Falling Rocks Based on the Quantification Method,” Japan Society of Civil Engineers, 415 / IV-12 (report), pp. 155-161, 1990.3. Tatsuo Noguchi, Katsuya Okada, Tomoyasu Sugiyama, Hideo Kitani, Yasuhiro Tsuchida, “Method for evaluating the stability of soft rock slopes along railway lines”, Proceedings of JSCE, No. 742 / VI-60, pp. 149-158, 2003.9. Japan Road Association, “Opposhi Handbook”, pp. 300-303, 2000.6. Road Conservation Technology Center, “Road Disaster Prevention Inspection Guide (Torrential Rain / Snow)”, pp. 35-39, 2007.9. Yukito Murakami, Kanji Kajiuchi, “Fundamental study on the mechanism of falling rockfall”, Geotechnical Society papers, Vol. 27, no. 1, pp. 109-116, 1987.3. Yukito Murakami, Kanji Kajiuchi, “On the Risk Assessment Method for Falling Rocks”, Proceedings of the Geotechnical Society of Japan, Vol. 28, no. 3, pp. 197-203, 1988.9. Okuzono, M., Iwatake, K., Ikeda, K., Sakai, K., "Observation of rock fall risk by vibration", Applied Geology, Vol. 21, No. 3, pp. 9-12, 1980.3. Kumagai Kaneo, Kiya Hideo, Yoshioka Osamu, “Basic Experiments for Judgment Risk Determination by Vibration Measurement”, Railway Technology Research Institute Bulletin, pp. 1-17, 1983.10. Kenji Ogata, Hiroyuki Matsuyama, Nobuyuki Amano, “Determination of rock fall risk using vibration characteristics”, JSCE Proceedings, No. 749 / VI-61, pp. 123-135, 2003.12. Landslide Team, Sediment Management Research Group, Incorporated Administrative Agency, “Slope Slope Vibration Measurement Manual for Unstable Rock Block Extraction (Draft)”, Public Works Research Institute Data, No. 4051, 2007.7.7. Masaru Takemoto, Yu Fujiwara, Seiya Yokota, Takashi Mitsuka, Kuniomi Kai, Ei Okamoto, “Development of a field survey and judgment system using the rock fall risk vibration survey method—Development of a system for judging the risk of rock fall locally— "The 65th Annual Scientific Lecture, Japan Society of Civil Engineers, 2011. Takahiro Fukada, Fumiaki Kamihan, Takaomi Ma, Hideki Saito, “Experiment and Analysis on Vibration Characteristics of Rigid Body Embedded in Ground that Simulates a Roll”, 46th Geotechnical Research Conference (Hachinohe), 2012. . Takashi Okimura, Nobuyuki Torii, Sadahiro Sugawara, Masaki Yoshida, “A Proposal of a Rockfall Risk Assessment Method on Road Slopes, Landslide”, Vol. 39, No. 1, pp. 22-29, 2002. Takashi Okimura, Nobuyuki Torii, Masaki Yoshida, Tetsuo Watanabe, Naohiro Sasaki, "Study on the mechanism of rock fall by model experiments", 38th Geotechnical Engineering Conference (Akita), 2003. Geotechnical Society, "Introduction to Geotechnical Formulas", pp. 134-135, 2001.5. Takahiro Fukada, Ryoji Izuminami, Yasuki Mori, “Consideration of system construction and measurement results for vibration measurement of rocks on slopes”, 65th Annual Conference of Japan Society of Civil Engineers (Hokkaido), 2011.9. Geotechnical Society, “How to Determine Ground Constants for Design: Soil”, p. 23 and p. 80, 2007.12. Geotechnical Society, “Utilization of N value and c · φ”, p132, 2005.10.

  In view of the above situation, an object of the present invention is to provide a rock fall risk evaluation method for rocks on slopes based on vibration measurement by a simple method.

In order to achieve the above object, the present invention provides
[1] In the rock fall risk assessment method for rocks on slopes based on vibration measurements, the natural frequency of the rocks is identified from vibration measurements during the vibration of the rocks, and the depth of penetration of the rocks is estimated. vibration is to grasp the entire shape of the boulders the embedment based on depth, to evaluate the rockfall risk of the boulder based on stability F _R for overturning said the stability F _S boulder against sliding of the boulder A rock fall risk assessment method for rocks on slopes based on measurement, wherein the sliding force of the rocks is the ground pressure of the ground and the slope direction component of the weight of the rocks, and the resistance of the rocks is the ground pressure of the ground and the bottom surface of the rocks The stability F _S against the sliding of the boulder and the stability F _R against the falling of the boulder are as follows:
F _S = [P _P + W cos θ · tan φ + (ab + 2bd) · c] / (P _A + W sin θ) (6)
F _R = [W cos θ × (b / 2) + P _P × (2/3) · d] / [W sin θ × (h / 2-d)] (7)
P _A = [(1/2) γd ² · tan ² (45 ° −φ / 2) −2cd · tan
(45 ° −φ / 2)] × a (8)
P _P = [(1/2) γd ² · tan ² (45 ° + φ / 2) +2 cd · tan
(45 ° + φ / 2)] × a (9)
Here, F _S : Stability against sliding of rocks on the slope
P _A : Main earth pressure (kN)
P _P : Passive earth pressure (kN) of ground
W: Weight of rolling stone (kN)
θ: Slope slope (°)
φ: Ground shear resistance angle (°)
a: Depth in the direction of the slope of the boulder (m)
b: Width of rolling stone slope direction (m)
d: Depth of rolling stone (m)
c: Adhesion strength of ground (kN / m ² )
F _R : Stability against falling of a rock on the slope
h: height of the boulder (m, h = h ₀ + d)
h ₀ : Height of the exposed part of the boulder (m)
γ: Unit volume weight of the ground (kN / m ³ )
a: Depth in the direction of the slope of the boulder (m)
It is characterized by being given by.

[ 2 ] In the rock fall risk assessment method for rocks on slopes based on the vibration measurement described in [ 1 ] above, narrow rocks from a wide range of railway slopes are narrowed down using the dipping ratio d / h ₀ as an index. It is used for primary screening.

According to the present invention, the inset depth of the boulder is estimated, the overall shape of the on-slope boulder is grasped based on the estimated inset depth, and the mechanical stability F of sliding and falling of the boulder is obtained. it is possible to evaluate the rock fall risk based on _S and F _R.

It is a figure which shows the experiment of the estimation method of the inset depth of the boulder using the fundamental vibration which concerns on this invention. It is a figure which shows the natural frequency at the time of considering that the penetration depth is 0. It is a figure which shows the analysis model (three-dimensional finite element method) in an inclined ground. It is a figure which shows the item of the analysis model in an inclined ground. It is a figure which shows the eigenvalue analysis result in an inclined ground. It is a figure which shows the stability with respect to the sliding of a rolling stone. It is a figure which shows the stability with respect to the fall of a rolling stone. 3 is a schematic diagram showing an outline of a slope A. FIG. 3 is a schematic diagram showing an outline of a slope B. FIG. It is a drawing substitute photograph which shows the example of the rolling stone of the slope A. It is a drawing substitute photograph which shows the example of the boulder of the slope B. It is a vibration measurement image figure of a rock on a slope. It is a drawing substitute photograph which shows the vibration measurement condition of the boulder on the slope. It is a figure which shows the shape approximation of a rolling stone. It is a drawing-substituting photograph showing a survey boulder on a railway slope. It is a figure which shows the number data according to the generation | occurrence | production form (rolling stone type | mold / peeling type | mold) of the falling rock of 2005-2009.

In the rock fall risk evaluation method for rocks on slopes based on vibration measurement of the present invention, the natural frequency of the rock is identified from vibration measurement during the vibration of the rock, the depth of penetration of the rock is estimated, and the estimation vibration is to grasp the entire shape of the boulders the embedment based on depth, to evaluate the rockfall risk of the boulder based on stability F _R for overturning said the stability F _S boulder against sliding of the boulder A rock fall risk assessment method for rocks on slopes based on measurement, wherein the sliding force of the rocks is the ground pressure of the ground and the slope direction component of the weight of the rocks, and the resistance of the rocks is the ground pressure of the ground and the bottom surface of the rocks The stability F _S against the sliding of the boulder and the stability F _R against the falling of the boulder are as follows:
F _S = [P _P + W cos θ · tan φ + (ab + 2bd) · c] / (P _A + W sin θ) (6)
F _R = [W cos θ × (b / 2) + P _P × (2/3) · d] / [W sin θ × (h / 2-d)] (7)
P _A = [(1/2) γd ² · tan ² (45 ° −φ / 2) −2cd · tan
(45 ° −φ / 2)] × a (8)
P _P = [(1/2) γd ² · tan ² (45 ° + φ / 2) +2 cd · tan
(45 ° + φ / 2)] × a (9)
Here, F _S : Stability against sliding of rocks on the slope
P _A : Main earth pressure (kN)
P _P : Passive earth pressure (kN) of ground
W: Weight of rolling stone (kN)
θ: Slope slope (°)
φ: Ground shear resistance angle (°)
a: Depth in the direction of the slope of the boulder (m)
b: Width of rolling stone slope direction (m)
d: Depth of rolling stone (m)
c: Adhesion strength of ground (kN / m ² )
F _R : Stability against falling of a rock on the slope
h: height of the boulder (m, h = h ₀ + d)
h ₀ : Height of the exposed part of the boulder (m)
γ: Unit volume weight of the ground (kN / m ³ )
a: Depth in the direction of the slope of the boulder (m)
Given by.

  Hereinafter, a method for evaluating the risk of falling rocks on a slope on a slope based on vibration measurement according to the present invention will be described.

  First, a method for estimating the penetration depth of a boulder using vibration will be described.

  In order to establish a quantitative rockfall risk assessment method, it was important to understand the vibration characteristics of rocks and to consider the dynamic mechanism of rock-type rockfalls. Therefore, we thought that it would be possible to quantitatively evaluate the risk of falling rocks by grasping the inset depth of the boulder using vibration and calculating the mechanical stability.

  FIG. 1 is a diagram showing an experiment of a method for estimating the inset depth of a boulder using basic vibration according to the present invention, and FIG. 2 is a schematic diagram of natural frequencies when the inset depth is assumed to be zero. is there.

  The present inventors have already simulated a boulder with a rigid body having a root in the ground, and changed the conditions such as the size, weight, ground hardness, depth of root of the rigid body, and the acceleration measured at the time of hammering. Through basic experiments to calculate the natural frequency from the waveform (Fig. 1) and eigenvalue analysis using a three-dimensional finite element method modeling rocks and ground, the following formulas (1) to (4) are used to insert the rocks. A method for estimating the depth is proposed (see Non-Patent Documents 9 and 29 above), and the average length from the two directions is obtained by the following equation (5), so that the estimated depth of the penetration depth is obtained. It has been proved that it can be estimated with an error of about ± 5 cm.

_{d = 0.396 (f / f 0} *) -0.394 ... (1)
f ₀ ^* = 0.719 Q ₁ Q ₂ +0.745 (2)
Q ₁ = ( 1 / 2π ) √ [EAg / B (1-v ² ) I _P W] (3)
Q ₂ = √ { (b / h ₀ ) ² / [ (b / h ₀ ) ² +1] } (4)
d (with upper bar) = (d _x + d _y ) / 2 (5)
Where d: estimated length of penetration depth (m)
f: Measured natural frequency of rolling stone (Hz)
f ₀ ^* : natural frequency (Hz) when a boulder (exposed part) is considered to be zero (see FIG. 2)
Q ₁ : Basic frequency (Hz) of a boulder (exposed part) when the ground is regarded as a spring
Q ₂ : Characteristic value determined by the shape of the boulder (exposed part) E: Deformation coefficient of the ground around the boulder (kN / m ² )
A: Bottom area (m ² ) of the boulder (exposed part)
g: Gravity acceleration (m / s ² )
B: Roll side (exposed part) short side length (m)
ν: Poisson's ratio (generally 0.3)
I _p : Shape factor W: Weight of the boulder (exposed part) (kN)
b: Rolling stone width (m)
h ₀ : height of the rolled stone (exposed part) (m)
d (with upper bar): Average penetration depth (m)
d _x : depth of penetration calculated from the natural frequency of impact in the x direction (m)
d _y : depth of penetration calculated from the natural frequency of impact in the y direction (m)
In the present invention, on the premise of the above, a rock fall risk evaluation method based on vibrations of rocks on a slope and mechanical stability will be described.

(1) Vibration of rocks on sloped ground The eigenvalue analysis (three-dimensional finite element method) on the horizontal ground described above is applied to the sloped ground 1, and the natural frequency of the rocks 2 on the slope is obtained.

  FIG. 3 is a diagram showing an example of an analysis model in an inclined ground according to the present invention, FIG. 4 is a schematic diagram of specifications of the analysis model in an inclined ground, and analysis conditions are those performed on a horizontal ground (Non-Patent Document 9 above) , 29), and the analysis case is 2 cases as shown in Table 1 and 18 cases (2 dimensions x 3 penetration ratios x 3 inclination angles) using the specifications shown in FIG. .

Eigenvalue analysis results in slope panel 1, the inclination angle θ to the horizontal axis, the vertical axis represents the natural frequency f _y of the inclination direction, shown in FIG. From FIG. 5, it can be seen that the natural frequency is almost constant without being affected by the inclination in any case.

(2) Rock fall risk based on mechanical stability Next, rock fall risk is defined using the mechanical stability of Roll 2 against sliding and falling on the slope. Here, regarding the modeling of the boulder 2, in addition to the research of Murakami and Kuchiuchi (refer to the above-mentioned Non-Patent Documents 22 and 23) in which the boulder is approximated to a cylindrical body, Okimura and Torii et al. (See 31).

The stability against sliding can be thought of as a safety factor against the destruction of the embedded ground. As shown in Fig. 6, the sliding force is the main earth pressure of the ground and the slope direction component of the boulder weight, and the resistance is the passive earth pressure of the ground. And it becomes the resultant force of the frictional force and adhesive force of the bottom and side of the boulder. Here, the frictional force on the side surface of the boulder is compared with other resistances such as adhesive force, considering that the coefficient of friction and soil pressure coefficient are less than 1 and that the depth of penetration is not large. And a small value. Therefore, in addition to the evaluation on the safety side, this is ignored in consideration of the simplicity of calculation, and the stability F _S with respect to sliding is defined by the following equation (6).

  On the other hand, the stability against the fall of the rolling stone is considered by the moment around the fulcrum as shown in FIG. The overturning moment is due to the slope component of the weight of the boulder, and the resistance moment is the combined moment due to the component perpendicular to the slope of the weight of the boulder and the passive earth pressure of the ground above the boulder.

Therefore, the stability F _R against overturning is defined by the following formula (7).

In addition, the main earth pressure and the passive earth pressure of the rooted ground in the following formulas (6) and (7) are the Rankine earth pressure (see Non-Patent Document 32 above) when there is shear resistance and adhesive strength, respectively. It is given by the following equations (8) and (9).
F _S = [P _P + W cos θ · tan φ + (ab + 2bd) · c] / (P _A + Ws in θ) (6)
F _R = [ W cos θ × ( b / 2 ) + P _P × ( 2/3 ) · d ] / [W sin θ × (h / 2-d)] (7)
P _A = [(1/2) γd ² · tan ² (45 ° −φ / 2) −2cd · tan
(45 ° −φ / 2)] × a (8)
P _P = [ ( 1/2 ) γd ² · tan ² (45 ° + φ / 2) +2 cd · tan
(45 ° + φ / 2)] × a (9)
Here, F _S : Stability against the sliding of the rocks on the slope P _A : Main earth pressure (kN) of the basement ground
P _P : Passive earth pressure (kN) of ground
W: Weight of rolling stone (kN)
θ: Slope slope (°)
φ: Ground shear resistance angle (°)
a: Depth in the direction of the slope of the boulder (m)
b: Width of rolling stone slope direction (m)
d: Depth of rolling stone (m)
c: Adhesion strength of ground (kN / m ² )
F _R : Stability against falling of a roll on the slope h: Height of the roll (m, h = h ₀ + d)
h ₀ : Height of the exposed part of the boulder (m)
γ: Unit volume weight of the ground (kN / m ³ )
a: Depth in the direction of the slope of the boulder (m)
Next, application and verification on an actual slope will be described.

(3) Survey slopes and rocks Apply the rock fall risk assessment method of the present invention to actual slopes and verify their effectiveness. 8 and 9 show representative cross sections of the slopes A and B, respectively.

  In FIG. 8, 10 is slope A, 11 is exposed rock, 12 is a lot of boulders, 13 is fallen wood, 14 is a simple fence, 15 is a rockfall fence, 16 is a masonry wall, 17 is a railroad track, and 18 is a road. 9, 20 is a slope B, 21 is a large number of boulders, 22 is an exposed rock, 23 is a work road, 24 and 26 are rockfall pawls, 25 and 27 are masonry walls, 28 is a railroad track, and 29 is a road. is there.

  For verification purposes, two locations, slope A shown in FIG. 8 and slope B shown in FIG. 9, where many unstable rocks exist along the slope, were selected as survey slopes. Since this is a test field, it is a place where rockfall countermeasures such as rockfall fences 15 and 26 on the railroad tracks 17 and 28 and a simple fence 14 on the slope are already taken.

  Slopes A and B are both homogeneous slopes on the left side of the track, and the slope slope is about 40 °. However, there are places where the slope of the slope is locally increased around the boulders.

As for geology, slope A has a cliff and slope B has thick sediment on the surface. Three simple penetration tests are carried out on each of the slopes A and B, and their approximate positions and N _d values are shown together. N _d values up to about surface 50cm becomes 10 to 30 about 1 to 5 mm, it deeper.

  In both cases, a large number of boulders 12 and 21 originated from the exposed rocks 11 and 22 above the slope, and twelve from slope A and 10 from slope B were selected as investigation target rocks.

  Drawing substitute photograph 1 (FIG. 10) and drawing substitute photograph 2 (FIG. 11) show an example of rolling stones existing on slope A and slope B, respectively. The rock type is rhyolitic welded tuff, and there are many hard and square shaped boulders.

(4) Vibration measurement method The vibration measurement device must be excellent in usability even on steep slopes along the railway where the roadway conditions and work conditions are not always good. In view of this, a device with a built-in preamplifier is adopted to provide a simple and compact system configuration (see Non-Patent Document 33 above). As shown in FIG. 12, an image of vibration measurement is obtained by fixing an accelerometer 32 to an uphill roll 31 and AD-converting an acceleration waveform when hit with a rubber hammer 33 into a personal computer PC 35. Further, the measurement can be performed by about two workers as shown in the drawing substitute photograph 3 shown in FIG. The acceleration waveform thus measured is subjected to fast Fourier transform, and the dominant frequency at which the Fourier spectrum is maximized is calculated as the natural frequency of the boulder (see Non-Patent Documents 9 and 29 above).

(5) Evaluation of the ground deformation coefficient on the slope The ground deformation coefficient is evaluated by the _Nd value obtained by a simple penetration test as a method that can be measured even on steep slopes. The N _d value and the N value generally have a relationship of N _d = (1 to 3) N (see Non-Patent Document 34 above).

Here, an important f ₀ ^* is in the denominator in the above equation (4) for estimating the penetration depth, and this f ₀ ^* is Q ₁ including the ground deformation coefficient in the above equation (3) [the above equation (1). ], It is better to estimate Q ₁ large so that the penetration depth is not excessively calculated. Therefore, N = N _d , E = 700 N (kN / m ² ) (refer to Non-Patent Document 34 above), which is a general relationship between the deformation coefficient and the N value, is used, and this corresponds to a dynamic strain level. As the double equivalent value (see Non-Patent Documents 9 and 29 above), the ground deformation coefficient is obtained by the following equation (10). In addition, if the exposed height of the boulders targeted in this application is about 1 m at the maximum and the depth of penetration is about 50 cm, which is half of that (the penetration ratio is 0.5 or more), it is considered stable enough. The evaluation was performed using the _Nd value at a position of 50 cm depth.

Further, the relationship between the adhesive strength c of the ground and the N value (see Non-Patent Document 35) is as follows: c = N / 16 (kgf / cm ² ) [= 6 N (kN / m ² ) used for the approximate stability calculation of the slope. ] Is evaluated by the following formula (11).

E = 2 × 700 N _d = 1400 N _d (10)
c = 6N _d (11)
(6) Approximate shape of exposed part of boulder In order to estimate the penetration depth by the method proposed by the present invention, it is first necessary to grasp the shape of the exposed part of boulder (see Non-Patent Documents 9 and 29 above). .

For this reason, as shown in FIG. 14, the external dimension of the exposed portion of the boulder 41 is approximated to a rectangular parallelepiped 42 having a dimension a in the slope running direction along the slope, a dimension b in the slope direction, and a height h ₀ perpendicular to the slope. To do. However, the weight is calculated by the following equation (12) as a half of an ellipsoid inscribed in the rectangular parallelepiped 42.

This is because, as described above, Q ₁ [Equation (1)] is greatly estimated in order not to calculate the penetration depth excessively, and as a result, the penetration depth can be estimated on the safe side. .

W = ρ · ( 4/3 ) π · (a / 2) · (b / 2) · h ₀ · 1/2 = 0.52 · ρ · a · b · h ₀ (12)
Here, ρ: unit volume weight of the boulder (kN / m ³ )
a: Depth in the direction of the slope of the boulder (m)
b: Width of rolling stone slope direction (m)
h ₀ : Height of the exposed part of the boulder (m)
(7) Estimation of penetration depth based on vibration measurement Table 2 shows the number of the surveyed rock, the size of the rock according to the notation of Fig. 14, the slope angle around the rock, and the natural vibration of the rock obtained as a result of vibration measurement. The numbers (f _x : natural frequency in the slope direction) and f _y : natural frequency in the slope direction are arranged. Vibration measurement is carried out twice in October 2009 and November 2011.

  Rolling stone A-3 was found to be 0, so it was not found during the 2011 survey. Therefore, A-12 was newly designated as a survey boulder. Roll stone B-9 could not be measured in 2011 due to fallen trees. In addition, since there is no significant difference in natural frequency over time, it seems that destabilization of the boulders did not progress significantly over the course of about two years.

  Furthermore, based on this vibration measurement result, the result of calculating the estimated depth of the penetration depth by the above formulas (1) to (4) is also shown in Table 2.

(8) Proposal of rock fall risk assessment based on mechanical stability Next, using the estimated average depth of penetration, the stability of sliding and falling rocks on the slope is expressed by the above formulas (6), ( Calculate according to 7).

  Table 3 shows the results of these calculations. As a result of calculation, the penetration depth is set to 0 for the case where the estimated length is negative.

  Here, A-1, A-3, A-4, A-10, B-2, and B are considered to be picked up from those stones whose depth of penetration is less than 50 cm, which is considered as a candidate for unstable rocks. -3, B-4, B-6, B-9, B-10. The boulder A-3 that had fallen at the time of the 2011 survey was calculated to have a root depth of 0, indicating that it was an unstable boulder.

Next, instead of evaluating the risk level only by the depth of penetration, when looking at the dipping ratio d / h ₀ of the boulder, A-1, A-3, A-4, B-6, etc. It is less than 0.25.

  Furthermore, as for those whose mechanical stability on the slope is less than 1.2, those for sliding are A-1, A-3, A-4, B-6, and those for falling are relatively low in exposure height. There was nothing less than 1.2 because we chose a boulder.

  As described above, the rock fall risk can be quantitatively evaluated by calculating the depth of penetration, the penetration ratio, the stability against sliding and falling.

On the other hand, for example, by conducting primary screening of those with an intrusion ratio d / h ₀ of 0.25 or less as unstable rocks, it is possible to narrow down the rocks that require detailed investigation from a wide range of railway slopes. It can also be expected to be an efficient risk assessment method in the field.

(9) Verification of the risk assessment method of the present invention In order to verify the effectiveness of the rock fall risk assessment method of the present invention, on-site confirmation of the depth of penetration (eight boulders) and rock fall risk vibration survey Comparison with the determination result (11 boulders) according to the method (hereinafter referred to as “existing method”).

  The surveyed boulders were actually excavated to confirm the condition of the rooted portion, with the average length of the rooting depth determined to be less than 50 cm. Table 4 shows the boulders for which the penetration depth was confirmed, the estimated depth of the penetration depth based on the vibration measurement, the measured length of the penetration depth and the average length thereof.

  Moreover, the photograph of the confirmation condition of the penetration depth of a boulder is shown in FIG. In order to clarify the roots in the ground, the boundary between the exposed part and the ground surface was clearly shown by spraying, and then the roots were excavated. In FIG. 15, (a) A-10: before excavation, (b) A-10: after excavation, (c) A-10: Rooting confirmation status, (d) B-3: before excavation, (e) B -3: After excavation, (f) B-3: Rooting confirmation status, (g) B-4: Before excavation, (h) B-4: After excavation, (i) B-4: Rooting confirmation status, (J) B-10: Before excavation, (k) B-10: After excavation, (l) B-10: Rooting confirmation status, (m) A-5: Appearance, (n) A-8: Appearance, (O) A-11: Appearance is shown.

  Since an actual boulder has a complicated shape of the root portion, the depth of the root portion often does not become a constant value, and the measured length varies. However, the actually measured average value of the penetration depth matches the estimated depth of the penetration depth based on the method of the present invention, and is a difference of about +5 cm at the maximum on the safe side.

  Next, the comparison of the risk evaluation results by the method of the present invention and the existing method will be described. It is 5 out of 11 boulders determined by the existing method that the determination of the method of the present invention and the existing method match. The determination contents are: A-3: unstable, A-4: unstable, B-2: stable, B-7: stable, B-9: stable (Table 3, comparison column of the method of the present invention and existing methods) Symbol “○”).

  The remaining six methods have been determined to be different from the method of the present invention and the existing method. In the existing method, these six boulders are all determined to be unstable. Of these six, those with a depth of insertion of less than 50 cm estimated by the method of the present invention are three of A-10: estimated length 27 cm, B-3: 18 cm, B-4: 9 cm ( Table 3, symbol “Δ”). Although the method of the present invention and the existing method are differently determined, it can be said that these rocks have a small depth of penetration and are easy to shake. However, even if the rock has a small depth of penetration and is easy to sway, it can be said that if the mechanical stability on the slope is calculated, the stability against sliding and falling is large, that is, the rock with a low risk of falling rocks. As for boulders A-10, B-3, and B-4, as shown in Table 4, the rooting depth was actually excavated and the rooting depth was actually measured, and the root according to the method of the present invention was measured. It has been confirmed that the average estimated length of the insertion depth and the measured average length are almost the same.

Further, the remaining three A-5, A-8, and A-11 (Table 3, symbol “*”) that have been determined differently by the method of the present invention and the existing method will be described. Looking closely at the measurement data (Table 3) of existing methods related to these stones, the RMS velocity amplitude ratio is less than 2 in either the x-direction or the y-direction (stable by criteria). The frequency also shows a value of 25.0 to 30.7 Hz, which is a value close to the criterion of 30 Hz. That is, it can be said that these three stones are located at the boundary between the stable region and the unstable region even in the determination by the existing method. In addition, as shown in Table 2, the rolling stones A-5, A-8, and A-11 have a flat and stable shape with a smaller exposure height (h ₀ ) than the two sides (a, b) of the bottom surface. Yes.

  From the above, there are some judgment results that differed between the method of the present invention and the existing method, but the evaluation by the existing method discriminates a rock that is easy to sway with a small depth of penetration, and the shape of the rock, It is considered difficult to judge the stability considering the depth and slope of the slope. As an index for evaluating the instability that will eventually lead to falling rocks, the mechanical stability against sliding and falling is prominent, and the effectiveness of the method of the present invention capable of calculating this is shown. I believe.

  In addition, this rock fall risk assessment method was applied to the actual slope along the railway, and its effectiveness was confirmed.

  The findings obtained in the present invention are summarized below as a conclusion.

   (A) The method for evaluating the risk of rockfall at the source is empirically based on statistical analysis of past rockfall cases, as the mechanism of rockfall occurrence has not been fully elucidated. . In this study, we focused on the inset state of the boulders and considered an objective and quantitative evaluation method related to the mechanical stability on the slope.

(B) In the method of the present invention, the natural frequency is specified from the vibration measurement at the time of vibration, and the depth of the inset of the rock is first estimated. If the depth of penetration is known, the overall shape of the rock on the slope can be grasped, and the risk of falling rocks can be evaluated on the basis of the mechanical stability F _S and F _R of sliding and falling of the rock. It is also conceivable to use it for primary screening to narrow down unstable rocks from a wide range of railway slopes using the penetration ratio d / h ₀ as an index.

   (C) The method of the present invention was applied to the risk assessment of the rolling stones on the actual slope along the railway. And, as a result of actually excavating the inset part of the boulder judged to be high in risk, it was found that the average inset depth of the boulder can be estimated. In addition, as a result of comparison with existing risk assessment methods, the effectiveness of the method of the present invention could be confirmed.

   (D) In the current situation where quantitative rockfall risk assessment methods have not been established, field engineers understand the method of the present invention using measuring instruments that are easy to handle even if they are not specialists. We believe that this is the first step in an evaluation method that can be judged. It is considered that the effectiveness of the method of the present invention can be enhanced by accumulating verification cases with the determination results performed by the conventional scoring method.

  The new rock fall risk evaluation method of the present invention can be applied not only to railways but also to other fields such as roads. In the future, efforts toward systematization of a new rock fall risk assessment method, such as methods for approximating the shape of actual boulders with complex shapes, methods for evaluating the deformation coefficient of ground, and further improving the accuracy of the inset depth estimation formula It is thought that it can be developed.

  In addition, this invention is not limited to the said Example, Based on the meaning of this invention, a various deformation | transformation is possible and these are not excluded from the scope of the present invention.

  The method for evaluating the risk of falling rocks on slopes based on vibration measurement according to the present invention can be used as the method for evaluating the risk of falling rocks on slopes based on vibration measurement by a simple method.

1 Inclined ground 2,41 Rolled stone 10 Slope A
11, 22 Exposed rocks 12, 21 Many boulders 13 Fallen trees 14 Simple fences 15, 24, 26 Fallen rock fences 16, 25, 27 Masonry walls 17, 28 Railroad tracks 18, 29 Roads 20 Slope B
23 Work path 31 Slope on the slope 32 Accelerometer 33 Rubber hammer 34 AD converter 35 PC PC
42 rectangular parallelepiped

Claims (2)

Identifying the natural frequency of the boulder from vibration measurements during the vibration of the boulder, estimating the depth of penetration of the boulder, grasping the overall shape of the boulder based on the estimated depth of penetration, A rock fall risk evaluation method for rocks on a slope based on vibration measurement based on vibration measurement for evaluating the rock fall risk of the rocks based on the stability F _S against the sliding of the rocks and the stability F _R against the fall of the rocks, The sliding force of the ground is the main soil pressure of the ground and the slope direction component of the boulder's own weight, and the resistance force of the boulder is the combined force of the ground pressure of the ground, the bottom surface of the boulder and the frictional force and the adhesive force of the side surface. The stability F _S with respect to sliding and the stability F _{R with} respect to the fall of the above-mentioned rolling stone are:
F _S = [P _P + W cos θ · tan φ + (ab + 2bd) · c] / (P _A + W sin θ) (6)
F _R = [W cos θ × (b / 2) + P _P × (2/3) · d] / [W sin θ × (h / 2-d)] (7)
P _A = [(1/2) γd ² · tan ² (45 ° −φ / 2) −2cd · tan
(45 ° −φ / 2)] × a (8)
P _P = [(1/2) γd ² · tan ² (45 ° + φ / 2) +2 cd · tan
(45 ° + φ / 2)] × a (9)
Here, F _S : Stability against sliding of rocks on the slope
P _A : Main earth pressure (kN)
P _P : Passive earth pressure (kN) of ground
W: Weight of rolling stone (kN)
θ: Slope slope (°)
φ: Ground shear resistance angle (°)
a: Depth in the direction of the slope of the boulder (m)
b: Width of rolling stone slope direction (m)
d: Depth of rolling stone (m)
c: Adhesion strength of ground (kN / m ² )
F _R : Stability against falling of a rock on the slope
h: height of the boulder (m, h = h ₀ + d)
h ₀ : Height of the exposed part of the boulder (m)
γ: Unit volume weight of the ground (kN / m ³ )
a: Depth in the direction of the slope of the boulder (m)
A rock fall risk assessment method for rocks on slopes based on vibration measurements. In rock fall risk assessment method of the slope on the boulder based on vibration measurement according to claim 1, the embedment ratio d / h ₀ of the boulder as an index, the primary screening Filter unstable boulder from wide railroad wayside slopes A method for assessing the risk of falling rocks on slopes based on vibration measurements.