By use of properties of slope failures at ground surface simulated in laboratory test and theoretical equations, evaluating method could be developed. Slope failures are divided into circular failure, toppling, wedge failure, planar failure and combined failure. If information from sensor is used appropriately, occurrence of these breakdowns can be evaluated.
A method to evaluate slope failure and slip surface includes four steps such as (1) slope failure itself, (2) shape of failure, (3) estimation of slip surface, (4) collapsed soil mass and failure direction using deformation data from several sensors installed in slope surface.
3.1 Detection of Slope Failure
Recognition of slope failure is predicted from deformation data of various sensors on the ground as shown in Fig. 4a. The sensors installed in Sections I and V do not change, but some of the sensors or all of them installed in Sections II, III and IV made some change in acceleration and angle. Slope failure condition could be detected by use of these information (Fig. 4b).
Figure 4. Multiple sensors installed in a slip surface
Accelerometer and the change of each displacement do not change in the normal range when the sensor moves on a predetermined slope. But when a sensor separates or fails from a slope, their data are diverged. Though they are meaningless data, this information can be used to confirm the occurrence of a slope failure (Fig. 5).
Figure 5. Movement data of each sensor as its sliding
3.2 Evaluation of Collapse Mode
The motion of the point located on the slope can be divided into slip, rotation and behaviour at failure. Slip is represented by plane failure of a slope, and rotation is defined as circular failure. The behaviour at slope failure is judged by diverged sensor data such as slope failure, debris flow and fallen rocks. In this way, the destructive pattern of a slope can be determined by rotational motion, linear motion and divergence (Fig. 6).
Figure 6. Simplified ground movement
It is possible to confirm simple movement using a sensor data installed on ground surface such as acceleration and rotation angle. Macroscopic collapse shapes (circular failure, planar failure and combined failure) are estimated by calculation of movement at each sensor point.
For example, if information obtained from A, B, C sensors are all rotation, it means circular failure. However, if A and C are in rotation and B did not show any change, it defines planar failure. It is defined as a combined failure when A, B, C sensors show rotation, linear and combined movements. In case of falling or collapsing, it is possible to judge the form of collapse by data divergence (Fig. 6).
This concept is compared with the results of laboratory test and to evaluate the collapse modes. The evaluation of the collapse mode is executed based on the fact that it is possible to distinguish the sliding, rolling (rotation) and movement at failure on a slope according to variation of acceleration and rotation angle measured by the sensor.
Figure 5 shows the change of the acceleration and the rotation angle due to the movement of the sensor installed on a slope surface by change of the inclination of a slope. No changes are generated with respect to the sliding motion of the slope. Slip motion can be judged by using this characteristics.
As shown in Fig. 7, when the acceleration and the rotation increase in proportion to the change of the angle of a slope, it is judged to rotate deformation, that is, circular failure. However, when the sensor is separated or broken down from the ground, the data will diverge in Fig. 8. When there is a sudden acceleration in a sensor and the data diverge as well, there is a dynamic collapse such as fallen rocks, debris flow etc. In particular, these characteristics of data are used in protection structure for debris flow and fallen rocks and it is possible to detect the occurrence of disaster.
Figure 7. Sensor data of each sensor as its rotating
Figure 8. Sensor data characteristics with a slope failure (collapse)
3.3 Activity Surface Estimation
To establish a method for predicting failure surface of a slope using variation of angle at ground surface, it is assumed that a block moves as follows (Figs 9 and 10).
(1) Soil mass is separated by crack and fault by failure
(2) Moving soil mass is like a rigid body: Deformation <<< Movement
(3) The height and angle of slip surface and upper ground surface are same at each block
(4) Deformation (angle, vector etc.) data at slip surface are the same value at ground surface
(5) Angle of variation of ground surface by ground deformation is parallel to angle of slip surface
(6) Location of start and end of slip surface defines as the location of upper and lower crack
Figure 9. A slice (i) of a slip surface
Figure 10. Start and end point for predicting for slip surface
At first, location of starting and ending point is determined for evaluating slip surface. And then any equation $f\left(z_i\right)$ is defined to estimate slip surface. $f\left(z_i\right)$ could be a simple (or quadratic, cubic, etc.) equation. Gradient of tangent line tani(θi) is calculated at coordinate xi based on deformation data from various sensors on ground, where θi is variation of slope angle. It must be the same value with deferential equation at a point; so, f ’(zi) = tani (θi). Thus, by calculating the gradient of tangent line at xi, we can obtain the correct solution and optimum solution of the coefficient of equation ( ai ,bi,ci, etc.). Finally slip (failure) surface could be determined. For a quadratic equation, starting and ending points of the slip surface are defined as ( xinidown, zinidown ), ( xiniup, ziniup) and the equation is generally expressed as $Z_{2 i}=a_{2 i} \times x_{2 i}^2+b_{2 i} \times x_{2 i}+c_{2 i}$. Several slip surfaces could be obtained by selecting the location of starting and ending points. The gradient of slip surface might be calculated using measured inclination data from each sensor.
Gradient of tangent line at each point (deferential value): $\frac{\partial z_{z i}}{\partial x_{z i}}=\tan _{2 i}$ (variation of slope angle) $x_i$ value at each point is a known value: $x_{2 i}\left(x_{21}, x_{22}, x_{23}, x_{24}, x_{25}\right)$
Using known point from Eqn (1) and (2) and gradient of tangent line of quadratic equation, slip surface could be calculated.
Equation of slip surface:
$x_{2 i}=a_{2 i} \times x_{2 i}^2+b_{2 i} \times x_{2 i}+c_{2 i}$
(1)
$\left(x_{\text {inidown }}, z_{\text {inidown }}\right),\left(x_{\text {iniup }}, z_{\text {iniup }}\right)$
(2)
By applying $\frac{\partial z_{z i}}{\partial x_{z i}}=2 a_{2 i} \times x_{2 i}+b_{2 i}$ and $\frac{\partial z_{z i}}{\partial x_{z i}}=\tan _{2 i}$ (variation of slope angle), calculate gradient at $x_{2 i}$
x21: tan2i($\theta_{21}$)=2a2i×x21+b2i
x22: tan2i($\theta_{22}$)=2a2i×x22+b2i
x23: tan2i($\theta_{23}$)=2a2i×x23+b2i
•••
x2n: tan2i($\theta_{2n}$)=2a2i×x2n+b2i
Calculating $a_{2 i}, b_{2 i}, c_{2 i}$: a correct solution or optimum solution.
Failure (slip) surface can be easily estimated by use of this method for each section (Fig. 11). In this study, second-order equation as an example is explained and it is possible to apply the method of estimating slip surface, such as high-order polynomials.
Figure 11. Calculation of tangent slope of each sensor
3.4 Estimation of Collapsed Soil Mass and Failure Direction
Using the method of 3.3, it is possible to estimate the two-dimensional slip surface of a slope on which various sensors are installed. The magnitude of the two-dimensional collapse can be calculated from information obtained from one cross-section, 2D. Then, combination of the 2D slip surfaces can be used to calculate the magnitude of 3D collapsed soil mass. It is possible to estimate 3D collapse magnitude (m3) by calculating and combining a plurality of two-dimensional areas using 2D slip surfaces. And direction or path of slope failure could be identified by using the centre of gravity of the volume.
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