2.1. Descriptions of Experiment Methods
The underground subway station model used for the inundation depth measurements is shown in
Figure 1. The experimental model was designed through an analysis of the specifications of a typical subway platform, and the model was scaled down to 1/20 of the actual platform. The model consists of staircases from the ground to B1F, staircases to B2F, and a flow supply device to simulate the rainwater inflow. The plan view of the model is shown in
Figure 2. The width of the model was 0.5 m and the length was 2.0 m. The width of the staircases to B1F was 0.1 m and that of the staircases to B2F was 0.2 m. In this model, the rainwater from roads of urban area was assumed to flow in directly through the staircases because most subway station entrances are directly connected to the ground level. The rainwater introduced into B1F was controlled through the flow adjustment value, and it was possible to determine the inflow points (P1, P2, P3, and P4) through valve adjustment. Thus, the inundation depth was changed according to the inflow points and flow rate. The green lines in
Figure 2 indicate the measurement sections (Sec. A, Sec. B, and Sec. C), which were determined to analyze inundation properties of the subway station model. At each line, inundation depth was measured using the laser image analysis algorithm. From the inundation depth measurements, evacuation safety was estimated by using the evacuation time and specific force.
To reduce damage to humans from the flooding of underground spaces, it is necessary to calculate the time required for evacuation in case of inundation and prepare evacuation routes [
1]. According to the Committee of Countermeasures against Inundation Disasters in Underground Spaces (CCIDUS) [
13], the time required for evacuating a person from underground spaces is:
where
is the underground evacuation interval;
;
is the inundation depth in the underground floor (m); and
is the distance from the farthest location in the underground space to the underground entrance of the staircase (m). From
tev, it would be possible to determine how fast a person should escape from the subway station. Furthermore, it is also important to notice which route is safer to evacuate. The aforementioned evacuation safety can be estimated from the specific force (
M0), which has been suggested as the criterion to evaluate the safety of a person [
1]. The specific force is calculated using the flow velocity and the inundation depth as follows.
where
u is the flow velocity and
g is the gravity acceleration. Ishigaki et al. [
1] reported that normal males can safely escape from an underground space if
M0 < 0.125. To calculate Equation (2), the flow velocity was measured using the large scale particle image velocimetry (LSPIV) method. LSPIV was adopted because the flow depth was not sufficient for use of a contact type measurement device.
2.2. Development of the Algorithm
In this study, an image analysis method was used instead of contact-type measuring instruments to measure the inundation depth inside the subway station platform model in a flood. The experimental setting used for the image analysis method is shown in
Figure 3, in which the laser sheet and floating particles were used to make the pixel value at the water surface be the local maximum. The laser sheet formed on the water surface was used to take an ortho-image, which is an image without distortion of relative distance, of the inundation cross section using a digital camera as shown in
Figure 3b. To spread the laser sheet to the water surface in a vertical direction, the reflection angle was adjusted using the mirror, as shown in
Figure 3. The light intensity of the laser sheet was the brightest on the water surface and then gradually decreased in the water. Therefore, to clearly recognize the water surface, light-reflecting particles were spread so that the highest intensity light could be generated on the water surface.
Previous researchers proposed the Hough transform [
6] and correlation coefficients between image frames [
14] to analyze the water level from the captured images. However, these methods were not enough to reflect fluctuations in the water surface caused by water waves [
6]. Therefore, it is difficult to apply the existing method to the underground subway station model, in which the shape of the water surface rapidly changes over time due to the influence of the water waves generated by staircases. In this study, laser images capable of clearly expressing sudden changes in the water surface inside the underground subway station model were used, and an image analysis algorithm was developed and used to analyze water depth inside the subway station. The water depth measurement algorithm that uses laser images is shown in
Figure 4. First, an image captured by the camera was divided into several images and read by software. To filter out noise in an instantaneous image, the time-average technique was adopted. The time-average method shown in Equation (3) is a general method used to mitigate bias from fluctuating motion [
15].
where
T is the recording time,
p is the pixel value of the instantaneously captured image, (
i,
j) are the coordinates of each pixel, and
is the pixel value of the time-averaged image.
Figure 4 is a graph showing both the time series of pixel values (
p(
i,
j)) and the time-averaged values (
(
i,
j)) at a position on the water surface. In an image, the pixel value of the brightest point was 255 and that of the darkest point was zero. The
y-axis in
Figure 5 normalized the pixel value using the maximum value, i.e., 255.
Figure 5 shows that the variation in the pixel value gradually converges over time. Therefore, the pixel value for the (
i,
j) coordinates of the time-averaged image is stored in an (
N × M) matrix.
To separate the water surface from the pixel information stored in the matrix, the pixel information of each column vector was read. For laser images, as the light source entered from the top of the water as shown in
Figure 3, the strongest light reflected from the water surface due to the injected particles, and it was converted into the highest pixel value for each column vector. Therefore, the pixel value of each column vector gradually increased around the water surface and decreased after the pixel passed through the water surface. According to these characteristics of laser images, the row number,
i, for which the pixel value of the column vector had the same value as the local maximum, was stored as the pixel position of the water surface. Equation (4) was used to find the local maximum value of the pixel value.
The denominator of Equation (4) indicates a pixel size, which ranged from 0.29–0.53 mm in this study, and pixel size depended on the resolution of the digital camera and distance from the measurement section. Thus, the precision of water surface detection depends on the pixel size of an image. Through the iterative calculation process, row numbers corresponding to the water surface were determined at each column vector of the matrix, and the water surface positions in the image were extracted.
Figure 6 shows the results of analyzing the column vectors of the time-averaged image matrix in accordance with the algorithm in
Figure 4. The
y-axis in
Figure 6 is the number of the column vector and represents the
i-index of the matrix. A larger
i-index refers to the lower part of the image. As the light was reflected by the water surface, the pixel value was low over the water surface and gradually increased near the water surface due to the influence of the light reflected by the water surface. The pixel value dramatically increased on the water surface due to the floating particles, and the positions where the pixel values showed the local maximum values according to Equation (4) were selected as the water surface. In addition, the water surface could be distinguished because the light intensity gradually decreased in the lower part of the image, as shown in
Figure 6. The positions of the water surface were determined as the
i-index of the pixel of the water surface where
i = 71 in
Figure 6a and
i = 73 in
Figure 6b. After the positions of the water surface were determined, the water depth was calculated using Equation (5).
where
h is the water depth,
is is the pixel number of the water surface,
ib is the pixel number of the bottom, and
δz is the scale of a pixel size in the vertical direction.
Figure 7 shows the water depth determination procedure according to the algorithm in
Figure 4, using images captured in Sec. A.
Figure 7a shows the instantaneous image. The water surface exhibited a bright light from the reflected laser, and two bright layers were visible from the reflection of the acrylic wall. As the instantaneous image exhibited large fluctuations in the water surface, shown in the figure, a water surface close to a straight line was expressed using the time-averaged image, as shown in
Figure 7b. The pixel values from
Figure 7b were stored in matrix form and converted to pixel values as shown in
Figure 6a. When the position of the water surface was determined at each location, the pixels of the water surface could be extracted, as shown in
Figure 7c.
2.3. Verification of Inundation Depth Measurements
To verify the water depth obtained through the analysis of laser images, the value was compared with the water depth measured from the experiment channel. A scenario in which flow (
Q = 3.78 × 10
−4 m
3/s) entered from all four staircases had sufficient water depth to allow the use of the digital point gauge. The measurement results of water depth were compared using both the image analysis method and the digital point gauge (KENEK PH-340, C & V, Gyeonggi-do, Korea), which had an accuracy of ±0.04 mm. The inundation depth was measured under the conditions that rainwater flowed in from all staircases to secure sufficient water depth for using the water-level gauge. The measurements were carried out at three sections, as shown in
Figure 2, and the comparison results were plotted in
Figure 8. The image analysis method recognized the bubbles, which occurred from the fallen water from the staircases at the left side of Sec. A, as shown in
Figure 8a, as the water surface. Conversely, the water level gauge read the water depth under the bubbles. These differences caused measurement errors when using the image analysis method, and the mean absolute percentage error was 7.67%. For Sec. B and Sec. C, the results using the image analysis method showed similar distributions to the measurements using the digital point gauge. Especially in Sec. C, the curvature of the water surface caused by the staircases to B2F was well reflected in both measurement methods. Thus, the error compared to the measurements using the digital point gauge was 2.97% for Sec C. These results indicated that the water depth analysis results using the laser images accurately represent the actual water depth changes.