Reconstruction and Measurement of Irregular Karst Caves Using BLST along the Shield Metro Line

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Accurate exploration of karst caves and the protection of springs.

Abstract

This study investigated the application of the borehole laser scanning technology (BLST) method in the detection of both dry and water-filled karst caves. In order to solve the problem of excessive laser attenuation during the detection, we designed a test for the characteristics of multiwavelength laser attenuation in water-filled karst caves and studied the influence exerted by various factors, including different wavelengths, different laser power levels, different suspended media, and effect of turbidity on the attenuation coefficient. During the test, we discovered the existence of a “blue-green window” with low turbidity and a “near infrared window” with high turbidity in karst cave water environments. Based on the general survey results of drilling and comprehensive geophysical prospecting, a quantitative method using targeted drilling was proposed to detect the spatial morphology of karst caves in complex environments. We also investigated the effects of complex environmental factors such as suspended media and high turbidity on the laser detection distance and accuracy in karst caves, and established a quantitative matching model of laser wavelengths, laser power, and complex environmental parameters. Based on this, we obtained the best acquisition mode for detecting lasers in different karst development environments. A high-precision, three-dimensional visualized model of a real karst cave was established to quantitatively obtain the characteristic parameters, such as accurate position, three-dimensional shape, space volume, and cave filling type, which was applied to the detection of karst caves along the Jinan subway line.

1. Introduction

As cities develop and urban populations increase rapidly, traffic congestion has become one of the greatest problems facing many cities in China. Metro systems, or subways, which makes full use of underground space and reduce congestion on the ground, have become an important part of urban infrastructure and a popular traffic choice for Chinese people in the 21st century [1,2,3,4]. Due to complex urban geologic conditions, a large number of metro tunnels have to pass through underground karst areas, such as the Jinan metro tunnel passing through water-rich hard rock karst cave areas, the Wuhan metro tunnel passing through honeycomb-shaped caves, and the Changsha metro tunnel passing through complicated underwater karst caves. The covertness of typical karst geological bodies such as karst caves increases the permeability of the rock structure and lowers relevant rock mechanical parameters, which may result in engineering disasters and hazards, including tunnel water bursting and inrush, water leakage, karst surface collapse, and shield cutterhead drooping, particularly when the caves bear both confined water pressure and shield tunneling disturbance [5,6]. It is no exaggeration that water inrush has become a serious threat to shield tunneling projects [7,8,9].

With the rapid development of computer technology, photogrammetry technology, and intelligent control technology, the detection of unfavorable geological bodies in tunnels and underground engineering projects utilizes more digital and quantitative methods and equipment with higher accuracy [10]. Currently, the common methods to detect cavity disaster sources, such as caves developed in the shallow karst areas, are drilling and geophysical exploration. The drilling method, as the most conventional and direct geological survey method, is especially suitable for detection in high-risk areas, such as underground karst caves. With a single borehole, one can obtain the approximate position, development height, and roof thickness of a karst cave at the borehole measuring point, while multiple boreholes can determine the horizontal boundary range of the karst cave. However, the drilling method lacks clear direction and is essentially a type of single-point detection method, during which the connection between boreholes can only be determined by empiricism and relevant calculation. This leads to the inevitability of blind areas, high costs, and consumption of time and labor [11]. The commonly used geophysical exploration methods, classified according to the exploration principles, include electrical methods (such as the high density electrical method), electromagnetic wave methods (such as the transient electromagnetic method and ground penetrating radar method), and seismic wave methods (such as the land sonar method) [12]. In the process of geophysical exploration, the detection capacity of geophysical exploration methods is limited by many factors, including the physical characteristics and spatial morphology of the detection medium or object, the geological structure and structural characteristics of the detection site, the hydrogeological conditions of the detection site, the topographic relief of the working face, the distribution of electromagnetic interference sources and interference bodies, the performance parameters of the devices, and the experience levels of the personnel operating the devices outdoors and processing and analyzing data indoors. Therefore, it is almost impossible to avoid fuzziness, multiplicity, and uncertainty in comprehensive geophysical exploration [13]. Consequently, drilling and comprehensive geophysical exploration methods cannot accurately detect karst cave boundaries in complex geological environments, rather can only deliver two-dimensional or even one-dimensional qualitative data with poor visualization effects and cannot provide quantitative parameters of karst caves, such as the accurate position and size information.

The rapid development and wide application of contactless drilling laser measurement technology provides a solution for the exploration of karst caves. The biggest advantage of this method is that the microlaser probe can adapt to various kinds of narrow channels and boreholes and can be inserted deeply into a cave to obtain the point cloud coordinate data. This method has been widely employed in many professional instruments for the exploration of poor geological structures, such as the Cavity Monitoring System (CMS) [14] and Cavity Autoscanning Laser System (C-ALS) [15]. Li [16] took the lead in applying borehole scanning technology in goaf detection, stability calculation, monitoring, and early warning. Luo [17] investigated the formation rules of point cloud grids and maximum angle triangles, the dominant vertex segmentation strategy, and the irregular triangle optimization method, and realized the three-dimensional modeling and visualization of scattered point clouds in complex goaf sections. Many scholars have also carried out a lot of research on point cloud data acquisition, reconstruction, and visualization [18,19]. At present, the research and relevant applications are mainly focused on the detection of goaf sections in relatively favorable environments, while the occurrence environment of karst caves along subway lines is extremely complex. Many scholars have carried out studies on laser transmission characteristics in water [20,21,22], most of which focused on the attenuation characteristics and detection effects of lasers in ocean water and showed that a “blue-green window” exists in ocean water; that is, blue and green lasers experience the least attenuation in ocean water [23]. However, the water environment inside a water-filled cave is much more complex than that in the ocean. Most of the media in a water-filled cave, such as CaCO₃, clay, and silt, are suspended. As a result, the optical reaction between the above-mentioned suspended media and the laser during its transmission is more complicated, and the attenuation characteristic of the laser is also more obvious, which result in the detection distance being extremely limited, and thus not meeting the requirements for karst cave detection. Moreover, the influence of complex environmental factors, such as cave humidity, dust concentration, water-filled media, and turbidity, on the laser point cloud detection and reconstruction is not clear. As a result, problems related to multinoise, multidistortion, and multinail factors in the karst cave model have not been effectively solved [24].

In summary, the cavity laser scanning method has the following advantages: (1) the ability to realize the quantitative and precise detection of cave position, size, filling state, and connectivity; (2) the ability to establish an actual and accurate cave model with a better visualization effect; (3) the ability to provide an accurate data basis to rationalize a treatment plan and guide the field workers to form reasonable treatment plans. For example, grout always runs out in the process of grouting the karst caves, which is mainly caused by groundwater flow or cracks in the connected pipes [25]. If the boundary shape, depth, size, volume, and internal connectivity of the karst cave can be accurately obtained, the stability evaluation of the surrounding rock in the shield tunnel will be largely improved, which is of great significance to the safe treatment of the karst areas. Therefore, we carried out an experimental study on the attenuation of a multiwavelength laser in complex karst cave water environment, the results of which will be used to guide the selection and optimization of laser detection in water-filled caves, in order to realize the maximum laser detection distance and the best detection effect of water-filled caves. The research achievements will be also applied to the Jinan subway project.

2. Multiwavelength Laser Attenuation Characteristics Test in Water-Filled Karst Caves

The main purpose of the multiwavelength laser attenuation test system is to investigate the attenuation characteristics of lasers with different wavelengths in water-filled caves in order to improve the detection distance of lasers in water. The test system includes a laser emission module, karst cave water environment simulation system, and a water turbidity and laser attenuation measurement system, as shown in Figure 1. Four kinds of suspended media were designed to simulate karst water, including silt, fine sand, clay, and CaCO₃. By controlling the quality of the suspended medium to simulate the water turbidity, five kinds of lasers with different wavelengths were designed, and the attenuation characteristics of lasers with different wavelengths and power levels in complex water-filled caves were studied through orthogonal tests.

2.1. Laser Attenuation Characteristics Test System

2.1.1. Multiwavelength Laser Emission Module

In order to study the influence of laser wavelength on attenuation characteristics more comprehensively, the laser emission module selected five kinds of lasers with typical wavelengths, as shown in

Table 1. Laser wavelength.

Type	Wavelength (nm)	Wavelength Selected (nm)
Blue-violet laser	405	405
Blue laser	450, 457, 473	450
Green laser	532	532
Near infrared laser	635, 660, 670, 671	650
Far infrared laser	808, 946, 980, 1047, 1064	808

. They were a blue-purple laser emitter (405 nm), blue laser emitter (450 nm), green laser emitter (532 nm), near infrared laser emitter (650 nm), and far infrared laser emitter (808 nm), respectively. The emitters had a glass window laser diode, emitted continuous dot lasers, employed an optical coated glass lens, and maintained a constant output power. Since the far infrared laser was beyond the normal observation wavelength range, this test adopted an infrared camera (modified from Canon EOS M3 camera) with a Canon Image Stabilizer lens and an infrared filter with a 780 nm wavelength. To observe the 808 nm laser beam more clearly, we used an f/4.0 aperture and set the exposure time to 1/160 and the ISO (International Standardization Organization) to 12800. During the test, we also utilized a laser-fixed triangle support, which ensured the stability of the fixed support with a maximum vertical adjustment range of 2 m; and a three-dimensional servo rotating head, which controlled the emission direction, angle, and height of the laser emitter. The head was equipped with a horizontal level to ensure horizontal emission of the emitter and avoid refraction with the glass as much as possible.

2.1.2. Simulation Module of Karst Cave Water Environment

This module can simulate the water turbidity under different suspended media conditions. According to the exploration data of spring strata, it was found that most of the suspended media in water-filled caverns are silt, clay, fine sand, and calcium carbonate. In this test, four kinds of suspended media were used: silt, clay, fine sand, and CaCO₃. Each medium was evaluated as one of five grades according to solubility, and the turbidity index was measured by a turbidity tester.

2.1.3. Measurement Module of Water Turbidity and Laser Attenuation

Turbidity, as a parameter to evaluate water quality, is used to quantitatively measure the degree of water opacity caused by particles. There are three main kinds of turbidity measurement methods: transmission, scattering, and scattering-transmission. Scattering-transmission measurement features the highest accuracy [23], and is also the most commonly method used at present. The water turbidity measurement module used a SGZ-200BS portable turbidimeter (made by Yuefeng Device Co., Ltd. Shanghai, China). Formazine was selected to prepare turbidity liquid samples with upper and lower limits. According to the international standard ISO7027, the unit of measurement of turbidity is NTU (Nephelometric Turbidity Unit).

The VLP-2000 laser power meter was selected in this test to measure the initial laser emission power and the power attenuated through the water simulator. The meter uses a pyroelectric probe and converts the laser light energy into thermal energy and then an electrical signal through the thermopile structure so that the laser power can be accurately measured. This device does not require wavelength calibration and features high resolution, fast measuring speed, convenience, and reliability. Its measuring range is 0–200 mw, and the accuracy can reach 0.1 mw. The laser power measurement module calculates the attenuation coefficient of the laser after passing through a certain distance of water by measuring the laser power before and after the attenuation of different wavelengths.

2.2. Definition of Laser Attenuation Coefficient

Here, we presume a collimated laser with a wavelength of $\lambda$ and radiation flux of $I(\lambda )$ enters into water perpendicular to the glass. During its transmission in the water simulator, if the transmission distance is $\mathrm{d}l$ and the radiation flux loss caused by water scattering and absorption is $\mathrm{d}I(\lambda )$, then the water attenuation coefficient is defined as:

$$C\left(\lambda \right)=-\frac{\mathrm{d}I\left(\lambda \right)}{I\left(\lambda \right)\mathrm{d}l}$$

(1)

Thus, the radiation flux of transmission distance $l$ of the laser in the water can be denoted as:

$$I\left(\lambda ,l\right)=I\left(\lambda ,0\right)\exp \left[-\underset{0}{\overset{l}{{\displaystyle \int }}}C\left(\lambda \right)\mathrm{d}l\right]$$

(2)

Presuming the attenuation coefficient remains constant during the transmission, Equation (2) can be modified as:

$$I\left(\lambda ,l\right)=I\left(\lambda ,0\right)\exp \left[-C\left(\lambda \right)\mathrm{d}l\right]=I\left(\lambda ,0\right)\exp \left[-l/l_0\left(\lambda \right)\right]$$

(3)

in which $l_0\left(\lambda \right)$ is also named the attenuation length.

In this test system, the laser first entered perpendicularly into and through the dry analog transparent box, and the laser intensity I₁ and I₂ detected initially and after the attenuation by the laser power meter were recorded. The splitting ratio of the beam splitting prism was set to K₁, and the attenuation rate of the glass before and after passing the transparent box was K₂. Under the condition of ensuring the vertical incidence of the laser, assuming that the transmittance between the glass and the air interface remains unchanged, the laser intensity after passing through the transparent box is:

$$I_2=I_1{K}_1{K}_2{}^2{T}_1{}^4$$

(4)

When the laser path remained constant, we filled the transparent box with water, and used the laser power meter to measure the light intensity at the initial stage and after attenuation, which were recorded as I_1′ and I_2′, respectively. It was assumed that the transmittance of the laser from the air to the transparent box glass was T₁, the transmittance of laser entering the water perpendicularly from the glass was T₂, the average attenuation coefficient of the laser in the simulated water in the transparent box was $\gamma$, and the length of the analog box was $l$. The light intensity after passing through the box was:

$$I_2^{\prime }=I_1^{\prime }{K}_1{K}_2{}^2{T}_1{}^2{T}_2{}^2{e}^{-\gamma l}$$

(5)

According to the Fresnel formula, under the condition of perpendicular entry of the laser,$T=\frac{4n_1{n}_2}{{\left(n_1+n_2\right)}^2}$, commonly the glass refraction index n₁ = 1.4985, and the water refraction index n₂ = 1.3228. It was assumed that the laser was attenuated to 1/1000 after passing through the dry, transparent analog box. By combining Equations (4) and (5), the average attenuation coefficient was:

$$\mathsf{\gamma }=-\frac{1}{l}\ln \left(\frac{I_2^{\prime }/I_1^{\prime }}{I_2/I_1}\times 0.927388\right)$$

(6)

3. Test Results

3.1. Attenuation Law of Lasers with the Same Wavelength in Different Suspended Media

Based on the above-mentioned test system, we recorded the laser emission power and attenuation power under the influence of different laser wavelengths, different suspended media, and different water turbidity grades, and calculated the corresponding laser attenuation coefficients using the above method.

(1) From the fitting curve in Figure 2a, it can be seen that when the laser wavelength is 405 nm, the suspended media are CaCO₃, silt, clay, and fine sand. For the laser suspended in the above media, the attenuation coefficient increases linearly with the increase of turbidity. The R² fitting degree values are 0.9956, 0.9802, 0.9945, and 0.9965, respectively. From the slope of the fitting curve, with the increase of turbidity, the increasing rate of the laser attenuation coefficient increases from CaCO₃ to clay, silt, and fine sand in turn. The particle size of CaCO₃ is about 5–10 μm, and the particle sizes of clay, silt, and fine sand are greater. When the laser wavelength is 405 nm, the rate of the laser attenuation coefficient increases with the increase of the medium particle size; that is, the slope of the fitting curve is γ _(CaCO3) < γ _(clay) < γ _(silt) < γ _(sand).

(2) When the laser wavelength is 450 nm, the fitting curve in Figure 2b shows that the attenuation coefficient increases linearly with the increase of turbidity in the solution of CaCO₃, silt, clay, and fine sand. The R² fitting degree values are 0.954, 0.9559, 0.9562, and 0.9964, respectively. With the increase of water turbidity, the increasing rate of corresponding attenuation coefficient is different in the CaCO₃, silt, fine sand, and clay media: the slope value of the fitting curve is γ _(CaCO3) < γ _(clay) < γ _(sand) < γ _(silt).

(3) When the laser wavelength is 532 nm, the attenuation coefficient also increases linearly with the increase of turbidity, and the R² fitting degree values are 0.9973, 0.9958, 0.9668, and 0.9938, respectively, as shown in Figure 2c. From the slope of the fitting curve, the attenuation coefficient rate increases from silt to CaCO₃, clay, and fine sand; that is, γ _(silt) < γ _(CaCO3) < γ _(clay) < γ _(sand).

(4) The attenuation coefficient of the 650 nm wavelength laser increases linearly with the increase of turbidity in the CaCO₃, silt, clay, and fine sand media, as shown in Figure 2d. The attenuation coefficient rate increases from silt to clay, CaCO₃, and fine sand; that is, γ_(silt) < γ_(clay) < γ_(CaCO3) < γ_(sand).

(5) According to Figure 2e, when the laser wavelength is 808 nm, the attenuation coefficient increases linearly with the increase of turbidity, and the R² fitting degrees rates are all higher than 0.98. Judging from the slope of the fitting curve, with the increase of water turbidity, the order of the increasing rate of attenuation coefficient from low to high is CaCO₃, fine sand, clay, and then silt. That is, the laser attenuation coefficient rate increases with the increase of the medium particle size.

3.2. Attenuation Law of Lasers with Different Wavelengths in the Same Suspended Media

3.2.1. CaCO₃ Suspended Medium

In CaCO₃ medium, comparing the lasers with wavelengths of 405 nm, 450 nm, 532 nm, 650 nm, and 808 nm, it can be seen from Figure 3a that the increasing rate of the laser attenuation coefficient is the lowest when the laser wavelength is 450 nm, and all of the attenuation coefficients are lower than those of other wavelengths. The cloud diagram of the laser attenuation coefficient with different wavelengths and different turbidity grades is shown in Figure 3b. When the laser wavelengths are 450 nm and 650 nm, there are two “ravines” with low attenuation coefficients. In order to compare the attenuation characteristics of 450 nm and 650 nm in depth, we adopted the above-mentioned fitting formula and solved the following two simultaneous equations:

$$Y=0.1784X+0.2174$$

(7)

$$Y=0.2508X-0.0796$$

(8)

When the turbidity is 4 NTU, the attenuation coefficients of the two lasers are equal. Thus, when the turbidity is lower than 4 NTU, the 650 nm laser is suggested, and when the turbidity is higher than 4 NTU, the 450 nm laser is suggested. However, considering that the turbidity of purified water is about 5 NTU and that the water environment in engineering projects is generally more turbid than purified water, the laser wavelength of water-filled cave detection should be 450 nm, requiring a blue wavelength laser.

3.2.2. Silt Suspended Medium

For silt, we compared lasers with wavelengths of 405 nm, 450 nm, 532 nm, 650 nm, and 808 nm. When the laser wavelength is 650 nm, the increasing rate of laser attenuation coefficient is the lowest with the increase of turbidity, as shown in Figure 4a. However, when the turbidity is relatively small, all the attenuation coefficients of the 450 nm laser are less than those of the 650 nm laser. With the increase of turbidity, the 650 nm laser is more advantageous. The cloud diagram of the laser attenuation coefficients with different wavelengths and turbidity grades in silt medium is shown in Figure 4b.

When the laser wavelengths are 450 nm and 650 nm, there are two “ravines” with low attenuation coefficients. In order to compare the 450 nm and 650 nm attenuation characteristics, we adopted the above-mentioned fitting formula and solved the following two simultaneous equations:

$$Y=0.2531X-1.2779$$

(9)

$$Y=0.1698Y+0.6587$$

(10)

When the turbidity is 225 NTU, the attenuation coefficients of the two are equal. Thus, when the turbidity is lower than 22.5 NTU, the 450 nm blue laser is suggested, and when the turbidity is higher than 22.5 NTU, the 650 nm near infrared laser is suggested. This is obviously different from the conventional marine water “blue-green window”. In karst cave water environments with high turbidity, the near infrared wavelength laser suffers less attenuation and can achieve longer detection distances.

3.2.3. Clay Suspended Medium

When the suspended medium is clay, the curve of attenuation coefficient with turbidity is shown in Figure 5a. We compared the lasers with wavelengths of 405 nm, 450 nm, 532 nm, 650 nm, and 808 nm. When the laser wavelength is 650 nm, the increasing rate of laser attenuation coefficient is the lowest with the increase of turbidity. When the turbidity is lower than approximately 25 NTU, the 450 nm laser attenuation coefficients are all less than 650 nm. With the increase of turbidity, the 650 nm laser is more advantageous. The cloud diagram of the laser attenuation coefficients with different wavelengths and different turbidity grades is shown in Figure 5b.

When the laser wavelengths are 450 nm and 650 nm, there are two “ravines” with low attenuation coefficients. We adopted the above-mentioned fitting formula and solved the following two simultaneous equations:

$$Y=0.3412X-1.6622$$

(11)

$$Y=0.2203X+1.602$$

(12)

When the turbidity is 27 NTU, the attenuation coefficients of the two are equal. Thus, when the turbidity is lower than 27 NTU, the 450 nm laser is suggested, and when the turbidity is higher than 27 NTU, the 650 nm laser is suggested. This follows the same law as for silt.

3.2.4. Fine Sand Suspended Medium

For a suspended medium of fine sand, we compared the lasers with wavelengths of 405 nm, 450 nm, 532 nm, 650 nm, and 808 nm. When the laser wavelength is 450 nm, the increasing rate of the laser attenuation coefficient is the lowest with the increase of turbidity. When the turbidity is lower than 40 NTU, the 450 nm laser attenuation coefficients are all less than those of lasers with other wavelengths, as shown in Figure 6a. The cloud diagram of laser attenuation coefficients with different wavelengths and different turbidity grades in fine sand medium is shown in Figure 6b. In order to compare the attenuation characteristics of 450 nm and 650 nm lasers in fine sand medium, we solved the following two simultaneous equations:

$$Y=0.30205X-0.89683$$

(13)

$$Y=0.5807X+0.40815$$

(14)

When the turbidity is −4.7 NTU, the attenuation coefficients of the two are equal. Since the water turbidity grades are all higher than 0, when the suspended medium is fine sand, the 450 nm laser is suggested.

From the above results, it can be seen that the “blue and green window”, which is widely used in marine water, is not suitable for the complex water-filled environment typical of karst caves. When a karst cave is filled with water in order to dissolve the particles of CaCO₃, silt, and clay, the attenuation coefficient of the blue light wavelength (450 nm) is the lowest when the turbidity is low, and the attenuation coefficient in the near infrared wavelength (650 nm) is the smallest when the turbidity is high. Chen [26] also mentioned the existence of a “near infrared window” in water with high turbidity. When the water contains medium fine sand with large particles, the precipitation rate is fast. However, some fine sand particles will still be suspended over the period of time when the attenuation coefficient of the blue laser with a wavelength of 450 nm is the smallest.

At present, the lasers are extensively applied in the detection of ocean water, which mainly includes a variety of ions, such as Na⁺, Mg²⁺, Ca²⁺, and Cl⁻. However, abundant suspended particles in the cave water and the particle size and mass can have great effects on the laser attenuation coefficient. The characteristics and weights of different suspended particles will lead to great differences in scattering intensity. Large wavelength lasers have greater penetration, resulting in different slopes of the fitted curve.

3.3. Attenuation Law of Lasers with Different Power Levels

In order to study the relationship between the laser attenuation coefficient and laser emission power in the complex water environment of a karst cave, we selected several laser emitters with a wavelength of 650 nm and emission power levels of 100 mw, 200 mw, and 300 mw, respectively, and used the same suspended medium in the water. Then, the corresponding laser attenuation coefficients were measured, and the laser attenuation coefficient turbidity curve was drawn, which is shown in Figure 7. According to the curve, when the suspended media are CaCO₃, silt, clay, and fine sand, the attenuation coefficient of a laser of the same power level increases linearly with the increase of turbidity. When the turbidity remains constant, the larger the laser emission power of the same wavelength, the smaller the corresponding attenuation coefficient will be, and when the turbidity is relatively high, the differences in the attenuation coefficients of lasers of different power levels are larger. Judging from the attenuation coefficients of lasers of different power levels, the lasers with higher power have lower attenuation coefficients in the water. However, high-power lasers cause harm to the operators. Therefore, the selection principle of laser power is based on ensuring the safety of personnel. It is better to select a laser with higher power to better meet the laser detection distance requirements of large water-filled karst caves.

3.4. Optimization Scheme of Longest Laser Detection Distance

First of all, the selection of the laser wavelength is mainly based on the suspended medium and turbidity of the cave water environments.

Table 2. Maximum detection range and laser wavelength selection recommendation.

Medium		Turbidity (NTU)	10	20	30	40	50
	Length (nm)
CaCO3	405		1.63	0.85	0.58	0.44	0.35
	450		1.95	1.03	0.70	0.53	0.43
	532		0.83	0.54	0.40	0.32	0.27
	650		1.61	0.79	0.52	0.39	0.31
	808		0.85	0.57	0.43	0.34	0.29
Laser wavelength suggested (nm)			450	450	450	450	450
Silt	405		1.02	0.61	0.44	0.34	0.28
	450		3.11	1.03	0.62	0.44	0.34
	532		1.12	0.70	0.50	0.40	0.32
	650		1.65	0.96	0.68	0.52	0.43
	808		1.05	0.55	0.37	0.28	0.23
Laser wavelength suggested (nm)			450	450	650	650	650
Clay	405		1.26	0.71	0.49	0.38	0.30
	450		2.23	0.76	0.45	0.33	0.25
	532		0.64	0.43	0.33	0.26	0.22
	650		1.02	0.65	0.47	0.37	0.31
	808		0.86	0.54	0.40	0.31	0.26
Laser wavelength suggested (nm)			450	450	650	650	650
SiO2	405		1.25	0.66	0.45	0.34	0.27
	450		1.84	0.76	0.48	0.35	0.27
	532		0.59	0.36	0.26	0.21	0.17
	650		0.63	0.32	0.22	0.17	0.13
	808		0.74	0.52	0.40	0.32	0.27
Laser wavelength suggested (nm)			450	450	450	450	450

gives the maximum detection ranges of a multiwavelength laser in different suspended media and with different turbidity levels. It can be seen from Table 2 that no matter what kind of suspended medium is used, the 450 nm wavelength laser is suitable in water environments with low turbidity, while for clay and silt media, when the turbidity is about 25 NTU, the detection distance of the 650 nm laser is longer. Combined with the field geological data and actual borehole data, by distinguishing the type of suspended medium and turbidity grade of water-filled karst caves, the laser with the appropriate corresponding wavelength is selected to increase the maximum detection distance.

Secondly, in the selection of laser power,

Table 3. Maximum detection range and laser power selection recommendation table.

Medium		Turbidity (NTU)	5	10	20	30	40
	Power (mw)
CaCO3	100		2.32	1.32	0.71	0.48	0.37
	200		4.63	2.17	1.05	0.69	0.52
	300		9.55	3.22	1.39	0.88	0.65
Maximum differential times			4.12	2.45	1.96	1.83	1.77
Silt	100		3.25	1.49	0.72	0.47	0.35
	200		5.78	1.93	0.83	0.53	0.39
	300		6.07	3.05	1.10	0.67	0.48
Maximum differential times			1.87	2.05	1.53	1.42	1.37
Clay	100		1.70	0.96	0.52	0.35	0.27
	200		3.77	1.75	0.85	0.56	0.42
	300		6.16	3.39	1.23	0.75	0.54
Maximum differential times			3.63	3.52	2.37	2.12	2.01
SiO2	100		1.14	0.68	0.37	0.26	0.20
	200		2.06	0.99	0.48	0.32	0.24
	300		4.31	1.36	0.57	0.36	0.27
Maximum differential times			3.77	2.01	1.55	1.42	1.36

gives the maximum detection distances of lasers of various power levels in different suspended media with different turbidity grades. When only considering the maximum detection distance, a laser with higher power should be selected to meet the long detection distance requirements for water-filled caves. However, to ensure the safety of personnel, the selected laser power is generally lower than 5 milliwatt, as it will otherwise cause harm to the operator’s eyes. Many devices put an emphasis on eye protection, such as the C-ALS produced by MDL (Measurement Devices Ltd) Company (UK) adopting FDA (Food and Drug Administration) IEC (International Electrotechical Commission) first-class laser eye protection and the CMS system produced by Optech Company of Canada adopting FDA 21 CFR1040 first-class laser eye protection. On the premise of ensuring the safety of personnel, a laser with higher power should be selected.

Thirdly, the evaluation of the detection environment is mainly based on the type of suspended medium in the water-filled cave and the corresponding turbidity. The specific types of suspended media can be preliminarily judged in combination with the sampled water quality. If the field conditions permit, the water quality turbidity can be sampled and detected for further quantitative grade classification [26].

4. Fine Measurement and Reconstruction of Complex Karst Caves

4.1. Borehole Laser Scanning Technology (BLST) Automatic Laser Scanning System in Karst Caves

At present, laser scanning technology has been widely used in tunnels and underground engineering projects, such as in the acquisition of rock mass structural plane information, the deformation of roadway surrounding rock, the establishment of rock mass models, and even for noncontact monitoring. Most of the above applications use vertical laser scanning technology in large operating spaces, however karst caves are usually concealed. Even if the location and depth of karst caves are obtained by drilling and comprehensive geophysical prospecting, the vertical laser scanner cannot enter the interior of the cave to assess the parameters due to instrument size limitation. Thus, it is necessary to use a laser detection system that can enter inside the cave through a narrow drilling channel. The C-ALS is the first laser automatic scanning drilling device developed by MDL (UK), which consists of a laser ranging module, three-dimensional servo mechanical control system, data transmission system, and data processing system. Its greatest advantage is that the laser probe is miniaturized with a diameter of only 5 cm, which can be used to enter the karst cave through narrow boreholes and carry out three-dimensional scanning of rock mass surfaces. The main structure of the C-ALS is shown in Figure 8.

The drilling laser scanning system is based on the laser ranging principle to obtain the point cloud coordinate data. The probe has a 3D navigation system that can read the depth of the probe in real time, so as to obtain the exact location of the karst cave. Through the three-dimensional mechanical servo rotation system, the three-dimensional scanning state of the laser ranging probe are controlled, and the three-dimensional point cloud coordinates of the inner wall of the cave are measured. Finally, the point cloud model is encapsulated to form a real cave model by using point cloud processing software to realize the precise exploration of the location, shape, and volume of the karst caves. The operation process is as follows: (a) Targeted drilling. Based on the results of drilling and comprehensive geophysical exploration, the location of the targeted drilling is determined and the drilling is carried out to provide the downward exploration channel for the laser probe. (b) The laser probe is lowered inside the cave, and the laser emission module is adjusted to prepare the cave point cloud for detection. (c) Point cloud scanning. The laser ranging module emits and receives the laser, and the corresponding point cloud coordinates are calculated according to the three-dimensional coordinates and angles. (d) Point cloud model processing. Through the C-ALS software, the point cloud model is obtained and then encapsulated to form a real cave model, in order to obtain the cave size, shape, volume, and other parameters, as shown in Figure 9.

4.2. Solution of Complex Cave Point Cloud Coordinates

One side of the laser ranging module is equipped with a laser transmitter and a laser receiver. After the laser emitter emits the laser, the laser transmitter transmits the laser for a certain distance until reaching the wall of the karst cave, where it is then transmitted back and received by the laser receiver. The distance between the laser emitter and the measuring point of the cave wall can be expressed as:

$$S=\frac{1}{2}c\Delta t$$

(15)

in which $S$ is the distance between the emitter and the measuring point on the cave wall, c is the transmission speed of the laser through the media, and $\Delta t$ is the time taken for the laser to be emitted and received.

After the distance $S$ is calculated using $c$ and $\Delta t$, the relative coordinate values of the karst cave wall point can be obtained based on the horizontal and vertical rotation angles of the laser ranging module. As shown in Figure 10, O is set as the laser emission point with the coordinates $\left(x_0,y_0,z_0\right)$, P is set as the point to be measured on the cave wall with the coordinates $\left(x,y,z\right)$, $\alpha$ is set as the horizontal rotation angle, and $\beta$ is set as the vertical rotation angle; then, the relative coordinate value of p is:

$$x=S\cos \beta \cos \alpha$$

(16)

$$y=S\cos \beta \sin \alpha$$

(17)

$$z=S\sin \beta$$

(18)

The absolute coordinate value of p is:

$$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\frac{1}{2}c\Delta t·\left[\begin{array}{ccc}\cos \beta \cos \alpha & 0& 0\\ 0& \cos \beta \sin \alpha & 0\\ 0& 0& \sin \beta \end{array}\right]+\left[\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right]$$

(19)

The factors affecting the accuracy of cave shape acquisition are as follows: the high irregularity of cave shapes, the laser detection beam being blocked by internal surrounding rock, irregular rock columns, and irregular fillings, which result in a single detection not covering the complete internal boundaries of a cave, and thus allowing the presence of local detection “blind spots”. The size of a dry karst cave is generally within the laser detection range. When there is a large water-filled cave, due to the rapid attenuation of lasers in water, the detection distance is limited, and single-station detection cannot cover the whole cave. Multistation detection is, thus, required for point cloud data splicing. The accuracy of laser ranging decreases with the increase of detection distance, resulting in low detection accuracy, as point clouds are dense near karst caves and are sparse far from the caves. Under these conditions, it is also necessary to carry out multistation detection to eliminate the local detection blind spots of the cave and ensure the refinement and accuracy of the cave boundary shape.

The key to the splicing of multiple detection point clouds is the transformation of the detection coordinate system. Taking the detection of two stations as an example, it is assumed that the coordinate system of one station is $o-xyz$ and the other is $o^{\prime }-x^{\prime }{y}^{\prime }{z}^{\prime }$. In the transformation process, the coordinate system $o^{\prime }-x^{\prime }{y}^{\prime }{z}^{\prime }$ can be obtained by rotating the coordinate system $o-xyz$ around the three coordinate axes and with the matrix translation, which can be expressed by Equation (20).

$$\left[\begin{array}{c}{x}^{\prime }\\ y^{\prime }\\ z^{\prime }\end{array}\right]=\nu R(\alpha ,\beta ,\gamma )\left[\begin{array}{c}x\\ y\\ z\end{array}\right]+T$$

(20)

in which the translated matrix T can be described by x₀, y₀, and z₀, the three translation amounts in the three-dimensional axes:

$$T=\left[\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right]$$

(21)

Equations (20) and (21) include 7 parameters: 3 rotation parameters ($\alpha ,\beta ,\gamma$), 3 translation parameters $\left(x_0,y_0,z_0\right)$, and a scale factor. The acquisition of the karst cave cloud coordinates can be regarded as a rigid process without any scale changes; thus, the scale factor v is 1 in the solution process. The rotation angles of the coordinate system $o-xyz$ around the x, y, and z axes are defined as $\alpha ,\beta ,\gamma$, respectively. The coordinate system $o-xyz$ is translated along x, y, and z axes into $o^{\prime }-x^{\prime }{y}^{\prime }{z}^{\prime }$. The rotation matrices around the x, y, and z axes are:

$$R_x(\alpha )=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \alpha & \sin \alpha \\ 0& -\sin \alpha & \cos \alpha \end{array}\right]$$

(22)

$$R_y(\beta )=\left[\begin{array}{ccc}\cos \beta & 0& \sin \beta \\ 0& 1& 0\\ -\sin \beta & 0& \cos \beta \end{array}\right]$$

(23)

$$R_z(\gamma )=\left[\begin{array}{ccc}\cos \gamma & \sin \gamma & 0\\ -\sin \gamma & \cos \gamma & 0\\ 0& 0& 1\end{array}\right]$$

(24)

Since $R\left(\alpha ,\beta ,\gamma \right)=R_x\left(\alpha \right)\cdot R_y\left(\beta \right)\cdot R_z(\gamma )$, the following can be obtained:

$$R(\alpha ,\beta ,\gamma )=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \alpha & \sin \alpha \\ 0& -\sin \alpha & \cos \alpha \end{array}\right]\left[\begin{array}{ccc}\cos \beta & 0& \sin \beta \\ 0& 1& 0\\ -\sin \beta & 0& \cos \beta \end{array}\right]\left[\begin{array}{ccc}\cos \gamma & \sin \gamma & 0\\ -\sin \gamma & \cos \gamma & 0\\ 0& 0& 1\end{array}\right]$$

(25)

$$R(\alpha ,\beta ,\gamma )=\left[\begin{array}{ccc}\cos \beta \cos \gamma & \cos \beta \sin \gamma & -\sin \beta \\ -\cos \alpha \sin \gamma +\sin \alpha \sin \beta \cos \gamma & \cos \alpha \cos \gamma +\sin \alpha \sin \beta \sin \gamma & \sin \alpha \cos \beta \\ \sin \alpha \sin \gamma +\cos \alpha \sin \beta \cos \gamma & -\sin \alpha \cos \gamma +\cos \alpha \sin \beta \sin \gamma & \cos \alpha \cos \beta \end{array}\right]$$

(26)

During the scanning of the cave point clouds at two stations, the three-dimensional coordinates of the laser emission points are obtained; that is, the corresponding translation matrix T is known, and the rotation adjustment state $R(\alpha ,\beta ,\gamma )$ of the laser emission probe and the corresponding coordinate system scanning results are also known. The point cloud coordinates in the coordinate system $o^{\prime }-x^{\prime }{y}^{\prime }{z}^{\prime }$ can be calculated and obtained by Equation (20). Based on this, the point cloud data of several stations can be converted and spliced, and the multistation exploration and point cloud splicing of complex karst caves and large-scale karst caves can be realized.

5. Case Study in Jinan Metro

5.1. Overview of the Project

Jinan is a historical and cultural city famous for various springs, which can represent the city culture. Therefore, in line with the idea of being responsible for the history and future of Jinan, during the metro construction, the spring must be properly protected, which brings more challenging requirements for the safe construction of the metro tunnels. At present, the planned Jinan rail transit line includes two levels: the urban core area fast line (Line R) is under construction, and the central urban area general line (Line M) is still in planning. The Jinan rail transit construction line is shown in Figure 11a. There are a large number of caves in the karst areas along Line R, while the planned line M will pass through the exposed and sensitive areas of the spring core. A large number of springs are exposed in the sensitive spring area, which has a shallow limestone roof and rich karst water. This area is classified as an extreme water-rich area with a large number of karst caves, weathering fissures, and structural fissures in magmatic rocks. Considering the complexity of groundwater in spring areas and the significance of protecting the springs, there will be great challenges in the safe construction of the Jinan metro.

The section of rail transit line R1 from Wangfuzhuang to Dayangzhuang in Jinan was constructed using the shield method. This section is located in the most water-rich degree area in the central and western part of Jinan. In this area, the water supply source is sufficient, the water output of a single fractured karst water well reaches 10,000 m³/d, and the cave is pressure-bearing. The maximum water level elevation is about 8 m above the arch of the shield tunnel. In the middle of the weathered limestone under the K30 + 460.3–K31 + 362.2 mileage section, the karst in this section has been largely developed and is rich in water. The pressure-bearing karst caves were easily exposed in the shield tunnel construction process, which in the future may induce water inrush disasters, threaten the safety of workers, and impede construction progress. The interval geological profile is shown in Figure 11b. When the shield machine tunneled to K31 + 342.355, the phenomenon of high water pressure and large-flow water inrush appeared at the tunnel face, and it was found that the water inrush increased. This could result in a series of problems, such as poor slag soil properties and transportation difficulty, seriously reducing the tunneling efficiency [29]. The inrush of water from the excavation face is shown in Figure 11c, showing an obvious large flow rate that is pressure bearing.

5.2. Detection of Complex Karst Caves and Three-Dimensional Data Acquisition

The main idea of this exploration is to accurately locate the karst cave based on the drilling and comprehensive geophysical prospecting methods, and then use the BLST method to obtain the morphology and characteristic parameters of the karst cave. On the basis of the results of comprehensive geophysical prospecting and drilling, the key points and abnormally complex areas are highlighted. The cross-hole resistivity CT method, owing to its high resolution, has great advantages in the detection of complex water diversion channels. Therefore, this method was adopted for fine detection to obtain the accurate positions of karst caves. In view of the fact that there are a large number of karst caves, pipelines, and cracks along the metro tunnel, only the disaster sources were selected for accurate laser scanning, such as karst caves and cracks, which are large in scale and present serious challenges in the grouting process. Targeted drilling was carried out and a karst cave point cloud model was reconstructed.

The three-dimensional laser scanning detection system consists of a microlaser probe, a directional rod, cable wires, and a point cloud data acquisition and processing system. The microlaser probe entered the interior of the cave through targeted drilling and scanned the cave quickly to construct the three-dimensional shape of the cave and then extract the corresponding characteristic parameters, including the volume and depth of the karst cave. The laser probe had a built-in 3D navigation module to measure the position and direction of the probe in the cave in real time, and accurately record the x, y, and z coordinates and azimuth of the probe. The probe, which integrates a camera and an infrared lighting system, is able to monitor the movement of itself in the borehole and eschew obstacles or depressions in time to avoid any damage. The fine detection of a karst cave mainly includes two parts: field detection and indoor data processing. First, the measurement and layout of boreholes should be carried out and arranged before laser scanning and detection, so as to fully know about the on-site detection environment. Then, the detection devices are assembled and debugged, confirming that the detection system works properly. The laser probe with cable wires is lowered along the pipe vertically to monitor the internal borehole environment in real time. When the probe reaches the predetermined cave position, the depth meter is read, the data is recorded, and the mechanical scanning and accuracy parameters are set; then, the microprobe begins to measure the point clouds, and the cavity scan system simultaneously collects the point cloud data. After the scanning task is completed, the probe moves up and the field collection work finishes. The detailed steps are shown in Figure 12.

Based on the results of field drilling and comprehensive geophysical exploration, the borehole scanning method was used to locate and quantitatively detect karst caves at 6 borehole locations (17#, 20#, 21#, 23#, 24#, 25#). The detection results are as follows: a karst cave with a volume of 3.02 m³ was measured at the borehole 17# location, at a depth of about 15.4 m; the detailed morphology and characteristic parameters of the karst cave are shown in Figure 12a, recorded as KC1. A cave with a volume of 3.89 m³ was measured at location 20#, at a depth of about 11.8 m; the three-dimensional model of the cave is shown in Figure 12b, recorded as KC2. A karst cave with a volume of 3.66 m³ was measured at borehole location 21#, at a depth of about 1 m; the three-dimensional model of the karst cave is shown in Figure 12c, recorded as KC3. A water-bearing cave with a volume of about 3.84 m³ was measured at location 23#, at a depth of about 15.7 m; the three-dimensional model of the cave is shown in Figure 12d, recorded as KC4. A half water-filled cave with a volume of 3.15 m³ was measured at borehole location 24#, at a depth of about 28.6 m; the three-dimensional model of the cave is shown in Figure 12e, recorded as KC5. A water-filled cave with a volume of 3.71 m³ was measured at borehole location 25#, at a depth of about 22.7 m; the three-dimensional model of the cave is shown in Figure 12f, recorded as KC6.

According to the above-mentioned detection results, the exact spatial position of the cave was obtained, including the corresponding horizontal coordinates and depth. Combining the tunnel route design diagram, the relative spatial position relationship between the karst cave and the tunnel was calculated. Figure 13a shows the exact orientation and distance of the karst cave in the circumferential direction of the tunnel; while Figure 13b shows the exact position of the karst cave in the excavation range in front of the tunnel, and the diagram of the vertical section and plane position between the cave and the tunnel. According to the spatial position relationships between karst caves and the tunnel, the distances and orientations between the karst caves and the tunnel were calculated, as shown in

Table 4. Parameters of irregular caverns.

Karst Cave Number	Orientation (°)	Vertical Distance (m)	Horizontal Distance (m)	Actual Distance (m)	Volume (m3)
1	317.39	2.9	2.4	5.14	3.02
2	42.89	6.5	5.8	10.09	3.89
3	31.32	3.3	0.7	4.43	3.66
4	7.67	2.6	0.8	2.65	3.84
5	170.19	3.6	1.2	3.70	3.15
6	90	0.9	0	-	3.71

.

6. Conclusions

(1) This paper discussed the application effect of laser point cloud scanning in dry caves and water-filled caves, designed a multiwavelength laser attenuation characteristic test for water-filled caves in order to solve the problem of excessive laser attenuation in the detection of water-filled caves, and investigated the effects of different laser wavelengths, different laser power levels, different suspended media, and different turbidity grades on the laser attenuation coefficient.

(2) The effects of laser wavelength, power, and karst cave water environments on the attenuation characteristics were revealed, and the existence of a “blue-green window” with low turbidity and “near infrared window” with high turbidity were discovered. The laser attenuation coefficients of different wavelengths increased linearly with the increase of turbidity, while the laser attenuation coefficients decreased with the increase of laser power. When the suspended media were CaCO₃ and fine sand, the attenuation of the 450 nm blue laser was the lowest; when the media were silt and clay, the attenuation of the 450 nm wavelength laser was the lowest with low cave water turbidity, and the attenuation of 650 nm wavelength laser was the lowest with high turbidity, for which 23.23 NTU and 27 NTU are the critical points of high or low turbidity, respectively.

(3) In this paper, an optimization scheme for the maximum laser detection distance in complex karst cave water environments was proposed, and the three-dimensional point cloud acquisition method for karst cave shapes was created. These methods can realize coordinate splicing of multistation detection point clouds in complex karst caves, and can be applied for the detection of karst caves along the Jinan metro line.