### Samples and equipment

Gypsum and calcium carbonate were selected as cement and sand was used as aggregate for the manufacture of test specimens. The proportion of materials (see Table 1) was designed based on He et al.31. A total of 10 specimens with a side length of 12 cm and a thickness of 3 cm were made according to the report. Some specimens have been shown in Fig. 1. During the experiments, the ambient temperature and humidity of the environment were maintained at 4°C and 70% respectively to prevent the moisture content of the specimens from evaporating too quickly.6. The REIGL VZ1000 3D laser scanner was used to monitor the moisture content in these experiments.

### Procedures and data processing

In this paper, the three experiments were designed to (1) assess sensitivity from relationships between laser reflection intensity and moisture content of samples; (2) explore the composite correlation of laser reflection intensity and two factors and how to correct for it and (3) investigate the accuracy of this method by comparing the recovered moisture content with the results measured by the drying method9.

#### Sensitivity experiment

To begin this process, a sample was scanned at 4 m and at normal incidence with a measurement interval of 24 h, then scanned at angles of incidence from 20° to 80° in 20° steps with a measurement interval 48 hours6while three other specimens were scanned at normal incidence with a measurement interval of 48 h at 4, 6, 8 and 10 m, respectively.

Each sample was immediately weighed and recorded accordingly after each scan. After the entire scan, all specimens were dried and their moisture content during each scan was calculated by the drying method.

The original laser reflection intensity of the obtained point cloud belonging to the sample area of ​​similar materials was extracted and output using Riscan support software.

The original laser reflection intensity is the ratio, which is usually less than zero, of the amplitude of the echo from the scanned target to that of the Lambertian white plane at the same distance and angle of incidence normal in extended target conditions30. To simplify the calculation, the original laser reflection intensity obtained was normalized between 0 and 1 according to

$$y , = {1}0^{{x/{1}0}} ,$$

(1)

where X is the original laser reflection intensity produced by the Riscan software and there is the normalized laser reflection intensity.

After the conversion, the normalized average intensity was taken as the laser reflection intensity of each scan, and the fit model between the laser reflection intensity and the moisture content of the samples was constructed and analyzed.

#### Angle of incidence and distance experiment

The second experiment mainly studied the laws of laser reflection intensity in response to the angle of incidence and the change in distance of the samples at two moisture contents which were calculated as the process of the first experiment. For an obvious comparison, the two humidity levels were below 2% and above 4% respectively. Specimens were placed at measurement distances of 2 m, 4 m, 6 m, 8 m, and 10 m, respectively. At each distance, they were rotated in steps of 10° depending on the article (see Fig. 2) from 0° to 80° during monitoring.

The process of receiving the returned laser pulse follows the radar range equation, which shows the relationship between received power, angle of incidence and distance26as following:

$${text{P}}_{{text{r}}} = {text{C}}rho {text{cos}}theta , /{text{R}}^{ {2}} ,$$

(2)

$${text{C }} = {text{ P}}_{{text{t}}} {text{D}}_{{text{r}}}^{{2}} eta_{{{text{sys}}}} /{4,}$$

(3)

where Pr is the received laser power, Pyou is the transmitted laser power, Dr is the receiver aperture diameter, ηsystem is the transmission coefficient of the optical system of the radar system, ρ is the average reflection coefficient of the extended target, R is the distance and θ is the angle of incidence26.32.

Since the method of receiving the laser pulse from the 3D laser scanner is similar to that of the radar system, the equation could be used to describe the process of receiving the laser pulse from the 3D laser scanner. Inside the receiver, the received laser power is transformed into laser intensity, so it can be considered that there is a functional relationship between them32as following

$$I , = , f , left( {P_{r} } right) , = , f , left( {theta , , R} right).$$

(4)

But this relationship is different in different receiving systems. Assuming the transformation model is a polynomial model26,30,32the composite relationships were established between the intensity of laser reflection and the angle of incidence as well as the distance of the samples at two different moisture contents, they were expressed as

$$I , = , lambda_{{1}} + , lambda_{{2}} R , + , lambda_{{3}} theta , + , lambda_{{4 }} R^{{2}} + , lambda_{{5}} theta^{{2}} .$$

(5)

Then, based on the selected normalization standard, the correction models were also established to correct the laser intensity data33. Their basic forms were:

$$i , / , i_{0} = , f , left( {theta , , R} right),$$

(6)

$$i_{cor} = , I , / , C,$$

(seven)

where θ is the radian of the angles of incidence, R is the distance, I is the laser reflection intensity at different angles of incidence and distances before correction, I0 is the selected standard intensity of the standard incidence angle and distance, Ihorn is the laser intensity corrected for different angles of incidence and distances, F(θ, R) is the established correction function, VS is the correction coefficient obtained from F(θ, R).

#### Precision experience

To study the accuracy of the method, the moisture contents obtained by laser scanning were compared to the actual moisture contents of each sample. The angle of incidence and the distance were fixed at 0° and 4 m. After each scan, the sample was also weighed and the subsequent process was the same as the first experiment.

The ambient temperature and humidity of the three experiments were the same, while the scanning method (see Fig. 3) was different. The designed scanning incidence angles and distances of the three experiments have been presented in Table 2.

According to the fitting model constructed in the first experiment, the moisture content of the sample was extracted from its laser reflection intensity and compared with its actual moisture content calculated by the drying method. The difference of the data obtained by two different measurement methods was used to calculate the RMSE based on the Bessel formula, and the RMSE was used to describe and evaluate the accuracy of the 3D laser scanning method under the monitoring conditions of 4 m and normal incidence.

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