A novel approach to measuring pore fluid sediment concentrations of debris flows in a volcanic torrent

. Pore fluid in a debris flow is not fully understood, despite its contribution to the fluidity of the debris flow. To observe sediment concentrations of the pore fluids in debris flows, we established a novel monitoring system in a volcanic catchment, in southern Japan. An observation culvert, 1.0 m in width, 1.5 m in height and 2.0 m in length, was placed along the stream bank. An intake covered by a grating was equipped on the side of the culvert so that only pore fluid of debris flows was led inside. Measurements of dielectric permittivities were conducted within the culvert and used for the calculation of sediment concentrations of the fluid. The sediment concentrations of the pore fluid were successfully measured for natural debris flows. The preliminary observation revealed that the volumetric sediment concentration of pore fluid varied from approximately 5 to 69 %, which were slightly smaller or similar to those of the entire debris flows. Successive occurrences of debris flow caused decreases in the sediment concentration of the pore fluids with each surge.


Introduction
Debris flows typically contain sediments of various grain sizes (i.e., from clay to boulders). Whereas coarser particles behave as solid phase in debris flows, water and finer particles such as clay and silt may compose pore fluids also as known as interstitial fluids. The fine sediments in pore fluids can influence the pore fluid pressure and shear behaviour [1].
To understand the flow mechanism of debris flows, detail measurements of debris flows are required in natural torrents as well as experimental flumes. As debris flows are severe and destructive phenomena, noncontact measurements such as ultrasonic sensors, vibration sensors, and videos are commonly used in debris flow observation stations [2]. Thus, internal information of natural debris flows is still insufficient.
Field observations of load and pressures at the channel beds have revealed the pore fluid pressures consists of predicted hydrostatic and excessive pressures [3,4]. The pore fluid pressures higher than the predicted hydrostatic pressures potentially influence the fluidity and run-out distance of debris flows [5]. The hydrostatic pressure can be estimated by the flow height and the concentrations of suspended sediment in the pore fluid. Recent studies revealed measurement results of the pore fluid pressure in natural torrents [6,7]. Information of the sediment concentrations of the pore fluid in a debris flow can be a breakthrough of understanding flow mechanism of debris flows. * Corresponding author: miyata.shusuke.2e@kyoto--uc.jp This study aimed to propose a novel approach to measuring sediment concentrations of pore fluids of natural debris flows. TDR (time domain reflectometry) measurements enabled us to estimate sediment concentrations of pore fluids. The measurement system was installed in a culvert with an intake of the pore fluids, which was fixed on the bank of a debris flow prone channel.

Application of TDR to sediment concentration measurement
A TDR measurement yields the dielectric permittivity of a target substance. If it is assumed that a debris flow consists of only water and sediment particles, the pore fluid is also composed by water and fine sediment particles. The dielectric permittivity of the pore fluid can be calculated using the volumetric mixing model. The square root of the complex dielectric permittivity of the turbid water is calculated using the dielectric permittivities of the water and the sediment particles, as follows: where Cf is the volumetric sediment concentration of pore fluid. The dielectric permittivities of water and sediment particles are known parameters ( = 78.3 at 25 °C and = 5.27 in this study). The value was referred from the previous study in which the sediment samples collected at this study site was applied for a dielectric permittivity test. The volumetric concentration is expressed as: Our previous study has demonstrated that the dielectric permittivity measurement is applicable to obtain volumetric suspended sediment concentrations of stream water higher than 2 % [8]. A comparison between the dielectric permittivity measurement and bottle samples in a glacier fed stream revealed that the 95 % confidence intervals of the estimated sediment concentration were approximately equivalent to the observed concentrations (i.e., 2SD ≈ 1.0) [9]. As the pore fluids of debris flows typically contain greater fractions of sediment particles than those of river flows, this method is expected to estimate the sediment concentrations of pore fluids.

Materials and Methods
The field observations were conducted in the Arimura River catchment, which is in a volcano, Sakurajima, southern Japan (Fig. 1). The volcano erupts frequently and supplies sediment to the headwaters of the catchment. The average channel slope is 1/4.2 and the catchment area is 4.22 km 2 [4]. The channel has ephemeral flows only during storms and experiences about 10 debris flows in a year. Check dams and channel works have been constructed to mitigate the damage of the debris flows. Various equipment such as camera, load cells, ultrasonic stage sensors have been established to observe the debris flows at the most upper check dam shown in Fig. 1b.
We installed an observation culvert about 50 m upstream of the check dam (Figs. 1b-d). The observation culvert was fixed at the left bank of the channel, and the gap between the culvert and the bank was filled with concrete and protected by boulders collected in the field. The culvert has the outlet with 1.5 m in height and 1.0 in width and equips intake window of 0.8 m by 0.8 m at the side. A grating of 0.033-m spacing was mounted on the intake window to filter coarser particles of debris flows. Therefore, the pore fluid, mixture of water and fine sediment particles, flowed through the culvert with the least disturbance to the debris flows.
Pressure-type water level gauges, TDR sensors, an electromagnetic velocity meter, and a vibration meter were installed in the observation culvert (Fig. 1e). The pressure water level gauges were installed at 10, 40, and 70 cm above the culvert bed. The TDR sensors were installed at the heights of 10, 30, 50, and 70 cm to measure dielectric permittivities and water temperatures. The TDR sensors were placed to avoid the influences of the wall and bottom surfaces and other sensors on the resultant permittivities. To validate the flows within the observation culvert, the flow velocity meter was placed close to the outlet. The vibration meter was fixed to the ceiling of the culvert. These measurements were conducted every 5 seconds and began in March 2021.
The entire debris flows were observed at the check dam (Fig. 1b). An ultrasonic velocity and flow stage meter, CCTV cameras and load cell system have been operated since 2012 [5]. When malfunctions of the velocity meter and/or flow stage meter, the velocity and flow depth were estimated from the video. The load cell system with the surface area of 2 m by 4 m is installed at the left bank of the dam crest and measured total weights of the debris flows at 100 Hz of the sampling rate. The volumetric sediment concentration of an entire debris flow Cv were obtained by dividing the weight per unit area by the flow depth. Precipitation was observed by a X-band MP radar.

Deposits in the culvert
Several debris flows and floods took place after the installation of the observation culvert in 2021. The photos during the evets showed that muddy fluids were discharged from the observation culvert. Substantial amounts of deposits probably brought by the pore fluids were found on the culvert bed after these events. The grain size distributions of the deposits in the culvert collected in April and June 2021 reveals that the fluids led into the observation culvert were the mixtures of water and the fine particles mostly less than 10 mm (Fig.  2). Even if the TDR sensor at the bottom was buried in the deposits, the sensor was not damaged and could continue measuring after removing the deposits. The measurement system proposed in this study was validated the robustness and sustainability with the appropriate maintenance works.

Sediment concentrations of pore fluid and entire debris flow
Debris flows with the peak discharge of 148 m 3 /s were observed on 15 May 2021 (Fig. 3). The volumetric sediment concentration of the entire debris flow at the check dam reached 63.7 %. The sediment concentrations of the pore fluid were measured successfully in the culvert during 13:53 -13:55 and 13:57 -13:59 (Cf30 and Cf50 in Fig. 3), which were slightly lower or similar with the concentrations of the entire debris flow (Cv). The measured Cf30 and Cf50 ranged from 33.3 to 42.2 % and from 35.0 to 54.6 %, respectively. Before 13:53, the resultant concentration values at the heights of 10, 30, and 50 cm (i.e., Cf10, Cf30, and Cf50) were about 60 %, suggesting these TDR  sensors were in the saturated deposit. A small debris flow at 9:20 brought the fine sediment into the culvert and buried the sensor at 10 cm height. The pore fluid of another debris flow at 13:20 probably caused further deposition reaching the sensor at the height of 50 cm (Fig. 3).
The resultant Cf values after removing the periods of buried TDR sensors ranged from 4.81 to 68.8 % by June 2021. During the observation period, Cf tended to decrease as the sequence of the debris flows. Because no eruptions occurred during this period, the catchment possibly lacked sediment to be delivered by the debris flows.

Conclusion
We proposed and demonstrated an approach to measure volumetric sediment concentrations of pore fluids of natural debris flows. An observation culvert with an intake enabled the pore fluids led into exclusively. The sediment concentrations of the fluids in the culvert were measured by applying the TDR technique. The sediment concentrations of the pore fluids varied greatly and tended to decrease as the series of the debris flows withing the 4-months period of little sediment supplies from the volcano. The combination of this measurement system and a load cell system is expected to contribute understanding the flow mechanism of debris flows.