## 3 Inversion Model of Seepage Velocity
### Numerical Example  
In order to measure the overall seepage field of the embankment, combined with the above coupling theory of the seepage field and temperature field (ignoring the influence of the temperature field on the seepage field), the primary goal is to obtain the stable temperature field of the embankment. The traditional monitoring methods are mostly point-based. The temperature of the dam is measured using resistance temperature sensors. Although the point-based measurement can obtain the accurate value of the monitoring point, it cannot obtain the continuous temperature change inside the dam. Therefore, this paper selects the DTS distributed optical fiber temperature measurement system to monitor the temperature field inside the embankment. In the DTS temperature measurement system, optical fiber can be used as both sensor and transmission medium to transfer deformation, temperature, damage, and other physical quantities; the dual use of optical fiber makes it possible to realize long-distance distributed distribution without forming a loop. In addition, the advantages of stability, small external interference, and strong corrosion resistance leads to the optical fiber's wide application in civil engineering structures, where good measurement results have been achieved. The DTS temperature measurement system is mainly divided into two parts, namely, the optical fiber temperature measurement host and the distributed temperature sensing fiber. The temperature measurement host includes lasers, optical devices, and data storage modules for transmitting and receiving optical signals; in this paper, a ZTT-GYXTW-4A1a built-in steel wire-reinforced four-core-armored optical fiber cable, and a stainless-steel hose two-core-armored optical fiber cable are used for comparative tests. Two model sinks with 5 m length, 0.6 m width, and 1.15 m height were established in the experiment. The wall was filled with sintered ordinary bricks and built with M5 cement mortar, with M10 mortar smeared on the surface. A slope was set at the bottom of the model sinks to form seepage, with a slope of 1:3 and an outlet hole drilled to calculate the seepage velocity. On the basis of the vertical height of 5 cm, the steel plate mesh was arranged, and two layers of filter cloth were laid on the steel plate mesh to prevent the medium from being taken away by the seepage water. In order to make force on the steel plate mesh uniform and prevent the stress damage of the filter cloth, gravel with a 10 cm thickness and slightly larger than the mesh hole size was laid between the two layers of the filter cloth. A 5 cm gap between the steel plate mesh and the foundation was reserved, and an outlet hole was set at the end of the sink to discharge the seepage water. Three PVC semi-tubes with a diameter of 4 cm were set on the edge wall of the model sink to simulate the concentrated seepage inside the embankment. The optical fiber was arranged as shown in the Figure 4, and yellow sand and clay were used to fill the two model sinks, respectively, denoted as medium I and medium II. The multi-line heat source method was adopted, and the double-row fiber was set. The fiber was set in the middle of the sink, and the sprinkler was set at the top of the sink to spray water evenly into the sink to simulate seepage. The change in temperature along the fiber during the whole process was recorded. The basic idea of the multi-line heat source method is as follows:  
1. Assume the seepage velocity \(v\), determining the heat flux \(q\) of the inner boundary and temperature \(T_{0}\) of the external boundary (the initial temperature of optical fiber before heating);
2. Calculate temperature distribution using the coupling model of the temperature field and seepage field under a uniform and stable seepage condition to obtain the numerical temperature value \(T_{2}\) at the optical fiber position;
3. Compare the temperature calculated using the coupling model \(T_{2}\) with the actual monitoring temperature \(T_{2}^{\prime}\).