## 2 Development of FBG Stress Sensor
### Design of Structure of FBG Sensor  
The whole structure of the stress sensor (Figure 7) mainly includes a spherical sensing head (a), connecting rod (b) and coupler box (c). Six sensing units are arranged into the sensing head to obtain the six normal stresses. In order to reduce the disturbance of the coupler box to the rock stress of the measuring point, the slender connecting rod is designed to connect the sensing head and the coupler, and act as the channel of the optical fiber. The coupler box is used for fusing the fibers derived from the sensing units and the temperature compensation unit, so that the sensor can output only one fiber, that is, one stress sensor only needs one FBG demodulator channel.  
The spherical sensing head includes a solid sphere, sensing units, sealing cover, and hemispherical shell. The solid sphere is the supporting structure of the sensing head (Figure 8). The surface of the sphere is arranged with six cylindrical holes along different directions to install the sensing units. The fiber wiring groove and the fiber outlet hole are also arranged in this manner. The fiber outlet hole and the connecting rod are connected by a threaded joint (Figure 9). After the sensing units and seal cover are installed into the solid sphere, two hemispherical shells are used to wrap them inside by screw fixation. As is shown in Figure 10, the included angles of the three measured directions in the upper hemisphere and the horizontal plane are all 45\({}^{\circ}\), and the included angles of their projections on the horizontal plane are all 120\({}^{\circ}\). In the lower hemisphere, the included angles of the three measured directions and the horizontal plane are all 30\({}^{\circ}\), while their projections on the horizontal plane are all 120\({}^{\circ}\). According to the measurement direction of each sensing  
Figure 7: FBG sensor structure: a, spherical sensing head; b, connecting rod; c, coupler box.  
unit, the specific expression of \([K]\) in Equation (7) under the _oxyz_ coordinate system can be calculated as follows:  
\[[K]^{-1}=\begin{bmatrix}-2.155&0.577&0.577&2.770&-0.385&-0.385\\ 1.488&-1.244&-1.244&-1.436&1.718&1.718\\ 1.000&1.000&1.000&-0.667&-0.667&-0.667\\ 0.000&1.578&-1.578&0.000&-1.822&1.822\\ 0.000&1.366&-1.366&0.000&-0.911&0.911\\ 1.577&-0.789&-0.789&-1.052&0.526&0.526\\ \end{bmatrix} \tag{9}\]  
Figure 8: Three-dimensional perspective of spherical head: a, solid sphere; b, sensing unit; c, sealed cover; d, hemispherical shell; e, threaded hole.  
Figure 10: Design of measuring direction of sensor head.  
Figure 9: Structure of solid sphere: a, mounting hole; b, fiber groove; c, fiber exit hole.  
Due to the embedding effect, the rock mass stress will be disturbed when the sensor is embedded. In order to reduce the secondary disturbance of the coupler box to the surrounding rock mass stress of the sensing head, a slender connecting rod is set between the sensing head and the coupler box (Figure 11). The coupler box is fitted with a wire plate inside, which is used to fix the fused fiber. The bottom of the box is fitted with a connecting hole and an outlet hole for the cable. The connection hole is used to connect the installation and positioning device of the sensor, so as to determine the three-dimensional attitude of the sensor during sensor installing.