# Experimental Study on the Dynamic Characteristics of Fractured Coal Under Cumulative Impact
## 2 Experimental Design
### SHPB System Configuration and Stress Equilibrium Verification  
Dynamic impact tests are conducted by using a 50 mm diameter split-Hopkinson pressure bar (SHPB) device, as shown in Figure 1. The SHPB device comprises three subsystems: a pressure bar assembly obtaining the striker, incident, transmission and absorber bars with elastic modulus of 210 GPa, a measurement system and a data acquisition-processing unit. Strain gauges are symmetrically bonded on incident and transmission bars, which are set  
Figure 1: Experimental procedures and equipment.  
at 1.8 m and 1.5 m from specimen interfaces, respectively, configured in full-bridge circuits for wave separation analysis. A constant gas pressure of 0.15 MPa is maintained for impact loading, with annular brass shim serving as a pulse shaper for waveform optimization.  
The experimental principle follows the elastic stress wave propagation theory under two fundamental assumptions: uniaxial stress state and dynamic stress equilibrium. The first assumption concludes that the specimen only has axial stress under the action of stress waves, and the dynamic stress equilibrium states that the stress always remains equal when the stress waves are repeatedly acted on the specimen. During the dynamic impact process, the incident strain, reflected strain and transmitted strain are recorded in the strain acquisition instrument. Then, by organizing the strain data output from the test according to the three-wave method [43], the strain rate \(\dot{\epsilon}(t)\), average strain \(\varepsilon(t)\) and stress \(\sigma(t)\) of the specimen can be obtained, as in Formulae (1)-(3) [44]:  
\[\dot{\epsilon}(t)=\frac{v}{l}(\varepsilon_{\rm i}-\varepsilon_{\rm r}- \varepsilon_{\rm t}) \tag{1}\]  
\[\varepsilon(t)=\frac{v}{l}\int_{0}^{t}{(\varepsilon_{\rm i}-\varepsilon_{\rm r }-\varepsilon_{\rm t})\rm d}t \tag{2}\]  
\[\sigma(t)=\frac{AE}{2A_{\rm s}}(\varepsilon_{\rm i}+\varepsilon_{\rm r}+ \varepsilon_{\rm t}) \tag{3}\]  
where \(t\) is the testing time (s); \(v\) is the P-wave velocity (m/s); \(l\) is the specimen length (m); \(\varepsilon_{\rm i}\) is the incident strain; \(\varepsilon_{\rm r}\) is the reflected strain; \(\varepsilon_{\rm t}\) is the transmitted strain; \(A\) is the cross-sectional area of SHPB bars (mm\({}^{2}\)); \(E\) is the elastic modulus of SHPB bars (GPa); \(A_{\rm s}\) is the specimen cross-sectional area (mm\({}^{2}\)).  
Dynamic stress equilibrium verification is a prerequisite for dynamic impact testing, serving as a fundamental criterion for experimental validity. Validation was performed on a 30\({}^{\circ}\) inclined fractured coal specimen after five cumulative impacts, as shown in Figure 2. The low transmitted signal observed in Figure 2 is due to the significant increase in internal microcracks within the fractured coal sample caused by multiple impacts, which leads to a reduction in the overall impedance of the sample. As the stress wave propagates through the sample, the transmission of the stress wave is hindered. The superimposed waveform of incident and reflected stresses demonstrates close agreement with the transmitted stress profile, confirming dynamic equilibrium attainment.  
Figure 2: Dynamic force balance during a SHPB test.