# Development of a Model Material for Dynamic Geotechnical Model Tests
## 7 Conclusions  
Based on orthogonal design and similarity theory, we developed a model material similar to actual rock from the field for the shaking table model test. The original rock; the similarity relations among the selection of quartz sand, ferric powder, barite, gypsum and cement configuration of the model material; and the sensitivity of the physico-mechanical parameters to the influence factors were analysed, and multiple linear regression analysis was performed to calculate the physico-mechanical parameters and the model with similar material proportions. The main conclusions are as follows:  
1. Four factors, including cementing material/solid material, gypsum/cementing material, quartz sand/aggregate and ferric powder/(barite powder + ferric powder), were designed, and orthogonal tests were conducted with five levels for each factor. Seven parameters, including density, tensile strength, compressive strength, dynamic shear modulus, dynamic elastic modulus, cohesion and internal friction angle, were obtained by ultrasonic, uniaxial compression, direct shear and splitting tests. Among them, the dynamic shear modulus and dynamic elastic modulus most effectively reflected the changes in the dynamic parameters of rock.
2. Samples of model materials composed of gypsum, cement, quartz sand, ferric powder and barite powder met the similar material requirements for sandstone in a large range of model tests.
3. The analysis of the sensitivity of various factors showed that the density was mainly influenced by barite powder, ferric powder affected the tensile strength and compressive strength, the internal friction angle was mainly affected by the cementation material proportion, the cohesive force of the main was affected by gypsum and the quartz-sand ratio, and the dynamic shear modulus and dynamic modulus of elasticity were mainly affected by the cementation material proportion.
4. The quantitative relationship between the physico-mechanical parameters and proportions of components in the model material was obtained through sensitivity analysis and multiple linear regression analysis of influencing factors. The proportions of components in model materials obtained through this calculation efficiently configured the required model materials. The failure mode, failure process and physical parameters of the model materials simulated the behaviour of the sandstone samples taken from the field.  
Figure 13: Comparison of failure evolution process. (**a**) Uniaxial compression curve; (**b**) direct shear curve.  
**Author Contributions:** Experimental design (J.T. and C.A.); Experimental analysis (J.T. and Z.S.); Data were analyzed (Q.W. and R.K.); writing--original draft preparation (J.T.); funding acquisition (L.W. and Q.W.). All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Chinese National Key R&D Program (No. 2019 YFC1509705), the National Natural Science Foundation of China (Grant Nos. 41931295, 41877258, 41877259).  
**Institutional Review Board Statement:** Not applicable for studies not involving humans or animals.  
**Informed Consent Statement:** Human studies are not involved in this paper.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.