## 1 Introduction  
Northeastern China is one of the most important energy production and consumption regions of China. An increasing number of industrial wastes are produced year on year, such as fly ash (FA), slag, and oil fuel ash [1; 2]. Oil shale ash (OSA) is the by-product of oil shale, which is considered as a substitute for conventional oil. Because of the low oil extraction from oil shale, a large amount of OSA has accumulated, which has been an urgent problem to be solved [3; 4]. Soil stabilization is an effective measure to recycle residue wastes [5; 6]. Compared with use in construction materials, such as cement, asphalt, and concrete, the application of waste residues in soil stabilization has the advantages of high utilization, low price, and simple technology. The stabilized soils often possess greater strength, swell properties, or resistance to erosion after freeze-thaw (F-T) cycles [7]. FA is one of the most commonly used additives. [PERSON] and [PERSON] [8] stabilized several different types of soils by using Class C FA. The strength and durability tests indicated that the FA-treated soils showed substantial improvement in soil performance for multiple soils. [PERSON] et al. [9] mixed different percentages of FA with soft soils and investigated the usefulness of FA as a soil additive. The result revealed that the CBR (California bearing ratio) and shear strength of the mixed soils increased with increasing FA percentage. Many attempts have also been made to utilize OSA in soil stabilization. [PERSON] [10] studied the viability of using soils stabilized by OSA as subgrade filling based on compaction, unconfined compression, durability, and resilient modulus test. It was found that the significant increase in strength, durability, and resilient modulus was due to the cementing property of OSA. The testing data and the mixture design of the modified soil are an important reference for use in highway construction. [PERSON] et al. [11] investigated the physicochemical interaction and structure formation processes of several types of clayed soils with OSA. The obtained results showed that after hydration, the strength of the mixture increased as a result of the partial dissolution of the surface of hard particles and the growth of flocculation formations. In fact, the great engineering property of OSA-stabilized soils is mainly attributed to the cementing property of OSA [10; 12; 13]. It has been revealed in previous literature that the combination of fuel ash waste and FA as additives has a significant effect on soil stabilization [14; 15]. However, research on the application of soils stabilized by both OSA and FA is scarce, especially on the dynamic resilient modulus of the modified soil. As the most important index in pavement structure design, dynamic resilient modulus can truly reflect the dynamic mechanical property of subgrade materials subjected to repeated traffic loading. Previous studies have focused on the influencing factors of resilient modulus, such as stress state, moisture content, and physical properties of subgrade materials. [PERSON] [16] established the prediction model of resilient modulus relating to shear stress and bulk stress. This model was then revised by introducing confining pressure and deviator stress [17]. In consideration of the main influencing factors of resilient modulus, a formula was also given to predict the resilient modulus in pavement design by AASHTO (American Association of State Highway and Transportation Officials) [18]. According to the deformation characteristics for a series of subbase and subgrade materials, [PERSON] et al. [19] created the relationship between resilient modulus and elastic modulus. Subgrade materials are usually subjected to partially saturated conditions or regular moisture variation affected by seasonal variation. To obtain more effective constitutive models for unsaturated soils, an enhanced method incorporating matric suction with stress factors to calculate resilient modulus was proposed [20]. [PERSON] et al.