## 1 Introduction  
Calcareous sediments characterized by unique grain morphology are widely distributed near coral reefs [1]. They are commonly adopted as a building material in offshore engineering, ranging from conventional geotechnical applications (e.g., foundations, embankments, and retaining walls) to offshore hydrocarbon industries [2; 3; 4; 5]. Understanding the engineering properties of calcareous sand is therefore of great importance. Over recent decades, the mechanical properties of calcareous sand have received global focus at both the academic and the practical levels. Across several studies, grain crushing under heavy loads was recognized as the major problem for calcareous sands, which is often associated with a loss of soil strength and the occurrence of ground deformation [6; 7]. [PERSON] et al. [8] conducted ring shear tests on calcareous sands under different levels of loading stress, and the formation of a shear band, along with the evolution of particle breakage, were examined. [PERSON] et al. [9] performed a series of cyclic loading tests on samples of Dog's Bay carbonate sand, and the development of volumetric strain due to grain crushing was explained based on the micromechanics at the grain contact level using numerical simulations. Moreover, a detailed summary of recent advances on grain crushing was also given by [PERSON] et al. [10]. Despite increased research efforts, most attempts in previous studies focus on quantitative descriptions of the crushability of grains, whereas measures to mitigate the effects of grain crushing for calcareous sands are rather limited.  
As far as the weakness of the grain contacts of calcareous sands as compared to quartz sands is concerned, much evidence has shown that an admixture of rubber chips in sands from recycled scrap tires is useful for absorbing the energy at grain contacts, in particular, under dynamic loads [11; 12]. As a matter of fact, the number of disposed tires in China exceeds 50 million per year [13], and thus there is a very large stock of rubber particles from recycled tires. As a type of lightweight material, an admixture of rubber with soils has been adopted in recent engineering applications, yielding satisfactory performance. In particular, as a backfill material, rubber soil can effectively improve the bearing capacity of foundations [14; 15; 16]. Moreover, as a hydrophobic material, rubber virtually does not react with underground water, hence the adverse impact on the environment is small [11]. However, previous research in this regard mainly uses quartz sand as the base sand. A question arises herein as to whether rubber chips can be adopted to effectively mitigate the adverse effects of grain crushing in calcareous sands.  
With the aim of addressing the above concerns, a systematic laboratory program was carried out using rubber-calcareous sand mixtures with different rubber contents. Both a one-dimensional oedometer and a resonant column apparatus were adopted in this study, thus affording an explicit view on various engineering performances (i.e., grain crushing behavior and modulus reduction) of rubber-calcareous sand mixtures. The outcomes of this study will not only provide convincing evidence on the role of rubber chips in a mixture, but can also serve as a useful reference for engineering applications of rubber-calcareous sand mixtures in offshore engineering and for relevant theoretical developments.