## 1 Introduction  
Calcareous sand is widespread along the coastline of the South China Sea, the Red Sea, Australia, the Gulf of Mexico, and other tropical or subtropical regions [1], making it an essential component of construction materials in coastal structures. Usually, calcareous sand consists of the reworked shell fragments and skeletal debris of marine organisms [2, 3]. Calcareous sand has unique features, such as irregularly shaped particles, a porous interior, a polygonal angle, and crushable grain [4]. As a result, the mechanical behavior of calcareous sand can be considerably different from siliceous sands due to their diverse mineral resources and particle characteristics [5, 6]. Several conventional geotechnical applications, including grouting, densification and deep mixing, have been explored to enhance siliceous sand's bearing capacity and liquefaction resistance [7]. The development of new technologies and materials, such as microbially induced calcite precipitation treatment [8, 9, 10] and nano-modification [11, 12, 13], have attracted great attention due to their low cost, low pollution, and harmless impact on the environment. However, when the MICP is performed in clay soil, the ground improvement cost is increased due to clay soil's low permeability [14]. The production of carbonate precipitation is affected by environmental factors, such as calcium concentration, bacterial concentration, pH, and temperature [15]. MICP treatment is suitable for treating artificial calcareous sand islands far from the inland and with a poor construction environment. Microbially induced calcite precipitation (MICP) is a modern technology that utilizes biological metabolic processes to improve soil properties [16; 17; 18]. The fundamental chemical reactions governing the MICP process can be defined as follows [8; 19]:  
\[\text{CO(NH}_{2})_{2}+2\text{H}_{2}\text{O}\to 2\text{NH}_{4}{}^{+}+\text{ CO}_{3}{}^{2-}\]  
\[\text{Ca}^{2+}+\text{CO}_{3}{}^{2-}\to\text{CaCO}_{3}\downarrow\]  
Soil improvement methods include environmental friendliness, a far transmission distance, low disturbance, and controllability of the process [10]. MICP has been applied to solve practical engineering problems, such as increasing soil strength and stiffness [19; 20], reducing soil permeability [21], repairing cracks in the structure [22], and controlling erosion [23]. MICP treatment has recently been demonstrated to improve calcareous sand's static strength and liquefaction resistance due to the calcite crystal precipitation between the sand particles, which strengthens the soil structure [16; 1; 24]. The composition, shape, and pore structure of calcareous sand particles are more suitable for calcium carbonate precipitation than siliceous sand [1; 25; 26]. However, studies on the dynamic properties of MICP-treated calcareous sand, such as the small-strain dynamic shear modulus and damping ratio, are rare. The dynamic shear modulus and damping ratio are essential for analyzing soil's dynamic response during dynamic loading conditions, such as earthquakes, traffic, and wave loads [27]. Over the past few decades, the dynamic properties of naturally occurring calcareous sand have been extensively investigated in the laboratory [28; 29]. For example, the small-strain shear modulus and damping ratio of calcareous sand under an isotropic or anisotropic stress consolidated state have been studied [30; 31; 32; 33]. The effects of confining stress, pore ratio, relative density, grading and particle size, and particle breakage on the dynamic properties have also been discussed [5; 29; 30; 31; 32; 33; 34; 35]. [PERSON] et al. [34] discovered that the effect of the void ratio on shear modulus is more pronounced at low void ratios, and the maximum shear modulus increases as the void ratio decreases. [PERSON] and [PERSON] [5] conducted resonant column and cyclic triaxial tests on two marine calcareous sand samples and reported that as the effective confining pressure grows, the shear stiffness ratio rises while the damping ratio decreases.