## 1 Introduction  
Loess deposits are widely distributed in northwest China and they cover an area of about 640,000 km\({}^{2}\), roughly equivalent to 6.7% of China's total land area [1, 2]. Geohazards as well as failures in earth constructions frequently occur in these regions due to the local geomorphic features coupled with the special characteristics of loess, leading to non-negligible losses of human lives and properties [3, 4, 5, 6]. Loess is water sensitive; the deterioration of its mechanical properties due to water infiltration is acknowledged to contribute greatly to the occurrences of many geo-hazards and this has been extensively studied, with attention having largely been paid to the loess' collapsibility and shear strength behavior [7, 8, 9]. Despite this, the role that is played by the loess' tensile characteristics has been increasingly recognized. For example, the weak tensile strength of loess was noted to be a primary reason for ground fissures [6] and, furthermore, a large amount of loess landslides present in the form of a cracking-sliding failure mode. This is a mode which is characterized by the development of tensile fractures on the crests of slopes followed by sliding movement [2, 10]. Therefore, a clear understanding of the tensile behavior of loess is of practical significance. The tensile strength of soil can be measured using direct methods (e.g., uniaxial and triaxial tensile tests) or indirect methods (e.g., a flexure beam test, double punch test, unconfined penetration test or Brazilian tensile test) [11; 12; 13; 14; 15; 16; 17; 18]. The direct methods have advantages such as their ability to reveal a definite stress-strain relationship and their straightforward manner in determining tensile strength; however, difficulties in specimen clamping, misalignment, stress concentration and friction at the ends of the specimen could lead to considerable inaccuracy of the measurements [19; 20]. The superiority of indirect methods lies in the simplicity of their specimen preparation and testing procedures; however, the tensile strength needs to be deduced based on stress distribution theory, highly relying on the assumed mechanical and boundary conditions. In the past decades, with the development of testing methodology and apparatus, the tensile behaviors of various types of soils were investigated [21; 22; 23; 24; 25]. As for loess, [6] showed that its tensile strength decreased with an increase in its water content and a decrease in its dry density. A similar observation was made by [26], which examined the tensile characteristics of Q\({}_{3}\) loess around Lanzhou city using an unconfined penetration test (UPT) and found that the tensile strengths that were derived from the UPT were lower than those that were measured in a direct tension test and that they were well correlated with the unconfined compressive strength. A comprehensive review of the studies of the tensile strength of Malan loess was presented by [2] and the results indicated the dependency of the tensile strength on the water content, dry density, test method, specimen size and loading rate. In addition, the tensile behavior of loess was perceived to be significantly affected by its texture and structure; for example, [PERSON] et al. (2016) observed that the tension resistance of fractured loess was controlled by the orientation of the joints plane [27] while [PERSON] et al. (2019) illustrated that a vibration-induced change in the microstructure of loess led to its tensile strength degradation [28]. While these existing studies have revealed the main factors influencing the tensile behavior of loess, the mechanism behind the evolution of the tensile characteristics with the change in water content, density and soil structure was rarely investigated and poorly understood. The water content is no doubt among the most critical factors affecting loess' tensile characteristics [8; 9].