## 1 Introduction  
With the improvement of environmental concerns all over the world, sustainable development has attracted much attention in the construction industry. People urgently need a low-cost, reusable, energy-saving, and environment-friendly building material to replace the industrial building materials with high pollution and high energy consumption [1]. Earth as a natural construction material has been widely used throughout the world since ancient times. It has many advantages, such as easy use of local materials, low cost, energy savings, environmental protection, and simple construction. Therefore, under the background of international sustainable development, it will burst out with new vitality with the development of science and technology [2, 3]. According to statistics, approximately 30% of the world's population still lives in houses built of earth materials. The strength of earth materials is low (compressive strength of 0.5-7 MPa), nevertheless, they are perfectly suitable for low-rise buildings of 1-3 stories and even more [4]. Therefore, in some developing countries (especially low-income countries), this occupancy ratio is more than 50% [5, 6]. In China, it is also conservatively estimated that more than 60 million people live in earth buildings [7]. However, there are some common problems in earth structures, such as large material discreteness, weak structural measures, imperfect seismic calculation and analysis methods, and so on. Earth structures were seriously damaged in previous destructive earthquakes, such as the 2008 Wenchuan M8.0 earthquake [8], the 2010 Yushu M7.1 earthquake [9], and the Haiti M7.0 earthquake [10]. This poses a great threat to the safety of people's lives and property, seriously restricting the development of earth structures [11; 12]. Among them, the constitutive equation of earth under uniaxial compression, as an expression to describe the full stress-strain response of earth specimens under uniaxial compression, is an indispensable physical equation in nonlinear analysis and numerical simulation of earth structure. Its establishment played an important role in the development of calculation, analysis, and design methods for earth structures, and it has been widely studied by scholars. At present, research on earth materials focuses on material modification. The mechanical properties and durability of earth materials are enhanced by adding different components to them [13; 14; 15]. It is important to note that there is a distinct lack of official international guidelines for laboratory testing of earth materials. Therefore, both the determination of the mechanical properties of materials, such as compressive, flexural and bending resistance, and the durability testing of earth materials (spray test, drip test, etc.) are borrowed from the test methods used for industrial construction materials [16; 17]. Their applicability to earth materials is open to debate. The conclusions obtained from related studies are often difficult to compare because of the different shapes and sizes of the specimens. Therefore, it is necessary to study the mechanical properties of earth materials from the perspective of experimental test methods. A new contribution to the establishment of relevant experimental test standards is needed. The determination of uniaxial compressive strength test methods for earth materials is still an open problem. The establishment of uniaxial compressive constitutive equations for earth materials has also been studied by some researchers. [PERSON]. et al. and [PERSON]. et al. [18; 19], respectively, carried out uniaxial compression tests on adobe bricks in archeological relics of Turkmenistan and Peru, and established the uniaxial compression test equations suitable for adobe bricks based on the test results. [PERSON] et al. [20] carried out uniaxial compression tests on adobe blocks with different shapes and sizes.