## 1 Introduction
In these studies, the proportion of cement added could be 0%, 2%, 4%, 8%, or 16%. The results of compaction tests indicated that when 2-8% cement was added on the dry side, maximum dry density increased with cement paste content. When the cement paste content reached 16%, dry density decreased. In addition, similar tendencies were observed on the wet side. [PERSON] et al. [16] described experiments involved the addition of cement (1%, 2%, 3%, 5%, and 7%) and a moisture content of 10% [16]. Another study involved the addition of cement (2%, 9%, and 12%) and the application of varying moisture content levels (4%, 6%, 8%, 12%, and 13.4%) to conduct a series of tests aimed at investi  
Figure 1: Distribution areas and bird view picture of mudstone in Taiwan: (**a**) The outcrops locations of mudstone (redrawn from [PERSON] (2002)); (**b**) The famous badland slope situated along the northern exit of Chungliao Tunnel. gating the effectiveness of cement paste addition [24]. [PERSON] and [PERSON] [22] added granulated blast furnace slag (GBFS) and cement to the soil to investigate the geotechnical properties of mixtures, including physical properties, compaction characteristics, unconfined compression strength, and Unconsolidated Undrained (UU) triaxial compression test results [22]. Studies have focused on the strength related to hydraulic conductivity; [PERSON] et al. [25] discussed that hydraulic conductivity could increase the uniformness of settlement and long-term safety showing the importance of hydraulic conductivity [25]. [PERSON] et al. [26] also used cement to improve weak marine clay and found that strength is influenced by cement- and density-related factors. This indicates that the effect of density on strength is comparable to that of cement [26]. On the other hand, the moisture content used for preparing specimens applied in unconfined compression and triaxial compression tests affects results substantially. Several studies have applied high moisture content during specimens' preparation [20; 27; 28]. [PERSON] et al. [28] applied moisture content levels of 1.8-, 2.0-, and 2.2-fold the liquid limit (LL) of kaolinite to prepare specimens [28]. Another study applied low moisture content to prepare specimens that primarily comprised ordinary Portland cement (OPC) and local lithomargic clay collected in the Dakshina Kannada district of India. In the study, clay was dried at 105 \({}^{\circ}\)C then screened and mixed by weight with varying proportions of cement (2.5%, 5%, 7.5%, and 10%). Water was added according to optimum moisture content (OMC). Thereafter, the obtained soil was put into a bag for curing for a given numbers of days before the specimen was removed for subsequent tests [29]. Similar methods were also proposed in other studies [15; 16; 22; 30]. When we take practicality and on-site conditions into consideration, clay clods substantially affect engineering construction [24; 31]. Soil gradation and the coefficient of uniformity (C\({}_{\text{u}}\)) both affect soil static strength [32]. Furthermore, OMC percentage and the wet side of compaction tests can be adopted when hydraulic conductivity and the strength of compacted clay are taken into account [33]. Soil saturation also affects strength [34; 35]. Thus, we applied multiple preparation methods, soil gradations, and dry density levels to prepare untreated samples in the study. Varying amounts of cement paste were added into samples subjected to compaction test treatment to increase the generalizability of the study. The relationships between elastic modulus and unconfined compression strength were discussed in many studies, with E\({}_{50}\) recommended as the elastic modulus [19; 26; 33; 36]. [PERSON] et al. [19] and [PERSON] et al. [26] investigated and discussed the relationship between E\({}_{50}\) and q\({}_{\text{u}}\), with favorable outcomes reported [19; 26]. The present study used compression tests to clarify the relationship between elastic modulus and compression strength. The triaxial test included confined undrained (CU) and UU tests.