## 1 Introduction  
To protect the environment surrounding waste landfill sites, especially nuclear waste landfill sites, the landfill site needs to be isolated from its surroundings by a barrier made of low-permeability materials [1]. Expansive clays such as montmorillonite and kaolinite are materials commonly used to make barriers because of their low permeability coefficient [2; 3; 4]. The permeability coefficients of montmorillonite and kaolinite are in the range of \(10^{-11}\) to \(10^{-12}\) m/s [5]. Nevertheless, there is one unavoidable shortcoming in using these two materials. Both montmorillonite and kaolinite are sensitive to water, especially montmorillonite. When the moisture content of clay changes, the strength and volume of clay also change sharply. In particular, the dehydration of clay always causes shrinkage cracks, which could damage the integrity of the barrier [6; 7; 8]. Many studies have shown that adding quartz to clay can solve this problem. The addition of quartz can reduce the water sensitivity and enhance the strength of clay while maintaining a low permeability coefficient [9; 10; 11]. Clay-quartz mixtures are suitable materials for building barriers of waste landfill sites. The traditional method used to determine permeability coefficients of clay-quartz mixtures is the variable head permeability test. Because of the low permeability coefficients of clay-quartz mixtures, the variable head permeability test is effort- and time-consuming. Many scholars use consolidation test data to calculate the permeability coefficients of mixtures based on [PERSON]'s one-dimensionalconsolidation theory [9; 12]. This method is also time-consuming and there is a considerable gap between the measured and predicted permeability coefficients. It is therefore necessary to establish a simple, nondestructive, and accurate method for determining the permeability coefficients of clay-quartz mixtures. As a fast, convenient, and nondestructive tool, nuclear magnetic resonance (NMR) technology has been widely used in petroleum engineering, coal engineering, and geological engineering [13]. The transverse relaxation time (\(T_{2}\)) distribution can reflect the pore characteristics of porous media [14; 15; 16]. Previous studies have proposed prediction models of permeability coefficients for sandstones, coals, and shales based on NMR technology [17; 18; 19; 20]. These models were proposed based on the Schlumberger Doll Research model (SDR model) and Timur-Coates model (TC model) [21; 22; 23]. Almost no studies have been performed to confirm the applicability of these two models in predicting the permeability coefficients of clay-quartz mixtures with different mineral compositions. In the TC model, which is also called the free fluid model, the volumes of free water and bound water in porous media are used to predict the permeability coefficient. In the \(T_{2}\) spectrum, the \(T_{2}\) cut-off is used to discriminate between the free water and the bound water. The traditional method for determining \(T_{2}\) cut-offs of sandstones, coals, and shales is the centrifugal method [24; 25; 26]. It has been verified by experiments that there are two problems in applying this method to clay-quartz mixtures: (1) Compared with sandstones, coals, and shales, clay-quartz mixtures have a lower strength, so they might be damaged during centrifugation, and (2) the pore size of the mixture is very small, so little water can be removed by centrifuging at the maximum centrifugal velocity. Some scholars have calculated \(T_{2}\) cut-offs of shales based on the evaporation tests at increasing temperatures [27; 28; 29]. According to [PERSON], most water in clayey soil evaporates, even at room temperature [30; 31]. It is unreasonable to determine the \(T_{2}\) cut-off directly by an evaporation test at increasing temperatures. An improved method based on evaporation tests to determine \(T_{2}\) cut-offs of clay-quartz mixtures needs to be proposed.