# Experimental Analysis on Pre-Stress Friction Loss of Crushed Limestone Sand Concrete Beams
## 1 Introduction  
Recently, manufactured sand has been deemed to be a suitable alternative to river sand for the application and substitution of concrete aggregate [1; 2]. The crushed limestone sand is generally more angular, has rougher surface texture and larger amounts of fine sand. Compared with normal concrete, CLS concrete has high elastic modulus, strength and mechanical behavior [2]. Because of the advantages above, crushed limestone sand (CLS) concrete is widely used in pre-stressed structures [3; 4]. The design for pre-stressed structures involves consideration of the effective force at each stage of loading, together with material properties and individual circumstances. Existing empirical formulas are employed to estimate pre-stress loss caused by elastic shortening, creep, shrinkage, friction, relaxation of the pre-stressed tendon and temperature [5; 6; 7; 8; 9]. Numerous factors influence the pre-stress loss of CLS concrete, including the type of cement, aggregates used, the mix of concrete, etc. CLS concrete with large elastic modulus is sensitive to the increase in concrete age, and the creep and shrinkage is more obvious than normal concrete [2]. When compared with long-term pre-stress loss [5; 6; 7; 8], the instantaneous loss caused by friction also significantly affects the initial pre-stress force of the tendon [10; 11; 12; 13; 14; 15]. The effective force inevitably decreases due to the friction loss between the pre-stressing tendon and duct [10]. Nowadays, extensive laboratory tests on pre-stress friction loss have been carried out. The Anchorage-Measurement-Access (AMA) system is the main experimental idea proposed for estimating the pre-stress friction loss [16]. Two full-scale pre-stressed concrete girders were constructed [17] and the influence at various pre-stress levels was discussed. The actualfriction loss measured at low pre-stress levels was larger than the theoretical results, with the two eventually converging as the pre-stress level increased. The average pre-stress friction loss accounted for 10-20% of the initial tensile stress. Local bending of tendons at the continuous joint of pre-stress concrete girders may develop eccentricity, which leads to friction loss [18; 19]. As the eccentricity increased, a pre-stress friction loss of 2.5% occurred. During experimental measurement and practical monitoring, the friction loss was shown to contribute a certain proportion of the tension control stress [20; 21; 22; 23]. Therefore, the relevant estimation and calculation method had been explored and improved. [PERSON] et al. analyzed the relationship between the friction torque and tangent angle of curved duct under different tension levels, before effective formulas were derived to consider friction loss [24]. [PERSON] simulated the space curve tendon means of the iterative method and proposed key parameters to predict the friction loss [25]. [PERSON] et al. described the interactions between the tendon and concrete by the finite-element method, before establishing the numerical procedure to represent the friction and bond at the interface [26]. The friction loss is considered in two parts: the length effect and curvature effect. The deviation coefficient \(\kappa\) and friction coefficient \(\mu\) are provided in current specifications for these effects [27]. These coefficients are determined by concrete properties, duct straightness and surface of tendon and its surrounding material. However, the properties of CLS concrete differ in elastic modulus, strength and surface texture [28; 29]. Moreover, current on-site construction technique has been rapidly improved to strictly control duct straightness. At the same time, various duct-forming materials are utilized to satisfy requirement in engineering. There have been great differences between the friction loss predicted by specifications and measured values in some cases. The definition of friction loss should be dependent on specific conditions.