); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xieiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. ); 1314418097886163.com (Y.Q. ); [EMAIL_ADDRESS] (L.X)  
Xiejiangfu  
1 College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830046, China; [EMAIL_ADDRESS] (I.Q. Due to the difficulty in measuring \(K_{0}\) values directly in the field, numerous approaches have been proposed to calculate \(K_{0}\) from both theoretical derivation and experimental data. For instance, [PERSON] proposed an equation which is most widely used:  
\[K_{0}=\frac{\sigma_{h}}{\sigma_{v}}=\left(1+\frac{2}{3}sing^{\prime}\right)\frac {1-sin\varphi^{\prime}}{1+sin\varphi^{\prime}}\approx 0.95-sin\varphi^{\prime} \tag{3}\]  
or approximately:  
\[K_{0}=1-sing^{\prime} \tag{4}\]  
for loose deposits and normally consolidated clays, where \(\varphi^{\prime}\) indicate the effective internal friction angle of the soil. This equation has been widely adopted in engineering practice for many years. Contrary to a common misconception, as [PERSON] [4] had pointed out, this equation is a result of theory deduction instead of an empirical formula. It was deduced from the stress field in a wedge prism of loose granular materials. [PERSON] [3] pointed out that the stress on the central vertical plane is the horizontal pressure at rest. Equation (4) is a widely accepted representation of \(K_{0}\) because it is easy to use and provides good enough prediction. Both experiments [5] and analysis [6] have verified the equation's reliability. However, after years of application and research of this formula, there is considerable controversy about \(\varphi^{\prime}\). In practical engineering or scientific applications, internal effective friction angles are difficult to measure directly. Therefore, peak friction angle \(\varphi^{\prime}_{p}\)[7; 8; 9; 10] and critical state friction angle \(\varphi^{\prime}_{c}\)[6; 7; 11; 12; 13; 14] are often used as \(\varphi^{\prime}\) to calculate \(K_{0}\) values. Furthermore, it is worth noting that [PERSON]'s originally work aimed at loose deposit soil, for which peak friction angle \(\varphi^{\prime}_{p}\) equals the critical state friction angle \(\varphi^{\prime}_{c}\). When the equation is applied to other soil, it is hard to decide which friction angle is better. Although [PERSON]'s equation is widely accepted, his derivation has been criticized by many researchers. [PERSON] [15] affirmed that the soil state in the wedge prism was different from that in the commonly referred \(K_{0}\) state. [PERSON] [4] also discovered that the stress path in a wedge-shaped sand prism could not represent the one under typical \(K_{0}\) state.