## 1 Introduction  
The CPTu test can provide three independent parameters for various soil media: cone tip resistance \(q_{\text{c}}\), side wall friction resistance \(f_{\text{s}}\) and pore water pressure \(u_{2}\). The formula can also determine additional parameters, including net cone tip resistance \(q_{net}\), pore pressure ratio \(B_{q}\), and normalized cone tip resistance \(Q_{\text{t}}\). The CPTu test can be used to evaluate a wide range of geotechnical engineering parameters, such as the soil classification (SBT), gravity (\(\gamma\)), overconsolidation ratio (OCR), undrained shear strength of clay (\(s_{\text{u}}\)), effective internal friction angle of sand (\(\varphi\)), Young's modulus (\(E\)), static lateral pressure coefficient (\(K_{0}\)), consolidation coefficient (\(c_{\text{v}}\)), and the evaluation of soil liquefaction [1, 2].  
Numerous engineering projects characterize the Yellow River Delta. In this region, silty clay is distributed widely [3]. Establishing an inverse method for determining the mechanical parameters of silty clay based on in situ testing is of significant importance. In the research on inverse parameter determination through in situ testing of silty clay in the Yellow River Delta [4, 5], there is currently a need for more studies on internal friction based on the CPTu method. The internal friction angle is primarily obtained through sampling tests [6, 7, 8]. The internal friction angle is crucial in the inverse determination of lateral earth pressure coefficients and other related factors [9, 10]. It is of great value to study the inversion method of the internal friction angle of silty clay in the Yellow River Delta based on in situ testing [11].  
To assess the effective internal friction angle \(\varphi^{\prime}\) of different soils (including sand, silt, and clay) under the drained to undrained penetration circumstances, a plastic solution of effective stress was designed for the CPTu test. [PERSON] and [PERSON] [12] at Norges Tekniske Hyskole (NTH) suggested this method, and [PERSON] and [PERSON] [13], [PERSON] et al. [14], [PERSON] [15], and [PERSON] and [PERSON] et al. [16] perfected it. However, the NTH method is now only applied in Norway and a small portion of Sweden, and it is still not widely employed in other regions. Since soil's effective internal friction angle remains relatively consistent for soils with similar mineral compositions and particle distributions, this experiment extracted representative soil samples from a silty clay area site. Through indoor calibration chamber tests, it is possible to calibrate the suggested values for the effective internal friction angle so that they are suitable for this specific region. This approach offers a more efficient method for obtaining in situ parameters such as the effective internal friction angle and undrained shear strength during future exploration activities in the same region. Consequently, the aim of this paper has four aspects: (a) checking and evaluating the procedure of effective internal friction angle \(\varphi^{\prime}\); (b) data interpretation by the NTH method; (c) Comparing the interpretation value of the effective internal friction angle \(\varphi^{\prime}\) of silty clay in the Yellow River Delta in the indoor calibration chamber test with the \(\varphi^{\prime}\) reference value obtained from the indoor unit test.