# Experimental Study on Shear Creep and Long-Term Strength of Clay-Type Muddy Interlayer
## 2 Methodology
### Methods
#### 2.2.5 Creep Data Processing  
The creep test curve obtained by hierarchical loading is shown in Figure 5, and transforming it into separate loading creep curve is a key step in creep analysis. At present, the creep test data with hierarchical loading are mostly processed according to the principle of Boltzmann superposition [35]. Through the study of rheological mechanics for many years, [PERSON] [36] pointed out that geotechnical materials are highly nonlinear, so the creep curve can not be simply superimposed by the creep response of each load.  
The \"Chen's Method\" proposed by [PERSON] in 1964 and developed by his students has been more and more widely used in the study of geotechnical Rheology. The original intention of [PERSON]'s method is to use a simple method to derive the stress-strain time relationship from the test results, and apply \(n\) steps of load to only one sample to obtain the creep curves of \(n\) different samples of the same geotechnical material with \(n\) steps of different sizes of load. This is a simple method to solve the nonlinear effect caused by step loading. Its advantage is that by using suitable experimental techniques and methods, the use of graphical methods to establish the superposition relationship of real deformation processes can be applied regardless of whether the aftereffect is linear or nonlinear.  
[PERSON]'s method can be summed up to answer the following experimental questions [37]: assuming that the step loading of the sample is carried out with a step distance  
Figure 5: Full creep process curve of graded loading under different normal stresses ((**a**) \(\sigma\) = 100 kPa, (**b**) \(\sigma\) = 200 kPa, (**c**) \(\sigma\) = 300 kPa, (**d**) \(\sigma\) = 400 kPa).  
of \(\Delta\tau\) as shown in Figure 6a, and the test curve is obtained as shown in Figure 6b, how to infer the creep curve under one-time loading with the load of \(\tau_{n}=\sum\limits_{i=1}^{n}\triangle\tau_{i}\)?  
First, look at the material creep caused by the first level of loading, from time \(t_{0}=0\) to \(t_{0}=t_{1}\), the material is deformed by creep under the constant load \(t_{1}=\Delta\tau\). If the test is carried out to time \(t_{1}\) without adding the next level of load \(\Delta\tau\), the material deformation will continue to be along the dashed line since the material deformation has already entered into the steady-state creep at this time, so the effect of adding the acting load \(\Delta\tau\) to the specimen is that the dashed line occurs additional deformation between the dashed line and the solid line (shown in the shaded line region). It is possible to find, from this additional deformation, the creep value with \(t_{0}\) as the starting point in time and the creep increment \(\Delta\epsilon(t)\) due to the stress increment \(\Delta\tau\) with \(t_{1}\) as the starting point in time. Therefore, using the first stage of loading as a basis and superimposing the creep increment of the next stage of loading acting with the same continuation time, a one-time loading of \(\tau_{2}=2\Delta\tau\) creep curve is obtained. The continuation of the step loading, can be in the previous level of the creep curve on the same treatment, so that a one-time loading of \(\tau_{n}=\sum\limits_{i=1}^{n}\Delta\tau_{i}\) creep curve can be obtained, such as the dotted area to the left of Figure 6b, so that several creep curves under \(n\) different loads can be obtained from one specimen.  
When using this method, two points should be paid attention to: (1) when the next stage loading is carried out, the deformation should be carried out after the deformation has entered the steady creep under the previous load; (2) the time interval of step-by-step loading should be equal.  
Figure 6: [PERSON]’s loading method and creep data processing method ((**a**) Load diagram, (**b**) Deformation diagram).