# A Comprehensive Review of Open Caisson Modeling Technology: Current Practices and Future Prospects
## 5 Challenges and Future Directions
### Challenges
#### 5.1.2 Earth Pressure During Sinking  
The main concern when sinking a caisson foundation had been ensuring that it sinks safely. Because the end resistance distribution characteristics differ from those of medium-small-sized caisson foundations, different sinking construction regulating methods are inevitably required for different caisson foundation sizes [140]. The studies on the distribution of the earth's pressure on circular shafts were first performed by [141] and enhanced by [PERSON] [142] later on. He expanded [PERSON]'s theory to lined shafts, using the Mohr-Coulomb criterion to estimate the minimum earth pressure on shaft liners with \(\sigma_{\theta}=\sigma_{\mathrm{v}}=\sigma_{1}\) and \(\sigma_{r}=\sigma_{3}\) in the plastic zone. To take into consideration the effects of non-zero shear stress, he proposed to decrease the friction angle of sand from 30\({}^{\circ}<\Omega<\) 40\({}^{\circ}\). It was demonstrated that in granular soils, radial and hoop stresses decline as the radial distance to the shaft decreases, known as the arching effect. Meanwhile, radial stress progressively increases with depth. The arching effect makes the standard earth pressure  
Figure 13: Illustration of an open caisson shaft section, demonstrating distinctive construction features and the contact stresses acting on the walls during sinking. theories developed for plane strain situations by [143; 144] inappropriate, and results in overly conservative earth pressure predictions [145]. Since then, other researchers have developed techniques based on different models to determine the axisymmetric earth pressure acting on a shaft [146; 147; 148; 149; 150]. [PERSON] [151] proposed a conical failure surface for axisymmetric conditions. He adopted Coulomb wedge theory by using limit equilibrium theory, suggesting that lateral earth pressure initially increases up to a peak value and then gradually decreases to a value of zero. He considered that the value of earth pressure coefficient should lie between \(K_{a}\) and \(K_{0}\), not equal to 1 as assumed in [PERSON]'s theory. To evaluate the earth pressure acting on the cylindrical shafts, [PERSON] [146] expanded the slip line method by assuming that \(\sigma_{\theta}=\sigma_{v}=\sigma_{1}\) and \(\sigma_{r}=\sigma_{3}\) within the plastic zone, under active conditions, thus making the stress ratio \(\lambda=\frac{\sigma_{\theta}}{\sigma_{v}}=1\). He also argued that within the plastic zone, the hoop and radial stresses are equivalent to the major and the minor principal stresses. The hoop and radial stresses, acting along the shaft circumference and in the radial direction, respectively, are the normal stresses. The major and the minor principal stresses represent the maximum and minimum normal stresses, acting along principal directions where the shear stress is zero. Based on these assumptions, he concluded that, \(\lambda=\frac{\sigma_{\theta}}{\sigma_{v}}=1\). He used the Mohr-Coulomb failure criterion and approximated the failure surface as a straight line. [PERSON]'s theory was extended by [152]; considering \(\lambda\) as a variable, it was proven that for \(\lambda=1\), the minimum value of the lateral earth pressure can be obtained, suggesting the use of \(\lambda=K_{0}=1-\sin\phi\). The evolution of the normalized earth pressure (\(\frac{p}{a\gamma}\)) with the normalized depth (\(\frac{l}{a}\)) is presented in Figure 14, which provides comparative summary of earth pressure distributions calculated using various methods for a specific shaft geometry: height (h), radius (a), and soil properties (\(\phi\)). As all methods predicted pressures below at-rest and active values, their depth-wise pressure distributions varied significantly. [PERSON]'s and [PERSON]'s methods assume a unit earth pressure coefficient \(\lambda=1\), resulting in the minimum active earth pressure that aligns with predictions from the plastic equilibrium and slip-line methods producing constant earth pressures at depths below the surface.