accuracy

Predicting the bearing capability (qrs) of geogrid-reinforced stone columns poses a significant challenge due to variations in soil and rock parameters across different locations. The behavior of soil and rock in one region cannot be generalized to other regions. Therefore, accurately predicting qrs requires a complex and stable nonlinear equation that accounts for the complexity of rock engineering problems. This paper utilizes the Rock Engineering System (RES) method to address this issue and construct a predictive model.To develop the model, experimental data consisting of 219 data points from various locations were utilized. The input parameters considered in the model included the ratio between geogrid reinforced layers diameter and footing diameter (d/D), the ratio of stone column length to diameter (L/dsc), the qrs of unreinforced soft clay (qu), the thickness ratio of Geosynthetic Reinforced Stone Column (GRSB) and USB to base diameter (t/D), and the settlement ratio to footing diameter (s/D). Following the implementation of the RES-based method, a comparison was made with other models, namely linear, power, exponential, polynomial, and multiple logarithmic regression methods. Statistical indicators such as root mean square error (RMSE), mean square error (MSE), and coefficient of determination (R2) were employed to assess the accuracy of the models. The results of this study demonstrated that the RES-based method outperforms other regression methods in terms of accuracy and efficiency.

In this paper, an explicit family with higher-order of accuracy is proposed for dynamic analysis of structural and mechanical systems. By expanding the analytical amplification matrix into Taylor series, the Runge-Kutta family with  stages can be presented. The required coefficients ( ) for different stages are calculated through a solution of nonlinear algebraic equations. The contribution of the new family is the equality between its accuracy order, and the number of stages used in a single time step ( ). As a weak point, the stability of the proposed family is conditional, so that the stability domain for each of the first three orders ( 5, 6, and 7) is smaller than that for the classic fourth-order Runge-Kutta method. However, as a positive point, the accuracy of the family boosts as the order of the family increases. As another positive point, any arbitrary order of the family can be easily achieved by solving the nonlinear algebraic equations. The robustness and ability of the authors’ schemes are illustrated over several useful time integration methods, such as Newmark linear acceleration, generalized-𝛼, and explicit and implicit Runge-Kutta methods. Moreover, various numerical experiments are utilized to show higher performances of the explicit family over the other methods in accuracy and computation time. The results demonstrate the capability of the new family in analyzing nonlinear systems with many degrees of freedom. Further to this, the proposed family achieves accurate results in analyzing tall building structures, even if the structures are under realistic loads, such as ground motion loads.

In this paper, an explicit time integration method to determine the linear response of arbitrary structures subjected to dynamic loading is proposed. The total time of dynamic loading is divided into several time steps. For each two time steps, in modeling the acceleration over time domain, a second order polynomial with three unknown parameters is assumed. Validity and effectiveness of the proposed method is demonstrated through two examples where the results of this method are compared with those numerical methods. In this method, over two steps, six unknown responses (three responses for each time step) consisting of two displacements, two velocities and two accelerations are computed. This property reduces the computational cost of the proposed method as compared to Central difference, Houbolt, Newmark (linear and average), Wilson Ѳ etc. Furthermore, accuracy of the results obtained from the proposed method is better than other methods for single and multi-degree of freedom systems. Hence, as advantages of the proposed method, this method has appropriate convergence, accuracy and low computational time. Therefore, the novelty of this work is that for very small values of ∆t, this method is more precise and less time consuming rather than other existed methods. This is a useful instrument for the analysis of dynamic systems with very small values of ∆t under earthquake loading.