Certified solutions for hydraulic structures using the node‐based smoothed point interpolation method (NS‐PIM)

Num Anal Meth Geomechanics

Liu

et al. 2015

Water pipe cooling has been widely used for the temperature control and crack prevention of massive concrete structures such as high dams. Because both under-cooling and over-cooling may reduce the efficiency of crack prevention, or even lead to great harm to structures, we need an accurate and robust numerical tool for the prediction of cooling effect. Here, a 3D discrete FEM Iterative Algorithm is introduced, which can simulate the concrete temperature gradient near the pipes, as well as the water temperature rising along the pipes. On the basis of the heat balance between water and concrete, the whole temperature field of the problem can be computed exactly within a few iteration steps. Providing the pipe meshing tool for building the FE model, this algorithm can take account of the water pipe distribution, the variation of water flow, water temperature, and other factors, while the traditional equivalent algorithm based on semi-theoretical solutions can only solve problems with constant water flow and water temperature. The validation and convergence are proved by comparing the simulated results and analytical solutions of two standard second-stage cooling problems. Then, a practical concrete block with different cooling schemes is analyzed and the influences of cooling factors are investigated. In the end, detailed guidance for pipe system optimization is provided. temperature controlling, and block surface protection [3]. Among them, the water pipe cooling proves to be the most efficient and economic.Dating from the 1930s, the water pipe cooling technique was first used by the Bureau of Reclamation in Hoover Dam, of which the thin-walled metal pipes were embedded in the concrete block during construction period [1]. Since then, it spread over the world from common concrete to roller-compacted concrete (RCC), and from dams to sluices and other structures [4][5][6]. In the 1970s, a high-density polyethylene (HDPE) pipe with high thermal conductivity arose and soon took over metal pipe in hydraulic projects, such as Sayano-Shushenskaya Dam and Ertan Dam, because of its great flexibility for shaping [6]. Figure 1(a) shows the configuration of Jinping-I Arch Dam with 26 sections divided by temporary transverse joints. Each dam section was placed layer by layer at a vertical interval of 3 m. The cooling pipes were usually embedded in horizontal section planes like an S curve shown in Figure 1(b), with both vertical and horizontal pipe spacing of about 1.2-3.0 m. To keep the effectiveness, the pipe length should better not exceed 250 m. For those huge concrete structures like arch dams, which are first built by several parts and then joined together to meet their uneven deformations, the cooling process generally includes two stages. The firststage cooling begins several hours after the concrete placement, aiming to suppress the maximum concrete temperature rising. Before the joint grouting between neighboring parts, a second-stage cooling is carried out to make the inner temperature decrease till it gets near its...

\begin{matrix} center \\ center {bold-italicΡ}_{n + 1} (TList_i) > {\overset{P}{true}}_{n + 1} \Rightarrow \\ center {bold-italicU}_{n + 1} (TList_i, Mesh_j) > {bold-italicU}_{n + 1} (Mesh_j) \end{matrix}

and as the time steps tend to zero, Δ t max → 0,

U_{n + 1} ((), italicTList_i, italicMesh italic_j) \to U_{n + 1} ((), italicMesh italic_j) + 0

Because of the inherited overly stiff property for fully compatible FEM , the positive definite stiffness matrix K ( Mesh_j ) is an over‐estimation of exact K , which means

U_{n + 1} ((), italicMesh_j) < U_{n + 1}

and as the meshes are densified, d e → 0,

U_{n + 1} ((), italicMesh_j) \to U_{n + 1} - 0

Section: Methods Verification and Discussionmentioning

confidence: 99%

A 3D discrete FEM iterative algorithm for solving the water pipe cooling problems of massive concrete structures

Num Anal Meth Geomechanics

Liu

et al. 2015

“…For NS-PIM, there are two schemes available to create the needed shape functions, T3-scheme and T6/3-scheme (Cheng et al , 2010). The T3-scheme is a scheme using the vertexes of the background cells to create the shape functions.…”

Section: Briefing On Formulationsmentioning

confidence: 99%

“…The NS-PIM as one member of the meshfree methods has drawn a growing interest in the application of the static problems (Liu et al , 2005), the dynamic problems (Zhang et al , 2018), the heat transfer problems (Wu et al , 2009a), the thermoelasticity problems (Wu et al , 2009b), the contact problems (Li et al , 2007), the consolidation problems (Pan et al , 2018), etc. Plenty of excellent properties (Cheng et al , 2010; Zhang et al , 2011), such as good accuracy, a high convergence rate and even the upper bound solutions, have been found in these applications.…”

Section: Introductionmentioning

confidence: 99%

The forward and inversion analysis of high rock-fill dam during construction period using the node-based smoothed point interpolation method

Pan

2019

Purpose The meshfree node-based smoothed point interpolation method (NS-PIM) is extended to the forward and inversion analysis of a high gravelly soil core rock-fill dam during construction periods. Design/methodology/approach As one member of the meshfree methods, the NS-PIM has the advantages of “softer” stiffness and adaptability to large deformations which is quite indispensable for the stability analysis of rock-fill dams. In this work, the present method contains a reconstruction procedure to deal with the existence or nonexistence of the construction layers. After verifying the validity of the NS-PIM method for nonlinear elastic model during construction period, the convergence features of the NS-PIM and FEM methods are further investigated with different mesh schemes. Furthermore, the NS-PIM and FEM methods are applied for the forward analysis of a high gravelly soil core rock-fill dam and the convergence features under complex stress conditions are also studied using the rock-fill dam model. Finally, the NS-PIM method is used to calculate the Duncan–Chang parameters of the deep overburden under the high gravelly soil core rock-fill dam based on the back-propagation neural network method. Findings The results show that: the NS-PIM solution for construction analysis still possesses the property of upper bound solution even under complex stress conditions and can provide comparatively more conservative results for safety evaluation. Furthermore, it can be used to evaluate the accuracy of results and mesh quality together with the FEM solution which has the property of lower bound solution; the inversion analysis in this work provides a set of material parameters for the deep overburden under high rock-fill dam during construction period and the calculated results show good agreement with the measured displacement values and it is feasible to apply the NS-PIM to the forward and inversion analysis of high rock-fill dams on deep overburden during construction periods. Research limitations/implications In further study, the feasibility of three-dimensional problems, elastic–plastic problems, contact problems and multipoint inversion can still be probed in the NS-PIM solution for the forward and inversion analysis of high rock-fill dams on deep overburden. Practical implications This paper introduced a method for the forward and inversion analysis of high rock-fill dams during construction period using the NS-PIM solution. The property of upper bound solution ensures that the NS-PIM can provide more conservative results for safety evaluation. The inversion analysis in this work provides a set of material parameters for the deep overburden under high rock-fill dam during construction periods. Originality/value First, the analysis from forward to inversion for high rock-fill dams during construction period using the NS-PIM solution is accomplished in this work. A procedure dealing with the existence or nonexistence of the construction layers is also developed for the construction analysis. Second, it is confirmed in this work that the NS-PIM still possesses the property of upper bound solution even under complex stress conditions (the forward analysis of high rock-fill dams during construction period). Thus, more conservative results can be provided for safety evaluation. Furthermore, it can be used to evaluate the accuracy of results and mesh quality together with the FEM solution which has the property of lower bound solution. Third, the calculated material parameters of the deep overburden in this work can be used for further studies of the high rock-fill dam.

“…The node-based smoothed point interpolation method (NS-PIM) (Liu et al , 2011; Zhang et al , 2007; Cheng et al , 2009), as one member of the meshfree methods, has drawn a growing interest in the application of the static problems, the dynamic problems, the heat transfer problems, the thermoelasticity problems, etc. Plenty of excellent properties, such as good accuracy, a high convergence rate and even the upper bound solutions, have been found in these applications (GR Liu and Zhang,2008; Zhang et al , 2011; Zhang et al , 2008).…”

Section: Introductionmentioning

confidence: 99%

Meshfree method analysis of Biot’s consolidation using the node-based smoothed point interpolation method (NS-PIM)

Pan

et al. 2018

Purpose The purpose of the article is to extend the node-based smoothed point interpolation method (NS-PIM) for soil consolidation analysis based on the Biot’s theory. Design/methodology/approach The shape functions for displacements and pore pressures are constructed using the PIM separately, leading to the Kronecker delta property and easy implementation of essential boundary conditions. Then, a benchmark problem of 2D consolidation under ramp load is solved to investigate the validity of this application. Meanwhile, convergence features of different solutions are studied. Furthermore, the incompressible and impermeable condition under instant load is investigated. The results calculated by the NS-PIM solution with different orders of shape functions are compared. Finally a 2D consolidation problem in construction period is solved. An error estimation method is applied to check the mesh quality. Findings The results of the NS-PIM solution show good agreement with those certified results. Useful convergence features are found when comparing the results of the NS-PIM and the FEM solutions. A simple method is introduced to estimate the errors of the model with rough grids. The convergence features and error estimation method can be applied to check the mesh quality and get accurate results. More stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions under the incompressible and impermeable condition. Research limitations/implications It cannot be denied that the calculation of NS-PIM solution takes more time than that of the FEM solution, and more work needs to be carried out to optimize the NS-PIM solution. Also, in further study, the feasibility of more complicated and practical engineering problems can still be probed in the NS-PIM solution. Practical implications This paper introduced a method for the consolidation analysis on the situation of construction loads (“ramp load”) using the NS-PIM which is quite indispensable in many foundation problems. Also, more stable results can be obtained using the NS-PIM solution with lower order of pore pressure shape functions than that with same order of shape functions. Originality/value This study first focuses on the situation of construction loads (“ramp load”) in the NS-PIM consolidation analysis which is quite indispensable in many foundation problems. An error estimation method is introduced to evaluate the mesh quality and get accurate values based on the convergence features of the FEM and NS-PIM solutions. Then, the incompressible and impermeable condition under instant load is investigated, and the analysis show that the NS-PIM with lower order of pore pressure shape functions can get stable results in such conditions.