Page 75 - 水利学报2021年第52卷第5期

Multivariate parameter simulation of 3D fracture network in dam foundation based on
improved autoregressive flow model

ZHANG Yichi，LÜ Mingming，GUAN Tao，WANG Jiajun，YU Jia，REN Bingyu
（State Key Laboratory of Hydraulic Engineering Simulation and Safety，Tianjin University，Tianjin 300072，China）

Abstract： In stochastic modeling of 3D discrete fracture network （DFN） in dam foundations， the key lies
in the estimation of multidimensional joint distribution of geometric parameters of fractures including dip，
dip direction， aperture etc. However， existing DFN modeling methods are based on classic distributions，
which ignore the correlations among parameters and cannot realize the high precision probability density esti⁃
mation of the multidimensional joint distribution of fracture parameters. To solve those problems，this paper
proposes an improved autoregressive flow model——Density Peak Clustering Autoregressive Flow （DPCAF），
in which the Gaussian mixture distribution and DensityPeak clustering algorithm are used to modify the
base distribution in normalized feature space. This model makes up for the deficiency of autoregressive flow
which lacks consideration of fracture dominant partitioning in distribution estimation， and enhances the fit⁃
ting ability to multi-modal joint distributions. Furthermore，a method of multivariate parameter simulation of
3D fracture network using DPCAF model is proposed， which takes the correlations among fracture parame⁃
ters into account，and can realize the accurate maximum likelihood estimation and sampling from the multi⁃
dimensional joint distribution. Engineering application shows that the DPCAF model can better fit the com⁃
plex multidimensional joint distributions of fracture parameters compared with classic distribution-based meth⁃
ods， and have the advantage of construct the correlation structures among fracture parameters， which fur⁃
ther ensure the reliability of DFN models.
Keywords： hydropower engineering； rock mass of dam foundation； discrete fracture network； multivariate
parameter simulation；autoregressive flow model
（责任编辑：李福田）

（下转第 564 页）
Heat exchange model between river-lake and atmosphere during ice age

YANG Kailin
（State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin，
China Institute of Water Resources and Hydropower Research，Beijing 100038，China）

Abstract：The heat exchange model between river-lake and atmosphere is the basis for calculating and ana⁃
lyzing the temporal and spatial variation law of ice formation，development and melting. Based on the exist⁃
ing research results of solar radiation，long-wave radiation，evaporation and convection models，and on the
basis of on-site observation of ice conditions and historical weather data， a nonlinear model of heat ex⁃
change between rivers， lakes and atmosphere is established， which is suitable for ice age calculation and
analysis. A solar radiation calculation model considering sunny day scattering is proposed. The atmospheric
long-wave inverse radiation is calculated by Iziomon formula，and evaporation and convection are calculated
by Russian winter formula. Based on the fact that the observed temperature T s of snow or ice surface is
close to air temperature T a，a multi-parameter nonlinear heat exchange model between rivers，lakes and the
atmosphere is linearized at T s=T a，and then the heat exchange coefficient h sa is determined by linear regres⁃
sion using historical weather data. The research proves that：（1） the wind speed of low-lying river cannot
be estimated correctly by the wind level or wind speed data of meteorological stations；（2） h sa obtained from
historical weather data of typical years can be used to predict heat exchange in other years；（3）h sa is propor⁃
tional to T a，and the average value of h sa in Beijing，Shenyang，Baoding and Baotou is > 10.0 W/（m·℃）；
2
and （4） the average values of h sa in Mohe and Lhasa are slightly smaller than those in Beijing and other
areas.
Keywords：ice age；solar radiation；long wave radiation；evaporation and convection；linearization；heat ex⁃
change coefficient
（责任编辑：耿庆斋）

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