用灰色理论确定边坡最优监测点及安全系数
王贵成1, 2,曹 平2,林 杭2,张钦礼2,孙顺利2
(1. 商丘师范学院 地理系,河南 商丘,476000;
2. 中南大学 资源与安全工程学院,湖南 长沙,410083)
摘 要:采用基于位移判据的强度折减法分析边坡的稳定性。在坡高为20 m、坡角为45°的均质土坡的临界滑移线内外,按照坡面上、中、下各自布置3个监测点共9个监测点,通过FLAC3D自带的FISH语言,开发数据记录工具,记录不同监测点的水平位移与折减系数,并分析它们的关系。为了确定最优监测点以减少工作量和经费,运用灰色理论软件,通过对安全系数序列和各个观测点的水平位移序列进行灰色关联度分析,得出各个观测点的水平位移观测序列与安全系数序列之间的灰色(邓氏)关联度和相对关联度,通过分析对比关联度确定最优监测点;利用GM(1,1)预测模型对安全系数和最优监测点的水平位移进行预测。研究结果表明:与安全系数序列的邓氏关联度较大的1,2,4,5监测点可作为最优监测点;当安全系数为1.120 47时,各个监测点的水平位移达14.910~40.842 m,临界安全系数为1.120。
关键词:安全系数;检测点;位移;灰关联度;预测
中图分类号:TU44 文献标识码:A 文章编号:1672-7207(2007)03-0574-05
Determination of optimum monitoring point of slope and
safety factor using grey system theory
WANG Gui-cheng1, 2, CAO Ping2, LIN Hang2, ZHANG Qin-li2, SUN Shun-li2
(1. Department of Geography, Shangqiu Teachers College, Shangqiu 476000, China;
2. School of Resources and Safety Engineering, Central South University, Changsha 410083, China)
Abstract: Stability of the slope was analysed using the method of the strength reduction based on the displacement criterion. The target was a homogeneous, 20 m high soil slope that its dip angle was 45°. 9 monitoring points were set at the upper, middle and lower part of the slope surface totally inside and outside of its critical landslip line. FISH language of the FLAC3D was used as a computer language tool to program, horizontal displacements and the reduced coefficients of all monitoring points were recorded and their relationships were studied. In order to determine optimum monitoring point and save expenses, grey system theory was applied to get the degrees of grey incidence and the relative incidence between the array of the safety coefficient and the array of monitoring points’ horizontal displacements to determine the optimum monitoring points. The safety coefficient and the horizontal displacement of the optimum monitoring point was forecast using the GM(1,1) model, and the mutation characteristic of the forecast value was analyzed to determine its critical safety factor. The results show that the points 1, 2, 4, 5 can be the optimum monitoring points, because its Dengs’ degree of grey incidence with the safety coefficient is bigger than others. When the safety coefficient is 1.120 47, the horizontal displacements of the monitoring points is 14.910-40.842 m. The critical safety factor is 1.120.
Key words: safety factor; monitoring point; displacement; the degree of grey incidence; forecast
边坡稳定性分析的一个重要指标是安全系数,随着计算机技术的发展,人们采用强度折减法对其进行 计算[1-7]。如何判断边坡是否达到失稳状态是强度折减法实施的关键。在此,本文作者采用位移判据[7-11]判断边坡的失稳性,并以文献[1]中均质边坡的各观测点水平位移模拟数据为分析对象,运用灰色理论进行分析,根据各观测点位移的发展趋势,由灰色关联度理论,确定最优监测点;运用灰色预测理论,对临界安全系数进行预测。
1 均质土坡监测点和位移方式
1.1 监测点位置的确定
为便于讨论,选取文献[1]中的均质土坡作为分析对象。该边坡高20 m,坡角为45°。按照平面应变建立FLAC3D计算模型。该模型共816个单元,1 176个节点。边界条件为:下部固定,左右两侧水平约束,上部为自由边界,计算模型见图1。通过对比不同监测点在不同位移方式下的曲线,并由方程拟合得到它们所对应的安全系数,定量分析监测点位置和位移方式选取的合理性[12-14]。容重γ=25 kN/m3,弹性模量E=103 MPa,泊松比μ=0.3,粘结力c=42 kPa,内摩擦角φ=17°,模型长为105 m,高为40 m,边坡高为20 m,边坡角为45°。
图1 均质土坡计算模型
Fig.1 Calculation model of the homogeneous soil slope
通过数值计算,当边坡破坏时出现1条滑移线,如图2所示,这里将该滑移线称为临界滑移线。在滑移线内外布置若干点,具体位置见图2:坡面上、中、下分别布置3个监测点,以此3个监测点为基准沿水平方向每隔10 m另布置6个监测点,整个坡体监测点数为9个。
图2 土质边坡监测点布置
Fig.2 Location of monitoring points of the homogeneous soil slope
1.2 观察点的位移
通过FLAC3D自带的FISH语言,开发数据记录工具,记录不同监测点的水平位移与折减系数的关系,如表1所示。从表1可见,只有点1,2,4和5的位移曲线存在突变特征,所以,定性上可认为将这4个点作为监测点是有效的。由图2所示监测点位置可见,这些点均位于临界滑移线以内。
表1 土质边坡监测点水平位移与折减系数的关系
Table 1 Relationship between horizontal displacement and the reduction factor of the monitoring points
2 水平位移与安全系数的灰色关联性分析
2.1 邓氏关联度分析
设安全系数序列为,点i的水平位移序列为,即:
设各序列的初值像为X0和Xi(i=1,2,…,9),则点i的水平位移序列与安全系数序列在第k个观察值的关联系数为[15-16]:
则第i个观察点的水平位移序列与安全系数序列的邓氏关联度为:
运用式(1)~(4),根据表1中的观察值,运用灰色理论软件,可求得各观察点水平位移序列与安全系数序列的邓氏(普通)灰色关联度(见表2)。
2.2 灰色相对关联度分析
令
, (5)
, (6)
,
(7)
则两序列X0与Xi之间的灰色相对关联度为:
。 (8)
根据式(5)~(8),由表1中的观察值,运行灰色理论软件,可求得各观察点的水平位移与安全系数的相对关联度,见表2。
从表2可以看出,点1,2,4和5的邓氏关联度均大于0.889 3,而点3和6~9的邓氏关联度均小于0.638 3,说明点1,2,4和5的水平位移与安全系数的变化规律非常相似,步调一致,同步增大,也就是说,点1,2,4和5作为边坡的水平位移观察点恰当;点3和6~9与安全系数的相对关联度较大,皆大于0.845 9,说明这些点水平位移增加的速度与安全系数增加的速度相近。由于安全系数增加缓慢,这些点水平位移增加的速度也较慢,故这些点不宜作为观察点。
表2 各观察点水平位移与安全系数之间的灰色关联度
Table 2 The relative incidence degree of horizontal move and safety coefficient of all points
3 重要监测点水平位移的GM(1,1)模型预测
设
(9)
为某观察点的水平位移序列的1-AGO序列(即一次累加生成算子序列),Z(1)为X(1)的紧邻均值生成序列,则其GM(1,1)的时间响应预测序列为[17]:
。 (10)
其中:
k=1, 2, …, n; a=[a, b]T=(BTB)-1BTY; (11)
,。 (12)
对于重要监测点1,2,4和5的水平位移序列以及安全系数序列,各取其靠近原点的时间点10~14的观测值,运行灰色理论软件,可得到其5步预测值,如表3所示。
表3 重要监测点水平位移及安全系数的5步预测值
Table 3 The forecast values of the horizontal move and safety coefficient of the important points
从表3可以看出,当安全系数为1.120 47时,各个监测点的水平位移达14.910~40.842 m,据工程实际经验,相对于初始状态,认为其位移量已达“∞”,即滑坡已经发生。因此,确定其安全系数的临界值为 1.120 47。
4 结 论
a. 选取均质土坡作为分析对象,由数值计算,确定了临界滑移线;在滑移线内外按规律共布置9个观测点;通过FLAC3D自带的FISH语言,开发数据记录工具,记录了不同监测点的水平位移与折减系数的关系。
b. 为了减少监测工作量,运用灰色理论软件,通过对土质边坡9个观测点的位移序列与安全系数序列灰色关联度进行分析,根据关联度的大小特征确定了位移敏感点即最优观测点。其中,点1,2,4和5的水平位移序列与安全系数序列的邓氏关联度较大,作为边坡的水平位移观测点恰当;点3和6~9不宜作为观测点。
c. 通过运用GM(1,1)预测模型对最优观测点位移和安全系数进行预测,根据工程实际,经分析对比位移数列的突变特征,确定临界安全系数为1.120 47。
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收稿日期:2007-01-05
基金项目:国家教育部博士生专项基金资助项目(20060533071);国家自然科学基金资助项目(50274074)
作者简介:王贵成(1962-),男,河南武陟人,博士研究生,副教授,从事地质、资源经济与可持续发展研究
通讯作者:王贵成,男,博士研究生;电话:13975184784;E-mail: wangguicheng6@163.com