基于灰色马尔科夫模型的地基承载力预测

陈飞宇; 董利飞; 王苗; 王凡顺

doi:10.19509/j.cnki.dzkq.2022.0073

基于灰色马尔科夫模型的地基承载力预测

doi: 10.19509/j.cnki.dzkq.2022.0073

陈飞宇^1a,,
董利飞^{1a, 2, ,},
王苗^1b,
王凡顺³

基金项目:

重庆市“三峡水库岸坡与工程结构灾变防控工程技术研究中心”开放基金项目 SXAPGC18YB04

重庆市“三峡水库岸坡与工程结构灾变防控工程技术研究中心”开放基金项目 SXAPGC21MS04

重庆三峡学院校级青年项目 19QN10

重庆三峡学院土木水利硕士研究生开放基金 TMSL20YB18

重庆三峡学院研究生科研创新项目 YJSKY21020

详细信息

作者简介:
陈飞宇(1994—)，男，现正攻读土木水利专业硕士学位，主要从事基础工程方面的研究工作。E-mail: fychen19@163.com

通讯作者:
董利飞(1988—)，男，副教授，主要从事岩石力学与工程安全、非常规油气开发等方面的教学和研究工作。E-mail: lfdong2012@sina.com

中图分类号: P642
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出版历程
- 收稿日期: 2021-06-20

Prediction of foundation bearing capacity based on grey Markov model

Chen Feiyu^{1a
,},
Dong Lifei^{1a, 2
, ,},
Wang Miao^1b,
Wang Fanshun³

摘要

摘要:
地基是工程建设的基础，其承载力计算和预测十分关键，决定着建筑工程上部结构的安全性与稳定性。为实现小数据量、短周期、较高精度的地基承载力预测。本研究提出以地基静载试验数据为依据，利用灰色模型进行计算，结合马尔科夫优化，建立灰色马尔科夫预测模型，预测固定荷载作用下的地基沉降，进而明确相应沉降下的基地承载力。同时，将该模型与传统的灰色GM(1, 1)模型、指数曲线拟合模型进行对比，分析3种模型的优劣。结果表明，案例一中，静载试验下的地基承载能力完好，灰色马尔科夫模型、GM(1, 1)模型、指数曲线模型预测值与实测值的平均相对误差依次为1.55%，3.80%，10.22%，灰色马尔科夫模型精度最高，更契合地基静载试验，能准确有效地明确地基承载力；案例二中，地基在静载试验下发生破坏，破坏前灰色马尔科夫模型预测值与实测值的平均相对误差仅为0.5%，预测效果良好。破坏时，地基沉降迅速增加，加载点模型预测值与实测值的相对误差出现异常，骤增至26.29%，以此可判断破坏前一级加载序列荷载为该地基的极限承载力。运用此模型指导地基静载试验，在保障工程施工安全的前提下，相邻试验点可以适当减少静载试验次数，节约工程施工成本，为信息化地基静载试验提供一个新的计算工具。
- 地基承载力 /
- 灰色马尔科夫模型 /
- 灰色GM(1, 1)模型 /
- 预测
Abstract:
Foundation is the foundation of engineering construction, and its bearing capacity calculation and prediction are very critical indetermining the safety and stability of the superstructure of the building project. To realize the foundation bearing capacity prediction with small data volume, short period, and higher accuracy, this paper establishes the gray Markov prediction model to predict the foundation settlement under the action of fixed load and clarify the base bearing capacity, based on the foundation static load test data, the gray model for calculation, and Markov optimization. Meanwhile, the model is compared with the traditional gray GM(1, 1) model and exponential curve fitting model to analyze the advantages and disadvantages of the three models. The results show that in case one, the bearing capacity of the foundation underthe static load test is intact, and the average relative errors between the predicted and measured values of the gray Markov model, GM(1, 1) model, and exponential curve model are 1.55%, 3.80% and 10.22% in order, and the gray Markov model has the highest accuracy and fits the static load test of the foundation better, which can clarify the bearing capacity of the foundation accurately and effectively; in case two, the foundation The average relative error between the predicted and measured values of the gray Markov model before the damage occurred under the static load test was only 0.5%, and the prediction effect was good. When the damage occurred, the settlement of the foundation increased rapidly, and the relative error between the predicted and measured values of the model at the loading point was abnormal and increased to 26.29%, so that the load of the loading sequence at the first level before the damage could be judged as the ultimate bearing capacity of the foundation. Using this model to guide the foundation static load test, the number of static load tests can be appropriately reduced at adjacent test points under the premise of ensuring construction safety, saving the construction cost of the project, and providing a new calculation tool for the information foundation static load test.
- foundation bearing capacity /
- grey Markov model /
- grey GM(1, 1) model /
- prediction

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图 1 模型流程图

Figure 1. Model flow chart

下载: 全尺寸图片幻灯片

图 2 3种预测模型的绝对误差对比图

Figure 2. Absolute error comparison chart of three prediction models

下载: 全尺寸图片幻灯片

表 1 静载试验中地基荷载与沉降的实测数据

Table 1. Measured data of foundation load and settlement in static load test

加载序号	1	2	3	4	5	6	7	8	9
荷载/kN	92	138	184	230	276	322	368	414	460
沉降/mm	4.99	9.39	12.32	15.85	19.97	25.79	27.79	35.22	43.82

下载: 导出CSV

表 2 状态区域分布

Table 2. Distribution of state regions

加载序号	相对误差/%	状态划分	加载序号	相对误差/%	状态划分
2	-11.93	一	6	8.07	四
3	-4.55	二	7	-4.53	二
4	0.44	三	8	-1.11	二
5	3.15	三	9	0.41	三

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表 3 状态预测计算

Table 3. State prediction calculation

加载序号	初始状态	转移步数	状态一	状态二	状态三	状态四
5	3	1	0	0	1/3	1/3
4	3	2	0	1/3	0	1/3
3	2	3	0	0	0	1/3
2	1	4	0	0	0	1
合计			0	1/3	1/3	2

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表 4 3种预测方式的对比分析

Table 4. Comparative analysis of three prediction methods

加载序号	荷载/kN	沉降/mm	曲线拟合		灰色GM(1, 1)		灰色马尔科夫
加载序号	荷载/kN	沉降/mm	测值	相对误差/%	预测值	相对误差/%	预测值	相对误差/%
1	92	4.99	8.03	60.92	4.99	0.00	4.99	0.00
2	138	9.39	9.94	5.86	10.51	11.93	9.64	2.66
3	184	12.32	12.30	0.16	12.88	4.55	12.50	1.46
4	230	15.85	15.22	3.97	15.78	0.44	16.10	1.58
5	276	19.97	18.83	5.71	19.34	3.15	19.73	1.20
6	322	25.79	23.30	9.65	23.71	8.07	25.22	2.21
7	368	27.79	28.82	3.71	29.05	4.53	27.41	1.37
8	414	35.22	35.67	1.28	35.61	1.11	34.57	1.85
9	460	43.82	44.13	0.71	43.64	0.41	44.53	1.62
平均相对误差/%			10.22		3.80		1.55
平均绝对误差/mm			1.07		0.70		0.36

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表 5 静载试验中地基荷载与沉降的实测数据

Table 5. Measured data of foundation load and settlement in static load test

加载序号	1	2	3	4	5	6	7(破坏)
荷载/kN	160	240	320	400	480	560	640
沉降/mm	6.77	14.04	21.27	29.48	42.39	59.34	115.27

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表 6 对加载序号1~4号的沉降值修正

Table 6. Correction of settlement value for loading sequence number 1-4

加载序号	实测值	预测值	修正值
1	6.77	6.77	6.77
2	14.04	14.56	14.14
3	21.27	20.59	21.23
4	29.48	29.13	29.42

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表 7 2种预测模型的对比分析

Table 7. Comparative analysis of two prediction models

加载序号	荷载/kN	沉降/mm	灰色GM(1, 1)		灰色马尔科夫
加载序号	荷载/kN	沉降/mm	预测值	相对误差/%	预测值	相对误差/%
5	480	42.39	41.2	2.81	42.47	0.19
6	560	59.34	58.27	1.80	58.86	0.81
7(破坏)	640	115.27	82.42	28.50	84.97	26.29

下载: 导出CSV

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