﻿ 桩-土-结构相互作用分析中土动力模型的修正
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (11): 1473-1478, 1574.  DOI: 10.11908/j.issn.0253-374x.2018.11.001 0

### 引用本文

DENG Haoyun, JIN Xinyang, GU Ming, HUANG Jifeng. Modification of Soil Dynamic Constitutive Model in Pile-soil-structure Interaction Analysis[J]. Journal of Tongji University (Natural Science), 2018, 46(11): 1473-1478, 1574. DOI: 10.11908/j.issn.0253-374x.2018.11.001

### 文章历史

1. 同济大学 土木工程防灾国家重点实验室，上海 200092;
2. 中国建筑科学研究院 建筑结构研究所，北京 100020

Modification of Soil Dynamic Constitutive Model in Pile-soil-structure Interaction Analysis
DENG Haoyun 1, JIN Xinyang 2, GU Ming 1, HUANG Jifeng 2
1. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;
2. Institute of Building Structures, China Academy of Building Research, Beijing 100020, China
Abstract: The modified method of equivalent linear model was proposed when performing pile-soil-structure interaction. The dimension of near region was solved and the modified equivalent linear model was obtained. Then, the extensive numbers of the models were analyzed and the modified parameters were solved. Finally, the regression analysis was performed to obtain the empirical equation based on the extensive modified parameters. It is shown that the accuracy of pile-soil-structure interaction analysis under strong earthquake is improved with the modified method.
Key words: pile-soil-structure interaction    equivalent linear    near-field modification method    dynamic response

Ishihara[2]研究发现，强震作用下基础近场区域的土会产生较大的剪切应变，非线性强.若地基土选用等效线性模型，则结构动力分析得到的结果不够精确.Yoshida等[3]也指出，强震作用下土的动力模型采用等效线性模型会使结构的位移峰值增大.然而，当前在进行桩-土-结构相互作用分析时，这些误差往往被忽略.因此，在分析强震作用下桩-土-结构体系的动力响应时，需要对近场区域土的动力模型进行修正.常用的方法是将场地划分为规则的近场区域和远场区域，近场区域采用非线性模型，远场区域采用线性模型.Casciati等[4]建立了桩-土-结构模型并进行动力分析，其中近场区域使用等效线性模型，远场区域使用线性模型，验证了该模型具有良好的精度.然而，地基土的等效剪切模量和阻尼比是通过SHAKE91自由场分析求得后导入三维有限元模型的，未考虑上部结构对地基土的影响.

1 有限元模型 1.1 接触

1.2 结构阻尼

 $\mathit{\boldsymbol{C}} = \alpha \mathit{\boldsymbol{M}} + \beta \mathit{\boldsymbol{K}}$ (1)

 ${\xi _i} = \frac{\alpha }{{2{\omega _i}}} + \frac{{\beta {\omega _i}}}{2}$ (2)
 ${\xi _j} = \frac{\alpha }{{2{\omega _j}}} + \frac{{\beta {\omega _j}}}{2}$ (3)

1.3 重力荷载施加

1.4 等效线性模型

 $\frac{G}{{{G_{\max }}}} = \frac{1}{{1 + \frac{\gamma }{{{\gamma _{\text{d}}}}}}}$ (4)

 $\lambda = {\lambda _{\max }}\left( {1 - \frac{G}{{{G_{\max }}}}} \right)$ (5)

Abaqus软件中，等效线性模型可以通过Kelvin模型来反映土体在周期载荷下的滞回性.该模型由线弹性弹簧和阻尼装置并联组成，应力-应变关系为

 $\sigma = E\varepsilon + \eta \dot \varepsilon$ (6)

 ${\sigma _{ii}} = v{\varepsilon _V} + {\eta _v}{{\dot \varepsilon }_V} + 2\mu {\varepsilon _{ii}} + 2{\eta _\mu }{{\dot \varepsilon }_{ii}}$ (7)
 ${\sigma _{ij}} = \mu {\gamma _{ij}} + 2{\eta _\mu }{{\dot \gamma }_{ij}}$ (8)

 图 1 等效线性模型子程序流程图 Fig.1 Subroutine flow chart of equivalent linear model
1.5 人工边界及场地宽度

2 模型参数 2.1 结构参数

2.2 场地类型及参数

 $T = \sqrt {\sum\limits_{i = 1}^N {{{\left( {\frac{{4{h_i}}}{{{v_i}}}} \right)}^2}\frac{{2{H_i}}}{{{h_i}}}} }$ (9)

2.3 地震波的筛选及反演

 ${Q_{N, 1}} = \frac{{{Q_N}^\prime }}{{{Q_1}^\prime }} = \frac{{{x_1} + {y_1}}}{{{x_N} + {y_N}}}$ (10)

3 近场土修正方法 3.1 地基土修正区域

 图 2 近场区域土的剪切应变(20层结构，Ⅲ类(1)场地) Fig.2 Shear strain in the near-field soil (20-storey building, soil type Ⅲ(1))

 图 3 场地土分区 Fig.3 Soil partition

 图 4 各区域最大剪切应变 Fig.4 Maximum shear strain of each region
3.2 修正区域剪切模量

 图 5 不同模型结构水平位移对比 Fig.5 Comparison of structural lateral displacement among different models

(1) 由图 5a图 5c对比得出，随着场地周期增大，场地变软，等效线性模型与摩尔-库伦模型中结构水平位移的误差越大.

(2) 由图 5a图 5d对比得出，结构高度越大，等效线性模型与摩尔-库伦模型中结构水平位移的误差越大.

(3) 由图 5a图 5b对比得出，对相同的桩-土-结构模型，不同地震波作用下位移比ΔELM/ΔMC的值非常接近，表明同一模型下不同地震波对动力分析结果影响很小.

(4) 在强震作用下，采用修正等效线性模型得到的结构水平位移，比等效线性模型更接近摩尔-库伦模型的结果(ΔMELM/ΔMC的值比ΔELM/ΔMC更接近1)，故本文针对等效线性模型提出的修正方法是合适的.

3.3 近场区域修正系数及回归公式

 图 6 剪切模量修正系数 Fig.6 Modified coefficients of shear modulus

 $k = \left( {a + bT} \right){T^2} + \left( {c + dT} \right){T_1} + e$ (11)

4 试验算例

 图 7 算例的三维有限元模型 Fig.7 Three-dimensional finite element model of the example

 图 8 不同模型结构水平位移和层间剪力对比 Fig.8 Comparison of structural lateral displacement and storey shear among different models
5 结论

(1) 强震作用下，桩-土-结构模型的基础附近会出现强非线性区域，其宽度为超出结构宽度的50%，深度为结构宽度的50%.

(2) 本文分析了100个算例，得到桩-土-结构模型近场区域的修正系数，范围在1.03至1.81之间，并且随着场地变软，结构变高，修正系数增大.

(3) 本文对所有算例的修正系数进行回归分析，得到修正系数的经验公式，公式计算值和真实值的误差不超过2%.

(4) 在进行桩-土-结构相互作用分析时，相比等效线性模型而言，采用修正等效线性模型得到结构的动力响应与摩尔-库仑模型的结果更为接近，故本文提出的修正方法和经验公式具有较好的适用性和正确性.

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