نوع مقاله : مقاله پژوهشی

نویسندگان

• امیر ملک پور
• نیما صادقیان
• محمدجواد فرخی

دانشگاه گیلان

چکیده

در تحلیل احتمالاتی پدیده تحکیم خاک، نقش عدم‌قطعیت متغیرهای هیدرولیکی و ژئوتکنیکی و همبستگی میان مقادیر آنها از اهمیت ویژه‌ای برخوردار است. در تحقیق حاضر، فرضیه تاثیر همبستگی متغیرهای تصادفی هدایت هیدرولیکی و ضریب قابلیت فشردگی حجمی بر تغییرات زمانی تحلیل احتمالاتی تحکیم خاک مورد بررسی قرار می‌گیرد. نکته حائز اهمیت این است که در صورت تائید تاثیر همبستگی متغیرهای تصادفی مورد بررسی، بررسی نقش آنها به صورت منفرد موجب خطا در تعیین تغییرات زمانی تحکیم خاک می‌شود. بدین جهت در تحقیق حاضر، یک برنامه‌ رایانه‌ای در محیط MATLAB توسعه داده شد و از حل عددی معادله دیفرانسیل تحکیم خاک، به عنوان راه حل پایه در روش احتمالاتی شبیه‌سازی مونت‌کارلو استفاده گردید. سپس تأثیر اعمال همبستگی هدایت هیدرولیکی و ضریب قابلیت فشردگی حجمی به عنوان دو متغیر تصادفی تاثیرگذار، با استفاده از توابع کاپولا مختلف و در قالب تحلیل احتمالاتی دو متغیره تحکیم خاک در منطقه شفت استان گیلان بررسی شد. نتایج نشان داد که بهترین توزیع منفرد برازش داده شده بر هر یک از متغیرهای تصادفی مذکور، گوسی معکوس بوده در حالی که با اعمال تاثیر همبستگی، بهترین توزیع احتمالاتی مشترک از تابع کاپولا گوسی حاصل می‌گردد. همچنین خطای ناشی از عدم اعمال همبستگی متغیرهای تصادفی بر پدیده تحکیم، در عمق‌های خاک 2 و 4 متر به ترتیب 7 و 2/2 درصد به دست آمد. در انتها نتایج نشان داد که در شرایط عدم اعمال همبستگی متغیرهای تصادفی مورد بررسی در این تحقیق، سرعت پدیده تحکیم بیشتر از حالت اعمال همبستگی این متغیرها برآورد می‌گردد.

کلیدواژه‌ها

• تحلیل احتمالاتی مشترک
• خاک ریزدانه
• روش مونت‌کارلو
• توابع کاپولا

موضوعات

• ژئوتکنیک

عنوان مقاله [English]

Bivariate probabilistic analysis of temporal variations of pore water pressure during consolidation process in structural foundation

نویسندگان [English]

• Amir Malekpour
• Nima Sadeghian
• Mohammad Javad Farrokhi

University of Guilan

چکیده [English]

Bivariate probabilistic analysis of temporal variations of pore water pressure during consolidation process in structural foundation



Introduction

The consolidation and the subsequent settlement can lead to the land subsidence, building destruction, pipeline ruptures in water supply networks, and damage to the asphalt pavement. In soil consolidation analyses and many other geotechnical problems, the uncertainty of geotechnical variables and their spatial variations is of significant importance. As a result, the uncertainty-based approaches are currently employed to consider these problems rather than deterministic analyses. In this regard, some researches have demonstrated the considerable influence of the random variables of hydraulic conductivity and volume compressibility on the soil consolidation phenomenon. However, the studies have rarely addressed the correlation between these random variables and its effect on the probabilistic consolidation analysis. The current research aims at investigating the impact of correlation between two random variables of hydraulic conductivity and volume compressibility using copula functions via the development of a computer program in MATLAB. The performance of different copula functions in the bivariate probabilistic analysis of consolidation and the temporal variations of pore water pressure distributions are studied in a case study in Guilan province of Iran.



Methodology

In this research, a computer program was developed in MATLAB to estimate the marginal distributions of two random variables of hydraulic conductivity and soil volume compressibility. Then the bivariate probability distributions of two random variables were obtained using two copula groups of Archimedean (Clayton, Gumbel and Frank) and elliptic (Gaussian and t-student). The bivariate distributions of random variables were applied to estimate the temporal pore water pressure distributions during consolidation in soil depths of 2 and 4 meters. The best joint probability distribution and the corresponding copula function was determined on MvCAT software based on the correlation of random variables and using certain criteria such as AIC, BIC, RMSE, and NSE. As a feature of developed computer program in this research,1000 pair values of hydraulic conductivity and volumetric compressibility were generated by copula functions (from the primary 24 field data) in order to create more accurate results. Then, after numerically solving the governing differential equation of consolidation using the implicit central finite difference method, the probability distributions of pore water pressure over time including the probability density functions (PDFs) and cumulative distribution functions (CDFs) were calculated using different copulas and compared with each other.



Results and Discussion

The results showed that the inverse Gaussian distribution properly fits to the marginal distributions of each single random variable, according to BIC criterion. In this research, Kendall’s correlartion coefficient showed a positive correlation between the random variables of hydraulic conductivity and soil volume compressibility. After 15 days from the beginning of consolidation with an initial loading of 400 kPa, the pore water pressures in the depth of 2 meters were estimated equal to 398.75, 398.9 and 398.95 kPa for Clayton, Gumbel and Clayton copulas, respectively. Whereas the pore pressure in the same depth were obtained equal to 399 and 399.05 kPa for Gaussian and t-student copulas, respectively. In the depth of 4 meters, Clayton, Gumbel and Clayton copulas, estimated the pore pressures equal to 399.54, 399.55, 399.54 kPa, respectively. It shows that Archimedean copulas create almost similar results in deeper regions within a soil layer. For elliptical copulas in the depth of 4 meters, the pore water pressures were calculated equal to 399.8 and 399.75 kPa for Gaussian and t-student copulas, respectively.



Conclusions

Considering the correlation of random variables, it is concluded that Archimedean copulas are more accurate in extreme values than elliptic copulas but elliptic copulas according to AIC, BIC and other evaluation criteria provide better balance between the number of parameters, the accuracy and the complexity of model. Generally, for both Archimedean and elliptic copulas, the temporal variations of pore water distributions show an increase in uncertainty with time via changing from sharp and narrow curves to flat and wide curves. Moreover, the consolidation rate (pore pressure dissipation rate) is slower for elliptic copulas than Archimedean copulas. Gaussian copula was found to be the best copula among all investigated copulas. The error of neglecting the correlation of random variables is bigger when a shallow foundation is to be designed by an engineer. Meanwhile, the consolidation rate is overestimated when the correlation of random variables is ignored.



Acknowledgement

The authors express their gratitude to the experts working in technical and soil mechanics laboratory of Guilan province for their collaborations and carrying out the experiments on the soil samples of this research.

کلیدواژه‌ها [English]

• Copula functions
• Fine-grained soil
• Joint probability analysis
• Monte-Carlo method