مدل‌سازي ناهمگوني تغيير شكل‌پذيري نهشتههاي طبيعي به‌كمك نظريه‌ي فضاي تصادفي

INVESTIGATION OF HETEROGENEITY IN NATURAL DEPOSITS USING THE RANDOM FINITE ELEMENT METHOD

در روابط ارايه‌شده براي محاسبه‌ي نشست شالوده‌هاي سطحي، متغيرهاي مورد استفاده به‌عنوان «پارامتر ورودي» حالت ميانگين دارند و تغييرات آنها در نقاط مختلف ــ كه در بيشتر خاك‌ها مشاهده مي‌شود و ناهمگوني ناميده مي‌شود ــ مورد توجه قرار نمي‌گيرد. در پژوهش حاضر با بررسي تفصيلي ويژگي مزبور، به‌معرفي فضاي تصادفي كشسان همسان براي استفاده در مدل‌كردن فضاي مسيله پرداخته‌شده است. مدول تغيير شكل خاك به‌عنوان متغير تصادفي، و توزيع قدر مطلق نرمال به‌عنوان توزيع مناسب براي اين پارامتر در راستاي افقي در نظر گرفته شده است. اين پارامتر طوري در فضا توزيع مي‌شود كه با فرض ثابت‌ماندن ضريب تغييرات، ميانگين آن از روند مشخصي در راستاي قايم تبعيت ‌كند. روند تغييرات ميانگين اين پارامتر در راستاي قايم مورد بررسي قرار گرفته و مفهوم عمق تبديل كه در آن روند مزبور در راستاي قايم تغيير مي‌كند معرفي ‌شده و با كمك گرفتن از روابط نظري ارايه‌شده براي مدول تغيير شكل كشسان به محاسبه‌ي اين عمق خواهيم پرداخت. حالت‌هاي محتمل توزيع اين پارامتر با استفاده از نظريه‌ي حوزه‌هاي ميانگين محلي (LAS) به‌منظور تامين همبستگي و استناد بر نتايج آزمايش‌هاي برجا و استفاده از نرم‌افزار MATLAB ترسيم شده و نهايتاً نظريه‌ي فضاي تصادفي به‌عنوان ابزاري قوي براي مدل‌سازي ناهمگوني خاك‌ها در كنار نظريه‌ي اجزاي محدود معرفي ‌شده است.

One of the main distinctions between geomaterials and other engineering materials is the spatial variation of their properties in different directions inside them. This characteristic of geomaterials, called heterogeneity, is studied herewith. Almost all natural soils are highly variable in their properties and rarely homogeneous. Soil heterogeneity can be classified into two main categories. The first is lithological heterogeneity, which can be manifested in the form of thin soft/stiff layers embedded in a stiffer/softer media, or the inclusion of pockets of different lithology within a more uniform soil mass. The second source of heterogeneity can be attributed to inherent spatial soil variability, which is the variation of soil properties from one point to another in space. Inherent spatial variability of geomaterials is itself divided into a random component, which is attributed to different depositional conditions, and the deterministic trends, which are attributed to the variations in soil properties, such as the increase in soil strength and stiffness with depth, due to the increase in confining pressure. Different elements of soil inherent spatial variability, such as mean, variance, and spatial correlation characteristics, are introduced. The settlement calculation for shallow foundations is based mainly on input stiffness parameters, which are used in an average sense in classic and traditional methods. Spatial variability, which is inherent to geomaterials, is not considered in conventional settlement prediction schemes for shallow foundations. This study focuses on the heterogeneity of a soil deformation modulus. Inherent variability, as the major source of heterogeneity, was modeled as a Gaussian stochastic field in a horizontal direction. In a vertical direction, a deterministic trend was invoked by assuming that the coefficient of variation (COV) remains constant, while the average follows a trend. It is found that for the deformation modulus, a transformation depth exists where its depth-varying trend changes direction. An empirical formula for the transformation depth of the deformation modulus is introduced. Realizations are produced, with the aid of the Local Average Subdivisions (LAS) theory, relying on in-situ test results and the proposed trend for the elastic modulus, leading to the conclusion that the random field theory is a powerful tool for modeling the heterogeneity embedded in soil materials. The random field theory can finally be adopted, in combination with the finite element theory, in order to model different problems.