【摘要】：顆粒破碎特性的影響因素有顆粒的強(qiáng)度、大小、圓度、粗糙度、風(fēng)化程度、相對(duì)密度、顆粒級(jí)配以及組構(gòu)等內(nèi)因和圍壓大小、應(yīng)力水平、加載路徑、加載速率、含水量、制樣方法等外因。揭示顆粒料破碎特性的途徑主要有室內(nèi)試驗(yàn)、數(shù)值模擬、原位測(cè)試及其間相結(jié)合的方法,隨著計(jì)算機(jī)技術(shù)的發(fā)展和數(shù)學(xué)、力學(xué)理論的進(jìn)步和日趨完善,近年來(lái),數(shù)值模擬方法成為研究堆石體顆粒料力學(xué)特性熱點(diǎn)課題,并取得了長(zhǎng)足的進(jìn)步,由于該課題的復(fù)雜性、不確定性等,但目前尚未形成系統(tǒng)準(zhǔn)確的數(shù)值模擬體系,仍面臨諸多關(guān)鍵科學(xué)技術(shù)問(wèn)題亟待解決。鑒于此,論文將圍繞堆石體顆粒料復(fù)雜形狀、破碎的模擬問(wèn)題開(kāi)展數(shù)值分析方法研究,以期從顆粒層面為研究顆粒料的宏觀力學(xué)特性探索一條數(shù)值模擬途徑,該課題研究成果將對(duì)建造堆石體工程的分析、設(shè)計(jì)、施工、維護(hù)等都具有十分重要的理論意義和實(shí)用價(jià)值。論文的主要內(nèi)容如下:(1)在考慮堆石料復(fù)雜顆粒形狀的基礎(chǔ)上,以凸多邊形作為基本單元,建立了二維離散單元的實(shí)用算法,并研制了用于模擬堆石料的二維離散單元法程序PDEM,采用本程序?qū)κ覂?nèi)試驗(yàn)進(jìn)行了數(shù)值模擬,且與PFC模擬進(jìn)行了比較,得到了與室內(nèi)試驗(yàn)一致的應(yīng)力變形規(guī)律;(a)推導(dǎo)了半解析方法計(jì)算任意多邊形的轉(zhuǎn)動(dòng)慣量的公式,為牛頓運(yùn)動(dòng)定律求解任意多邊形單元的轉(zhuǎn)動(dòng)問(wèn)題提供了方便;(b)采用線性搜索算法實(shí)現(xiàn)了求解多邊形間交點(diǎn)坐標(biāo),求解任意兩個(gè)多邊形之間的交點(diǎn)最多只要2(n+m)次,且易于編程實(shí)現(xiàn)。提出了由近似接觸判斷到真實(shí)接觸判斷的適用于多邊形的接觸判斷算法;(c)采用基于勢(shì)能原理的法向接觸模型,推導(dǎo)了求解多邊形-多邊形法向接觸力,結(jié)合切向摩擦定律構(gòu)成了一個(gè)完整的多邊形-多邊形接觸模型,為多邊形顆粒之間的相互作用提供了理論依據(jù);(d)基于以上原理和思路,研制了多邊形離散元計(jì)算程序PDEM,并對(duì)姜景山等的粗粒料二維模型試驗(yàn)進(jìn)行了數(shù)值模擬,且與PFC采用clump技術(shù)的模擬進(jìn)行了比較。通過(guò)與PFC模擬結(jié)果和試驗(yàn)結(jié)果的對(duì)比分析了論文方法、程序的可靠性。(2)針對(duì)具有尖角的堆石料在外荷載作用下容易發(fā)生顆粒破碎的現(xiàn)象,建立了一種將多邊形離散元(PDEM)和比例邊界有限元(SBFEM)兩種方法結(jié)合起來(lái)的新的模擬顆粒破碎的數(shù)值方法(SBFDEM),可以同時(shí)發(fā)揮這兩種方法的優(yōu)勢(shì),從顆粒尺度揭示顆粒破碎機(jī)理及其對(duì)宏觀力學(xué)效應(yīng)的影響。(a)將具有尖角的顆粒用多邊形單元表示,用多邊形離散單元方法分析顆粒運(yùn)動(dòng)及其相互作用規(guī)律,采用多邊形比例邊界有限單元法對(duì)單個(gè)顆粒進(jìn)行應(yīng)力應(yīng)變分析。每個(gè)顆粒既是離散元方法中一個(gè)獨(dú)立的離散單元,又是比例邊界有限元分析時(shí)的一個(gè)多邊形單元;(b)應(yīng)用Hoek-Brown準(zhǔn)則判斷任意單元中某個(gè)點(diǎn)的破壞,假定破壞點(diǎn)達(dá)到一定比例時(shí),此單元即破碎;破壞路徑假設(shè)為直線,對(duì)破壞點(diǎn)的分布采用加權(quán)最小二乘法進(jìn)行直線擬合得到破壞路徑;根據(jù)破壞路徑將單元一分為二,新產(chǎn)生的單元直接進(jìn)入下一步的離散元和比例邊界有限元的計(jì)算;(c)將相關(guān)理論形成了一套系統(tǒng)的用于分析顆粒破碎的方法,并基于MATLAB研制了相應(yīng)的程序SBFDEM。(3)應(yīng)用SBFDEM程序?qū)Χ咽显嚇舆M(jìn)行了不同圍壓下的雙軸壓縮試驗(yàn)數(shù)值模擬。分析了顆粒破碎對(duì)堆石料在雙軸壓縮條件下的力鏈演化、試樣變形以及宏觀應(yīng)力應(yīng)變關(guān)系等物理力學(xué)行為的影響;分析了不同初始顆粒粒徑分布對(duì)堆石料在雙軸壓縮條件下的顆粒破碎行為的影響。論文研究工作豐富和發(fā)展了離散單元法、比例邊界有限元法,研究成果為數(shù)值模擬堆石體顆粒料復(fù)雜形狀、顆粒破碎等關(guān)鍵問(wèn)題探索了一條高效、科學(xué)的途徑。
[Abstract]:The influence factors of the particle breaking property are the strength, the size, the roundness, the roughness, the degree of weathering, relative density, particle grading and the internal and confining pressure, the stress level, the loading path, the loading rate, the water content and the sample preparation method. The method of revealing the breaking property of the granular material mainly includes the indoor test, the numerical simulation, the in-situ test and the combination method, with the development of the computer technology and the progress and the perfection of the mathematics and the mechanics theory, in recent years, The numerical simulation method has been a hot topic in the study of the mechanical properties of the rockfill material, and has made great progress. Due to the complexity and uncertainty of the project, the numerical simulation system of the system has not yet been developed yet, and many key scientific and technical problems still need to be solved. In view of this, the paper studies the numerical analysis method about the complex shape and the broken simulation of the rockfill material, in order to explore a numerical simulation approach from the particle level to the study of the macro-mechanical properties of the granular material, and the research results will be used to analyze the construction of the rockfill. It is of great theoretical and practical value to design, construct, maintain and so on. The main contents of the paper are as follows: (1) On the basis of considering the complex particle shape of the rockfill material, a practical algorithm of two-dimensional discrete unit is established by using convex polygon as the basic unit, and a two-dimensional discrete unit method for simulating the rockfill material is developed, The numerical simulation of the indoor test is carried out by the program, and compared with the PFC simulation, the stress deformation law which is consistent with the indoor test is obtained; (a) the formula for calculating the moment of inertia of any polygon by the semi-analytical method is derived, The method of Newton's motion law is used to solve the problem of the rotation of any polygon element, and (b) a linear search algorithm is adopted to solve the coordinate of the intersection point of the polygon, and the intersection point between any two polygons can be solved by a maximum of 2 (n + m) times, and is easy to be programmed and implemented. In this paper, a contact determination algorithm for polygon based on approximate contact determination is presented, and (c) a normal contact model based on the principle of potential energy is used to derive the normal contact force of the polygon-polygon. In this paper, a complete polygon-polygon contact model is constructed in combination with the law of tangential friction, which provides a theoretical basis for the interaction between polygon particles; and (d) based on the above principles and ideas, a polygon discrete element calculation program (PDEM) is developed. The numerical simulation of the two-dimensional model test of the coarse aggregates such as Jiang Jingshan and the like is carried out and compared with the simulation of the PFC. The reliability of the method and the program is analyzed through the comparison with the results of the PFC simulation and the test results. (2) A new numerical method (SBFDEM), which combines the two methods of the polygonal discrete element (PDEM) and the proportional boundary finite element (SBFEM), is established for the phenomenon that the pile stone with the sharp angle is easy to crack under the action of the external load. The advantages of these two methods can be exerted at the same time, and the mechanism of particle breaking and its effect on the macro-mechanical effect can be revealed from the particle size. (a) the particles with sharp corners are represented by a polygonal unit, the particle motion and the interaction rule are analyzed by a polygon discrete unit method, and the stress and strain analysis of a single particle is carried out by using a polygonal proportional boundary finite element method. each particle is an independent discrete unit in a discrete element method, and is a polygon unit at the time of the finite element analysis of the scale boundary; and (b) the Hoek-Brown criterion is applied to judge the failure of a certain point in an arbitrary unit, and the unit is broken when the failure point is assumed to reach a certain proportion; the failure path is assumed to be a straight line, the distribution of the damage point is subjected to linear fitting by using a weighted least square method to obtain a failure path, and the unit is divided into two according to the failure path, and the newly generated unit directly enters the calculation of the discrete element and the proportional boundary finite element of the next step; (c) The relevant theory is used to form a system to analyze the particle breaking method, and the corresponding program SBFDEM is developed based on MATLAB. (3) The method of SBFDEM is used to simulate the two-axis compression test under different confining pressure. The influence of the particle size distribution on the particle breaking behavior of the rockfill material under biaxial compression was analyzed. In this paper, the discrete element method, the proportional boundary finite element method and the research results are enriched and developed, and a high-efficiency and scientific way is explored for the key problems such as the complex shape of the particle materials of the rockfill and the crushing of the particles.
【學(xué)位授予單位】：武漢大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：TV41

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