混凝土為目前最常使用的工程建築材料之一，隨著社會經濟的進步，工程結構朝著高樓層、大跨度的方向發展，而為了滿足使用與設計上的需求，混凝土的強度不斷的提升，從普通強度混凝土到強度大於42MPa的高強度混凝土。在1990年代，法國公司Bouygues研發出了活性粉末混凝土(reactive powder concrete, RPC)，使得混凝土抗壓強度可以在200MPa左右。而在1994年，Larrard等人首次提出了超高性能混凝土(ultra-high performance concrete, UHPC)的概念。
然而，純粹提高混凝土的抗壓強度並不能改變其具有高脆性、抗拉強度低的問題，一旦達到極限強度，混凝土便會瞬間爆裂以至於無法承受載重。加入鋼纖維將可增強其韌性、提升抗拉強度。因此，超高性能纖維強化混凝土(utra-high performance fiber reinforced concrete, UHPFRC)成為了目前研究與發展的新方向。
為了探討UHPFRC受力過程中，纖維與基材間的握裹行為及材料在不同受力狀態下的力學特性，本論文利用有限元素法結合纖維三維隨機分佈理論，建立了介觀尺度下，具隨機分佈纖維強化超高性能混凝土的數值模型，同時，為了降低模型建立的困難度，並縮短數值運算時所需之時間，本論文中利用樑元素模擬了光滑平直型鋼纖維，，並將結果與文獻中的實驗進行比較，驗證了分析結果之可靠性。
在本文中將以纖維拉拔模擬比較樑元素與實體元素模擬纖維之差異，並以此模型探討纖維與混凝土之介觀力學行為。另外，以單軸抗壓與三點彎矩試驗模型模擬超高性能混凝土在加入鋼纖維前後之抗壓、抗彎特性，並觀察試體內部之塑性應變及纖維受力情形。研究結果顯示，以樑元素模擬鋼纖維可以有效的縮短分析時間，並且得到良好的結果，亦可以透過剪力黏結模數的適當設定，模擬出纖維在不同基材強度下的黏結狀況。纖維帶給超高性能混凝土之韌性可以在三點彎矩模型中看到，且UHPFRC所能承受的最大力量與纖維含量之體積比略呈線性成長。纖維混凝土試體抗壓強度由外而內逐漸增強，與支承接觸附近則因應力集中和纖維分布較少呈現脆性破壞。

Concrete have been one of the most commonly used building materials in this years. Alone with the improvement of social and economic, engineering structurs have been a high floor and large-span. The strength of concrete constantly upgrading from normal strength concrete to concrete which strength is greater then 42MPa, in order to meet the needs of design. In the 1990s, French company Bouygues developed a reactive powder concrete (RPC), so that the compressive strength of concrete con be about 200MPa. And then Larrard first proposed the concept of ultra-high performance concrete (UHPC) in 1994.
However, purely to improve the compressive strength of concrete does not change its problem of high brittleness and low tensile strength. Once they reach the ultimate strength of concrete will burst instantly so that they can not bear the load. Added steel fibers will enhance its toughness and improve the tensile strength. Therefore, ultra-high performance fiber-reinforced concrete (UHPFRC) has become the new direction of the research and development currently.
In order to explore bond behavior of UHPFRC and mechanical properties of materials under different loading states between the fibers and the matrix, , the research used finite element method with three-dimensional random fiber distribution theory to set up the numerical model, which have random fibers distribution of ultra-high performance concrete in mesoscopic scale. Simultaneously, in order to reduce the difficulty of building model and shorten the time required when the numerical calculation, the research used beam elements to simulate the smooth and straight steel fibers, and compare with the results of experiments of literature to verify the reliability of the analysis results.
The difference of beam elements and solid element fiber simulation will discuss in the fiber pullout model, and used this model to investigate meso-mechanical behavior between fiber and concrete. In addition, used uniaxial compressive test and three point bending test model to investigate plastic strain and forced process of fibers. The results show that ues beam element to simulate the steel fibers can effectively shorten the analysis time and get good results. The toughness of UHPFRC can be seen in the model of three point bending test. The compressive strength of UHPFRC increase form outside to inside geadually.

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