臺灣博碩士論文加值系統

1999年9月21日，於台灣中部發生規模7.3之集集大地震，其中地震誘發邊坡破壞的問題成為台灣自然災害研究的重要課題之一。此外，台灣地處環太平洋地震帶上，地震活動頻繁，加上近幾年來山坡地開發增多，使得邊坡穩定成為工程施工中相當重要的一環。本研究主要針對邊坡土釘加勁機制與土釘設計上不同配置方式對邊坡抗震能力之影響進行深入探討。
本研究先模擬振動台土釘加勁模型邊坡坡面之側移量並與實際側移量進行比對，以驗證數值程式分析之有效性。由比對結果得知，側移量之模擬值與實測值並無法完全相符，模擬值約高估2倍。推測其原因可能為數值程式之動態模擬功能限制(土壤模式)或是模擬過程無法真實反應現場試驗之配置(邊界條件)所造成。然而，兩者之動態側移趨勢及模式仍有相當程度近似。
隨之，採用土釘加勁虛擬邊坡，在各種地震震度之當量地震加速度歷時曲線作用下，進行一系列二維有限元素法(Finite Element Method，FEM)之動態分析。再藉由改變土釘長度、土釘傾角、土釘間距及地震震度等影響因子，可探討各因子對土釘加勁邊坡耐震行為之影響。此外，採用有限元素法之C-ψ折減法(FEM C-ψ Reduction Method，以下簡稱FEM法)及極限平衡法之切片法(LEM Slice Method，以下簡稱LEM法)，可分析土釘加勁邊坡之靜態穩定性。
在土釘打設長度L方面，在坡高H=15 m (β =80∘)之陡高邊坡，土釘長度L由7 m (0.47H)增至12 m (0.8H)時，對地震最大水平位移比(δhmax/H)之降低效果較為顯著。降低量約為15 %。其餘在H= 5 m及10 m (β=60∘及70∘)之情況，改變土釘長度對邊坡之動態位移影響有限。
在土釘打設傾角α方面，在坡高H=15 m及β=80∘之陡峭邊坡，當土釘傾角α<15∘時，土釘傾角之大小對穩定性之影響有限，此乃由於土釘較能以接近正交之方式通過地震時之潛在滑動面並提供最佳抗滑力所致。反之，當α>15∘時，邊坡之地震最大水平位移比(δhmax/H)不減反增，推測其原因可能是土釘無法以接近正交之方式通過地震時之潛在滑動面所致。因此，在坡度β=90∘之陡坡，土釘打設傾角不應超出15∘。
在土釘打設傾角比(α / β)方面，在H=10 m且β=60∘之情況，邊坡穩定性仍舊隨土釘打設傾角之增加而提升，由於分析時採用之最大土釘打設傾角已達20∘，因此可得相當之傾角比(α / β)=0.33。在H=15 m及β=80∘之情況，一旦土釘打設傾角α>15∘，即傾角比(α / β)>0.19，地震最大水平位移比(δhmax/H)將大幅增加。由此可知，在相當陡峭之邊坡條件下進行土釘打設時，可採用之設計傾角比應限制在(α / β)=0 ~ 0.19。
在土釘打設間距Sv方面，土釘間距Sv由2 m降低至1 m(縮小1 m)，邊坡之坡頂、坡腹及坡趾各位置點之最大水平位移比(δhmax /H)之降低量約為土釘間距由1.5 m降低至1 m(縮小0.5 m)之2倍，此暗示邊坡穩定性對土釘打設間距Sv甚為敏感。因此，在土釘設計方面，打設間距為一相當重要之設計參數。
在地震震度方面，震度5級及6級所產生之最大水平位移比(δhmax/H)相差不大，而震度7級所產生之最大水平位移比(δhmax/H)分別約為震度5級及6級之1.5及1.75倍。
在土釘構件受力方面，土釘加勁材地震受力模式中顯示，土釘之地震軸向拉力發展程度遠大於其剪力及彎矩者，亦即土釘加勁邊坡之主要抗滑穩定力量源自於土釘軸向拉力之發展。因此，在土釘耐震動力設計方面，應著重土釘之抗拉強度，以發揮土釘加勁之最大效果。

關鍵字：土釘、有限元素法動態分析、極限平衡法、最大水平位移比，地震軸向拉力、相對安全係數

Due to situating at the circum-Pacific belt, earthquake is very active and frequent in Taiwan. The Chi-Chi earthquake (921 Quake) possesses a Richarter Magnitude of 7.3 triggered at the central part of Taiwan on 21, September, 1999 and caused large scale and extensive slope failure at the mountain region. As a consequence, the earthquake induced slope failure becomes one of the most critical issues in the relevant research of natural disaster prevention in Taiwan. Besides, because of the increasing reclamation of slope land the slope stabilization also comes to be an important work in the engineering construction. This study investigates the reinforced mechanism of soil nail in steep slope and the resistance capability of slope reinforced by soil nail with various installation configurations during the earthquake.
To verify the validity of numerical analysis, a numerical modeling was performed to simulate the lateral displacement of a soil nail reinforced model slope subjected to the vibration loading on a shaking table. The calculated lateral displacement profiles of the slope surface at each vibration step were then compared with those from the measurements. The comparisons indicate that the calculations are approximately two times larger than the measurements. The deviations between the calculation and measurement can be resulted from the inherent limitation of the function of numerical tool in dynamic aspect such as soil constitutive model or the incapability of simulation processes which unable to reflect the actual configuration of shaking table test such as boundary conditions. Nevertheless, the predicted tendency of lateral displacement under vibration loading is still coincident with the measurement to a certain extent.
Subsequently, a series of two-dimensional finite element dynamic analyses were performed to simulate the dynamic behaviors of the fictitious slope reinforced by soil nail and subjected to earthquake loadings. In the analysis, the earthquake loadings were applied by the input of various acceleration time series. To investigate the influence of various installation parameters of soil nail on the resistance behavior of reinforced slope subjected to earthquake loading, the length, the inclination angle and the spacing of soil nail were varied in the calculation. In addition, the finite element reduction method (or FEM method) and the limit equilibrium sliced method (or LEM method) were also adopted to analyze the static stability of the reinforced slope.
As to the length of soil nail L, for the steep slope with slope height H=15 m and slope angle=80∘,the maximum horizontal displacement ratio induced from earthquake loading can be apparently reduced for 15% when the L value is increased from 7 m (0.47H) to 12 m (0.8H). However, for the milder and lower slopes with H= 5 m, 10 m and the influence of length variation of soil nail on the horizontal displacement is insignificant.
Regarding the inclination angle of soil nail for the steep slope with slope height H=15 m and slope angle=80∘,the magnitude of value merely displays slight influence on the stability of reinforced slope as 15∘. This can be due to the fact that the soil nail can penetrate orthogonally through the potential sliding surface of the slope and provide an optimum resistance against the sliding of the slope. On the contrary, as 15∘ the maximum horizontal displacement ratio induced from earthquake is increasing instead of decreasing with the ascending value. This can be due to the intersection angle between soil nail and potential sliding surface has greatly deviated from 90∘ and is unable to give the best resistance to potential sliding surface during earthquake loading.
Concerning the ratio of inclination angle of soil nail to slope angle (α/β), for the slope with slope height H=10 m and slope angle β=60∘, the stability of reinforced slope increasing with the increase of α angle remains. Meanwhile for the maximumαvalue of 20∘used in the analysis, one can obtain the corresponding value of the ratio of inclination angle (α/β)=0.33. On the other hand, for the steep slope with slope height H=15 m and slope angleβ=80∘, the maximum horizontal displacement ratio (δhmax/H) induced from earthquake loading is greatly increased once the angleα>15∘, namely, the ratio of (α/β)>0.19. It is therefore suggested that the ratio of inclination angle of soil nail (α/β) value should be maintained at the range of 0 ~ 0.19 for the soil nail installed at the relatively steep slope.
Considering the spacing of soil nail Sv, in general the reduction of maximum horizontal displacement ratio (δhmax /H) induced from earthquake loading for the case of Sv descending from 2 m to 1 m (1 m reduction) is approximately twice of that from 1.5 m to 1 m (0.5 m reduction). This implies that the stability of reinforced slope is significantly influenced by the installation spacing of soil nail.
About the earthquake intensity, the maximum horizontal displacement ratios (δhmax/H) generated by the intensities of level-5 (acceleration time series E5) and level-6 (acceleration time series E6) are approximately equivalent.

However, the (δhmax/H) value generated by the intensities of level-7 is nearly 1.5 and 1.75 times of those generated by the intensities level-5 and level-6 respectively.
For the forces of soil nail, the analyses indicate that the mobilization of axial tensile force in soil nail during earthquake is much more predominant than those of shear force and bending moment. Base on the analysis result, it can be concluded that the stabilization force of reinforced slope is mainly obtained from the mobilization of axial tensile force of soil nail. Consequently, in the resistance design of soil nail to earthquake loading, the tensile strength of soil nail should be emphasized to achieve a most efficient design of reinforcement in earth slope.

Keywords: soil nail, finite element dynamic analysis, limit equilibrium method, maximum horizontal displacement ratio, axial tensile force

目錄 I
圖目錄 IV
表目錄 VII
第一章、緒論 1
1.1研究動機與目的 1
1.2 研究方法 1
1.3 研究範圍 1
第二章、文獻回顧 2
2.1 地震規模 2
2.1.1 芮氏規模(Richter Local Magnitude, ML) 2
2.1.2 表面波規模(Surface Wave Magnitude, MS) 2
2.1.3 實體波規模(Body Wave Magnitude, mb) 3
2.1.4 地震矩規模(Moment Magnitude, M or MW) 3
2.2地震誘發之山崩（或邊坡崩塌）特性 5
2.2.1山崩之定義及破壞形式 5
2.2.2 山崩與地形性質(含坡度、坡向、坡形) 7
2.2.3 山崩與地層特性(含地質材料、地質構造) 11
2.2.4 山崩與地表尖峰加速度（PGA） 13
2.2.5 山崩與震央或斷層之距離 15
2.2.6 山崩規模（面積、體積） 17
2.2.7 滑動深度 18
2.3土釘加勁邊坡 19
2.3.1 土釘設計要點 19
2.3.1.1 土釘構造及配置 19
2.3.1.2設計與分析方法 21
2.3.2 土釘施工方法 24
2.3.2.1 施工步驟 24
2.3.2.2 土釘施工特點及注意事項 24
2.4 土釘加勁邊坡模型試驗 26
2.4.1 模型試驗一 26
2.4.1.1 試驗配置 26
2.4.1.2 試驗監測及結果 26
2.4.2模型試驗二 28
2.4.2.1 試驗配置 28
2.4.2.2 試驗土壤材料 28
2.4.2.3 模型材料之力學性質與製作 31
2.4.2.3.1 模型土釘之性質與製作 31
2.4.2.3.2 模型面版之製作 32
2.4.2.4 輸入地震波型態及量測儀器 32
2.4.2.4.1 輸入地震波型態 32
2.4.3 振動台試驗結果 35
2.4.3.1 振動平台加速度歷時曲線與量測結果 35
2.4.3.2 輸入尖峰加速度之影響 38
2.5邊坡動態穩定性分析方法 39
2.5.1 擬靜態法（Pseudo-Static Method） 39
2.5.2 Newmark滑動塊體法(Newmark Sliding Block Method) 41
2.5.2.1 Newmark 分析理論 41
2.5.2.2 臨界加速度 43
2.5.2.3 地震累積位移量計算經驗公式 51
2.5.2.4 臨界破壞位移量 54
2.5.3動態數值分析 55
2.6 Plaxis-Dynamics有限元素法動態應力及變形分析程式 57
2.6.1 簡介 57
2.6.2 運動方程式 58
2.6.3 動態荷重 60
第三章、研究方法 61
3.1 研究流程 61
3.2振動台試驗資料蒐集 63
3.2.1 振動台試驗設備之配置與試驗結果 63
3.3 振動台試驗數值模擬之有效性驗證 64
3.3.1 建立幾何模型(尺寸、邊界條件及初始條件) 64
3.3.2 輸入材料參數 66
3.3.3 加載地震動力執行運算 67
3.4 全尺寸土釘加勁邊坡動態數值模擬及參數研究 70
3.4.1 地形因子(坡度β、坡高H ) 70
3.4.2 輸入土層及土釘材料參數 70
3.4.3 地震模式(地震震度) 73
3.4.4 建立數值幾何模式 81
3.4.5 應力分析及動力計算 83
3.4.6執行地震動力分析計算 84
3.5 全尺寸土釘加勁邊坡靜態穩定分析之參數研究 86
3.5.1 參數選用 86
3.5.2 建立數值幾何模式 88
3.5.3 穩定性安全係數計算及破壞模式分析 88
第四章、結果與討論 90
4.1振動台數值分析結果與量測資料之比對 90
4.1.1加速度歷時曲線 90
4.1.2 邊坡之受振位移型態 90
4.1.3 坡面水平位移量之位移比 92
4.2地震作用下土釘加勁邊坡動態動態行為之參數研究 94
4.2.1土釘長度L(m) 94
4.2.2土釘傾角α (∘) 98
4.2.3土釘間距Sv (m) 103
4.2.4地震動力 105
4.2.5傾角比(土釘傾角/坡角=α/β) 106
4.3地震作用下土釘加勁邊坡穩定性安全係數分析 109
4.3.1 土釘長度L 109
4.3.2 土釘傾角α (∘) 112
4.4 地震作用下土釘加勁邊坡之加勁材受力模式 116
第五章 結論與建議 125
5.1 結論 125
5.1.1 振動台實驗案例研究與數值模擬分析 125
5.1.2 土釘加勁邊坡穩定性影響因子參數研究 125
5.2 建議 128
參考文獻 129
附錄A 134
附錄 B 140
附錄 C 142

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