梳子壩應力及變形三維分析

Abstract

摘要 本研究以台中縣和平鄉博愛村境內松鶴一溪第5號梳子壩（無筋混凝土重力式梳子壩）為分析案例，在相同壩柱高度、壩寬及壩柱斷面條件下，選用四組不同壩柱開口寬度（L）與壩柱寬度（D）配置變化（D/L=0.667~0.683）之梳子壩，以STAAD /Pro程式，建立梳子壩體之3-D實體數值模式，並對下列四種外力組合作用狀況下，即Case 1 (壩體上游堆積土石由淨空(空壩)到土石流推擊)、Case 2 (淤滿後靜土石堆積狀態加最大地震力)、Case 3 (壩體上游土石流淤滿後土石流溢流)及Case 4 (壩體上游土石流接近淤滿時巨礫撞擊)等進行靜態3-D力學分析。同時，藉由分析結果，針對壩柱D/L比值以及土石流巨礫撞擊力作用在壩柱之不同分配方式，對壩體應力與變位分佈之影響進行探討。 在梳子壩壩柱最大變位方面，壩柱在外力作用於Z軸方向（水流方向）時在同方向之最大變位，發生在Case 4 (壩體上游土石流接近淤滿時巨礫撞擊)，土石流巨礫撞擊之壩柱上之狀況下。另外，在Case 1（壩體由空壩到土石流推擊）、Case 2（淤滿後靜土石堆積狀態加最大地震力）、Case 3（壩體上游土石流淤滿後土石流溢流）等三種狀況，壩柱頂端X軸（壩軸方向）、Y軸（重力方向）、Z軸（水流方向）之變位量，在維持D/L=0.675之條件下(L =壩柱開口寬度，D =壩柱寬度），變化不顯著。再者，在Case 4 (壩體上游土石流接近淤滿時巨礫撞擊)狀況，壩柱頂點Z軸（水流方向）之變位量，隨D/L比值之增加而減少；壩柱頂端X軸（壩軸方向）及Y軸（重力方向）之變位量，在維持D/L=0.675之條件下(L =壩柱開口寬度，D =壩柱寬度），變化不顯著。 在梳子壩壩柱最大應力方面，最大彎曲拉（壓）應力（σyy）、最大剪應力（σyz），均發生在Case 4 (壩體上游土石流接近淤滿時巨礫撞擊) 土石流巨礫撞擊之壩柱上之狀況下，且應力值皆隨D/L比值(L=壩柱開口寬度，D=壩柱寬度）之增加而減小。另外，比較最大彎曲拉（壓）應力（σyy）、最大剪應力（σyz）其值均為：Case 4 > Case 1 > Case 3 > Case 2 。而在維持D/L=0.667之條件下(L=壩柱開口寬度，D=壩柱寬度），最大彎曲拉應力（σyy）其值約為混凝土材料容許拉應力之80 %。最大彎曲壓應力（σyy）其值約為混凝土材料容許壓應力之6 %。最大剪應力（σyz）其值約為混凝土材料容許剪應力之71 %。最後，依據數值分析結果，壩柱在最大拉應力方面，土石流巨礫撞擊力由三支減為二支壩柱來分擔時，其最大拉應力σyy與混凝土容許拉應力σt之比值（σyy /σt），由0.53提昇為0.80（約增加51%），同時，最大剪應力σyz與混凝土容許剪應力σs之比值（σyz /σs），由0.48提昇為0.71（約增加48%）。由上述分析值可知，巨礫撞擊力之承擔方式修改後，混凝土之容許拉應力及剪應力可大幅發揮利用。因此，在壩體安定分析與應力檢算時，土石流巨礫撞擊力，可假設由相鄰之二支壩柱來承擔，以獲得較有效之材料強度應用。

ABSTRACT This study selects the No. 5 slit dam (gravity dam) situated at the Song-He No. 1 creek, Bo-Ai village, He-Ping, Taichung County as a case history for structural analysis. To maintain the dam height, cross section of slit column (or column) and the dam width unchanged, four sets of fictitious slit dam were analyzed under different column width/open size ratios or D/L ratio (D/L =0.667~0.683). Where, D and L respectively represent the width of slit column and the open size of slit in slit dam. Three dimensional (3-D) static structural analyses were performed on slit dam under various loading conditions, namely Case 1~Case 4, in which, Case 1 (Condition 1: debris accumulates at the upstream of slit dam, and Loading 1: driven force from none to a value induced from debris flow is applied), Case 2 (Condition 2: slit dam fully occupied by debris, and Loading 2: the maximum earthquake loading is applied), Case 3 (Condition 3: slit dam fully occupied by debris at the upstream, and Loading 3: debris flow overflows), Case 4 (Condition 4: slit dam is nearly occupied by debris flow at the upstream, and Loading 4: the impact force induced from the large boulder is applied). Meanwhile, through the analyses, the effect of D/L ratio and the configuration of impact force resulted from large boulder on the stress and displacement distributions of dam body are investigated. Regarding the maximum displacements occur at the slit column of slit dam, it is found that the maximum displacement at Z-direction (or Z-displacement at the flow direction of debris flow) takes place in the Case 4 (Condition 4: slit dam is nearly occupied by debris flow at the upstream, and Loading 4: the impact force induced from the large boulder is applied) as a large boulder impact the slit column. In addition, the variations of displacement at X-direction (or X-displacement at the direction of dam axis), Y-direction (or Y-displacement at the direction of gravity) and Z-direction are insignificant for Case 1, Case 2 and Case 3 if the D/L ratios are maintained at the value of 0.675. Moreover, for Case 4, the Z-displacement of column top is descending with the increase of D/L ratio whereas the variations of X- and Y-displacement are not obvious as the D/L ratio remains. Concerning the maximum stress occurs at the slit column of slit dam, both the maximum bending tensile (compressive) stress (σyy) and the maximum shear stress (σyz) occur in the Case 4 as the impact force induced from large boulder is applied. Meanwhile, the calculated stresses (σyy) and (σyz) are both decreasing as the D/L ratio increases. On the other hand, comparing the maximum values of stresses (σyy) and (σyz) for different loading cases, it can be found that: Case 4 > Case 1 > Case 3 > Case 2. Under the condition of D/L=0.667, the calculated maximum bending tensile stress (σyy > 0), maximum bending compressive stress (σyy < 0) and maximum shear stress (σyz) approximate to 80%, 6% and 71% respectively of the allowable stresses. Finally, according to the numerical results, the ratio of the maximum tensile stress to the allowable tensile stress of concrete (σyy /σt) and the ratio of the maximum shear stress to the allowable shear stress of concrete (σyz /σs) in slit column are increased from 0.53 to 0.80 (about 51% increment) and from 0.48 to 0.71 (48% increment) respectively if the impact force is carried by two slit columns instead of three. These imply that the allowable tensile and shear stresses of concrete can be largely mobilized to resist the external loadings if the distribution mode of loading is slightly modified. As a consequence, to achieve a beneficial and efficient utilization of material strength in slit dam stability analyses and stress computations for debris flow impact force, it is suggested to assume that the impact loading is simply taken by two slit columns.