高速公路边轴旋转超高方式横坡计算路基超高方式图:
说明∶
1.路基超高采用边轴旋转,整体式路基旋转轴为中央分隔带边缘线;分离式路基为行车道前进方向左侧路基边缘内侧1.0米处。
2.行车道和硬路肩超高,土路肩不超高。
3.图中所示符号∶
Ls--缓和曲线长,Lc--超高过渡段长;
X0--与路拱同坡的单向超高点至超高过渡段起点的距离,I1--路拱横坡度;
X--过渡段上任意点至超高过渡段起点的距离,I0--路肩横坡度;
Ib--弯道超高横坡度,hc--路基外缘最大抬高值,h″c--路基内缘最大降低值;
h″cx--x点路基内缘降低值,hcx--x点路基外缘抬高值.
4.超高方式:圆曲线为全超高路段,超高过渡段长度(LC)从缓圆点(HY)往直缓点(ZH)或从圆缓点(YH)往缓直点(HZ)点计算。先按超高渐变率p=1/330算出超高过渡段长度Lc,若Lc
5.图中尺寸均以厘米为单位,适用于设计时速V=80Km/h。
备注:正常路拱横坡(即直线段)为-2%;横坡计算按硬路肩比路缘带低为负。
一、整体式路基:
图上为一左转直线到圆曲线的超高方式图。半径为800m,缓和曲线长250m。
读图可得:R=800m,所以Ib弯道超高横坡度=4%;左转曲线,则黑线表示右幅,红线表示左幅;红点为直缓点;黑点为右幅超高起点;黄点为左幅超高起点;蓝点为缓圆点。
R=800,那么Lc=205 红点与黑点距离为:Ls-Lc=45m; 黄点到蓝点距离为TX:(lb-|i左|)/(lb+|i右|)*Lc=(4-2)/(4+2)*205=68.333m; 黑点到黄点距离(与路拱同坡的单向超高点至超高过渡段起点):X0=Lc-68.333=136.667m 。 由此可得: 1.直线段左右幅横坡都为-2%; 2.圆曲线上分2种情况: 曲线左转则:左幅横坡为-lb;右幅横坡为lb; 曲线右转则:左幅横坡为lb;右幅横坡为-lb; 3缓和曲线分为4种情况设桩号K: 曲线左转:第一缓和曲线上则: 左幅横坡= -2% -(K - (HY - TX)) / TX * (lb - 2%) 右幅横坡= -2% +(K - (HY - Lc)) / lc * (lb + 2%) 第二缓和曲线上则: 左幅横坡= -lb + (K - YH) / TX * (lb - 2%) 右幅横坡= lb - (K - YH) / lc * (lb + 2%) 曲线右转:第一缓和曲线上则: 左幅横坡= -2% +(K - (HY - Lc)) / Lc * (lb +2%) 右幅横坡= -2% -(K - (HY - TX)) / TX * (lb -2%) 第二缓和曲线上则: 左幅横坡= lb - (K - YH) / Lc * (lb + 2%) 右幅横坡=-lb + (K - YH) / TX * (lb - 2%) 将缓和曲线公式汇总: 设转向ZX,左转为-1,右转为1; 设路幅A,左幅为-1,右幅为1; 设与路拱同坡的过渡长TX,左转左幅或右转右幅Lc=TX,,即当ZX*A=1时, Lc=TX; 公式为: 第一缓和曲线: HP = -2% - ZX * A * (K - (HY - lc)) / lc * (lb - A * ZX * lz) 第二缓和曲线: HP = -ZX * A * lb + ZX * A * (K - YH) / lc * (lb - ZX * A * lz) 附:整体式路基excel VBA公式宏。详情见工作表“整体式横坡” Function ZTSHP(ByVal K As Double, ByVal A As Integer) '横坡 Dim JDZ, JDX, JDY, R, Ls1, Ls2, FWJ1, FWJ2, ZJ, ZX As Double Dim Jd, F, G, Xp, Yp, Z, Cd As Double Dim P1, P2, M1, M2, T1, T2, L, Q, E, ZH, HY, QZ, YH, HZ As Double Dim lz, TX1, TX2, HP, lb, lc, lc1, lc2 As Double If K >= 55749.0417429327 And K <= 56916.2270296347 Then '输入各个交点参数 JDZ = 56103.920309326: JDX = 2816128.1798: JDY = 519513.9394 FWJ1 = 5.41157452726532: ZX = 1: ZJ = 0.707859723988235 R = 770: Ls1 = 140: Ls2 = 140 ElseIf K >= 56916.2270296347 And K <= 57754.0176571982 Then JDZ = 57178.6462528066: JDX = 2817212.9035: JDY = 519334.7099 FWJ1 = 6.11943425125356: ZX = 1: ZJ = 0.248509674178336 R = 1500: Ls1 = 150: Ls2 = 150 ElseIf K >= 57754.0176571982 And K <= 58230.0640606573 Then JDZ = 57992.852*******: JDX = 2818026.2537: JDY = 519403.8139 FWJ1 = 8.47586182523049E-02: ZX = -1: ZJ = 0.232890273553729 R = 1400: Ls1 = 150: Ls2 = 150 Else End If FWJ2 = FWJ1 + ZJ * ZX P1 = Ls1 ^ 2 / (24 * R) - Ls1 ^ 4 / (2688 * R ^ 3) + Ls1 ^ 6 / (506880 * R ^ 5) P2 = Ls2 ^ 2 / (24 * R) - Ls2 ^ 4 / (2688 * R ^ 3) + Ls2 ^ 6 / (506880 * R ^ 5) M1 = Ls1 / 2 - Ls1 ^ 3 / (240 * R ^ 2) + Ls1 ^ 5 / (34560 * R ^ 4) M2 = Ls2 / 2 - Ls2 ^ 3 / (240 * R ^ 2) + Ls2 ^ 5 / (34560 * R ^ 4) T1 = M1 + (R + P2 - (R + P1) * Cos(ZJ)) / Sin(ZJ) T2 = M2 + (R + P1 - (R + P2) * Cos(ZJ)) / Sin(ZJ) L = R * ZJ + (Ls1 + Ls2) / 2 Q = L - Ls1 - Ls2 E = (R + (P1 + P2) / 2) / Cos(ZJ / 2) - R ZH = JDZ - T1 HY = ZH + Ls1 QZ = HY + Q / 2 YH = ZH + L - Ls2 HZ = YH + Ls2 '求直缓点,缓圆点等桩号 lz = 0.02 '直线横坡,这边先设置为+的 If R >= 420 And R < 550 Then '各个半径的圆曲线横坡和超高过渡长 lb = 0.06 lc = 275 ElseIf R < 710 Then lb = 0.05 lc = 240 ElseIf R < 960 Then lb = 0.04 lc = 205 ElseIf R < 1410 Then lb = 0.03 lc = 170 ElseIf R < 2500 Then lb = 0.02 lc = 135 Else End If If lc > Ls1 Then '当缓和曲线长小于Lc的情况 lc1 = Ls1 Else lc1 = lc End If If lc > Ls2 Then lc2 = Ls2 Else lc2 = lc End If TX1 = (lb - lz) / (lb + lz) * lc1 '求同向超高过渡段长长度 TX2 = (lb - lz) / (lb + lz) * lc2 If ZX * A = 1 Then lc1 = TX1 lc2 = TX2 End If If K < HY - lc1 Then HP = -lz ElseIf K < HY Then HP = -lz - ZX * A * (K - (HY - lc1)) / lc1 * (lb - A * ZX * lz) ElseIf K < YH Then HP = -ZX * A * lb ElseIf K < YH + lc2 Then HP = -ZX * A * lb + ZX * A * (K - YH) / lc2 * (lb - ZX * A * lz) Else HP = -lz End If ZTSHP = HP End Function