道路工程材料-图解法

有很多bug,暂时先放上来。

思路为：画一条竖线，令a等于a',如图求M；这是碎石与石屑两曲线求一个。

对于石屑和矿粉也要按相同的步骤求一个m。

探索错误中：

def qiuab(x1,y1,x2,y2): #求斜截式a,bX1 = float(x1)Y1 = float(y1)X2 = float(x2)Y2 = float(y2)if X1-X2 == 0:a,b = 0,0else:a = -((Y2-Y1)/(X1-X2))b = (X1*Y2-X2*Y1)/(X1-X2)return a,b
y=0def f(x,a,b): #求相应a,b下x得值global yy = a*x + breturn ydef A(x): #碎石的分段函数global yif x >=0 and x < 2.36:y=0elif (x >= 2.36 and x < 4.75):a, b = qiuab(2.36,0,4.75,4.6)y=f(x,a,b)elif (x >= 4.75 and x < 9.5):a, b = qiuab(4.6,4.75,9.5,19.8)y=f(x,a,b)elif (x >= 9.5 and x < 13.2):a, b = qiuab( 9.5, 19.8,13.2,34.5)y=f(x,a,b)elif (x >= 13.2 and x < 16 ):a, b = qiuab(13.2, 34.5,16,61.5)y=f(x,a,b)elif (x >= 16 and x < 19 ):a, b = qiuab(16,61.5,19,27)y=f(x,a,b)elif (x >= 19 and x < 26.5 ):a, b = qiuab(19,27,26.5,100)y=f(x,a,b)return ydef B(x): #石屑的分段函数global yx13, x12, x11, x10, x9, x8, x7, x6, x5, x4, x3 = 26.5,19,16,13.2,9.5,4.75,2.36,1.18,0.6,0.3,0.15y13, y12, y11, y10, y9, y8, y7, y6, y5, y4, y3 = 100,100,100,100,93.8,77.9,58.7,36,23,11,0if x >= 0 and x < 0.15:y = 0elif (x >= x3 and x < x4):a, b = qiuab(x3,y3,x4,y4)y=f(x,a,b)elif (x >= x4 and x < x5 ):a, b = qiuab(x4,y4,x5,y5)y=f(x,a,b)elif (x >= x5 and x < x6 ):a, b = qiuab(x5,y5,x6,y6)y=f(x,a,b)elif (x >= x6 and x < x7 ):a, b = qiuab(x6,y6,x7,y7)y=f(x,a,b)elif (x >= x7 and x < x8):a, b = qiuab(x7, y7, x8, y8)y=f(x,a,b)elif (x >= x8 and x < x9):a, b = qiuab(x8, y8, x9, y9)y=f(x,a,b)elif (x >= x9 and x < x10):a, b = qiuab(x9, y9, x10, y10)y=f(x,a,b)elif (x >= x10 and x < x11):a, b = qiuab(x10, y10, x11, y11)y=f(x,a,b)elif (x >= x11 and x < x12):a, b = qiuab(x11, y11, x12, y12)y=f(x,a,b)elif (x >= x12 and x < x13):a, b = qiuab(x12, y12, x13, y13)y=f(x,a,b)return ydef C(x): #矿粉的分段函数global yx13, x12, x11, x10, x9, x8, x7, x6, x5, x4, x3, x2, x1 = 26.5,19,16,13.2,9.5,4.75,2.36,1.18,0.6,0.3,0.15,0.075,0y13, y12, y11, y10, y9, y8, y7, y6, y5, y4, y3, y2, y1 = 100,100,100,100,100,100,100,100,97,94,92,70.5,0if x >= x1 and x < x2:a, b = qiuab(x1,y1,x2,y2)y=f(x,a,b)elif x >= x2 and x < x3:a, b = qiuab(x2,y2,x3,y3)y=f(x,a,b)elif (x >= x3 and x < x4):a, b = qiuab(x3,y3,x4,y4)y=f(x,a,b)elif (x >= x4 and x < x5 ):a, b = qiuab(x4,y4,x5,y5)y=f(x,a,b)elif (x >= x5 and x < x6 ):a, b = qiuab(x5,y5,x6,y6)y=f(x,a,b)elif (x >= x6 and x < x7 ):a, b = qiuab(x6,y6,x7,y7)y=f(x,a,b)elif (x >= x7 and x < x8):a, b = qiuab(x7, y7, x8, y8)y=f(x, a, b)elif (x >= x8 and x < x9):a, b = qiuab(x8, y8, x9, y9)y=f(x, a, b)elif (x >= x9 and x < x10):a, b = qiuab(x9, y9, x10, y10)y=f(x, a, b)elif (x >= x10 and x < x11):a, b = qiuab(x10, y10, x11, y11)y=f(x, a, b)elif (x >= x11 and x < x12):a, b = qiuab(x11, y11, x12, y12)y=f(x, a, b)elif (x >= x12 and x < x13):a, b = qiuab(x12, y12, x13, y13)y=f(x, a, b)return ydef D(x):global yy = 100.0/26.5 * xreturn yx = 1
xsd = 10
print(round(A(x),xsd),round(B(x),xsd),round(C(x),xsd),round(D(x),xsd))sshi = 0
sxie = 0
kfen = 0for i in range(10000): #目测x 在2.36到12.36间 求碎石A() 和 石屑B()t = i * 0.001 + 2.36a1 = A(t)           #下面的ab1 = 100 - B(t)     #上面的a'k = a1 - b1     #两者差值小于误差 认为相等if k > 0 and k < 0.01:print(t,a1,b1,k,D(t))sshi = 100 - D(t)print(sshi,"碎石")breakfor i in range(100000): #目测x 在0.15到1.18间 求碎石B() 和 石屑C()t2 = i * 0.00001 + 0.15a2 = B(t2)b2 = 100-C(t2)k2 = a2 - b2if k2 > 0 and k2 < 0.01:print(t2,a2,b2,k2,D(t2))sxie = 100 - D(t2) - sshiprint(sxie,"石屑")breakkfen = 100 - sshi -sxie
print(kfen,"矿粉")

运行结果：

0 31.9655172414 99.0689655172 3.7735849057
7.382 13.294714285714283 13.289726315789466 0.004987969924817648 27.856603773584904
72.14339622641509 碎石
0.24231 6.769400000000001 6.769200000000012 0.00019999999998887574 0.914377358490566
26.94222641509434 石屑
0.9143773584905688 矿粉

求出来的结果与图中，肉眼看的范围大概差不多

但是检验混合集料通过率与设计级配通过率范围误差太大。

更新！我知道了！

因为设计级配曲线的中值线也应该是分段函数！

如图：

所以把D(x)也变成分段函数就好了。

def D(x):global yx13, x12, x11, x10, x9, x8, x7, x6, x5, x4, x3, x2, x1 = 26.5, 19, 16, 13.2, 9.5, 4.75, 2.36, 1.18, 0.6, 0.3, 0.15, 0.075, 0y13, y12, y11, y10, y9, y8, y7, y6, y5, y4, y3, y2, y1 = 100, 97.5, 82.5, 71, 62, 48, 37, 27, 21, 15, 10, 6, 0if x >= x1 and x < x2:a, b = qiuab(x1, y1, x2, y2)y = f(x, a, b)elif x >= x2 and x < x3:a, b = qiuab(x2, y2, x3, y3)y = f(x, a, b)elif (x >= x3 and x < x4):a, b = qiuab(x3, y3, x4, y4)y = f(x, a, b)elif (x >= x4 and x < x5):a, b = qiuab(x4, y4, x5, y5)y = f(x, a, b)elif (x >= x5 and x < x6):a, b = qiuab(x5, y5, x6, y6)y = f(x, a, b)elif (x >= x6 and x < x7):a, b = qiuab(x6, y6, x7, y7)y = f(x, a, b)elif (x >= x7 and x < x8):a, b = qiuab(x7, y7, x8, y8)y = f(x, a, b)elif (x >= x8 and x < x9):a, b = qiuab(x8, y8, x9, y9)y = f(x, a, b)elif (x >= x9 and x < x10):a, b = qiuab(x9, y9, x10, y10)y = f(x, a, b)elif (x >= x10 and x < x11):a, b = qiuab(x10, y10, x11, y11)y = f(x, a, b)elif (x >= x11 and x < x12):a, b = qiuab(x11, y11, x12, y12)y = f(x, a, b)elif (x >= x12 and x < x13):a, b = qiuab(x12, y12, x13, y13)y = f(x, a, b)return y

求出结果如图：

0 31.9655172414 99.0689655172 25.1379310345
7.382 13.294714285714283 13.289726315789466 0.004987969924817648 55.757473684210524
44.242526315789476 碎石
0.24231 6.769400000000001 6.769200000000012 0.00019999999998887574 13.077
42.680473684210526 石屑
13.076999999999998 矿粉

但是尾巴上还是有一点的偏差，我又蒙了。

应该是我想的太理想化了，计算机程序的数字我还把握不住，哪里出错了我都不知道，break也是感觉放上去的，说不定后面的比前面的更符合要求，那break不就错过了。

如图

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