Niwelacja terenu
1. Obliczenie rzędnych wierzchołków siatki trójkątów
l1 [m] l2 [m] H [m] Hij [m] hij [m]
29 10,5 476 H11 476,3621 h11 2,3621
34 25,5 475 H12 475,7500 h12 1,7500
34,5 27 475 H13 475,7826 h13 1,7826
20 6,5 476 H14 476,3250 h14 2,3250
475 H21 475,0000 h21 1,0000
- -
34,5 13,5 474 H22 474,3913 h22 0,3913
32 11,5 474 H23 474,3594 h23 0,3594
39,5 32,5 474 H24 474,8228 h24 0,8228
34 27 473 H31 473,7941 h31 -0,2059
473 H32 473,0000 h32 -1,0000
- -
41 35,5 472 H33 472,8659 h33 -1,1341
474 H34 474,0000 h34 0,0000
- -
31,5 20,5 472 H41 472,6508 h41 -1,3492
28,5 22 471 H42 471,7719 h42 -2,2281
33 24 471 H43 471,7273 h43 -2,2727
H44 h44 -0,8077
26 5 473 473,1923
- wyznaczenie niwelety zerowej
ŁH1 := H11 + H44
ŁH2 := H14 + H41
ŁH3 := H12 + H13 + H21 + H24 + H31 + H34 + H42 + H43
ŁH6 := H22 + H23 + H32 + H33
n := 9
ŁH1 + 2�"ŁH2 + 3�"ŁH3 + 6�"ŁH6
Ho := Ho = 473.9473 m
6�"n
Ho = 474.0 m "Ho = 0.0527 m
2
2. Obliczenie objętości wykopów i nasypów
a := 48�"m - bok kwadratu
" dla trójkątów czystych
- wykopy trójkąty: 1,2,3,4,5,6
1 1
2 2
V1 := �"a �" + h12 + h21 V1 = -1963046.4 L V2 := �"a �" + h12 + h21 V2 = -1206259.2 L
(h ) (h )
11 22
6 6
1 1
2 2
V3 := �"a �" + h13 + h22 V3 = -1506777.6 L V4 := �"a �" + h22 + h23 V4 = -972787.2 L
(h ) (h )
12 13
6 6
1 1
2 2
V5 := �"a �" + h14 + h23 V5 = -1715328 L V6 := �"a �" + h14 + h24 V6 = -1346764.8 L
(h ) (h )
13 23
6 6
- nasypy trójkąty: 13,14,15,16,17,18
1 1
2 2
V13 := �"a �" + h32 + h41 V13 = 981158.4 L V14 := �"a �" + h32 + h42 V14 = 1757683.2 L
(h ) (h )
31 41
6 6
1 1
2 2
V15 := �"a �" + h33 + h42 V15 = 1675084.8 L V16 := �"a �" + h42 + h43 V16 = 2163801.6 L
(h ) (h )
32 33
6 6
1 1
2 2
V17 := �"a �" + h34 + h43 V17 = 1308211.2 L V18 := �"a �" + h34 + h44 V18 = 1182873.6 L
(h ) (h )
33 43
6 6
" dla trójkątów mieszanych trójkąty: 7,8,9,10,11,12
- trójkąt 7
3
h31
1 1
2 2
Vr := �"a �" + h22 + h31 Vn := �"a �" Vn = 4654.46 L
(h )
21
6 6 h31 + h21 h31 + h22
( )�"( )
Vw := Vr - Vn Vw = -459848.06 L
- trójkąt 8
3
h22
1 1
2 2
Vr := �"a �" + h32 + h22 Vw := �"a �" Vw = -27689.82 L
(h )
31
6 6 h22 + h31 h22 + h32
( )�"( )
Vn := Vr - Vw Vn = 340496.22 L
- trójkąt 9
3
h32
1 1
2 2
Vr := �"a �" + h23 + h32 Vn := �"a �" Vn = 203031.38 L
(h )
22
6 6 h32 + h22 h32 + h23
( )�"( )
Vw := Vr - Vn Vw = -107300.18 L
3
- trójkąt 10
3
h23
1 1
2 2
Vr := �"a �" + h33 + h23 Vw := �"a �" Vw = -8780.37 L
(h )
32
6 6 h23 + h32 h23 + h33
( )�"( )
Vn := Vr - Vw Vn = 690265.17 L
- trójkąt 11
3
h33
1 1
2 2
Vr := �"a �" + h24 + h33 Vn := �"a �" Vn = 191651.14 L
(h )
23
6 6 h33 + h23 h33 + h24
( )�"( )
Vw := Vr - Vn Vw = -210121.54 L
- trójkąt 12
3
h33
1 1
2 2
Vr := �"a �" + h34 + h33 Vn := �"a �" Vn = 252386.02 L
(h )
24
6 6 h33 + h24 h33 + h34
( )�"( )
Vw := Vr - Vn Vw = -132846.82 L
Objętoci wykopów i nasypów
ZE
TRÓJK
T WYKOP NASYP KWADRAT SPULCHNIENIEM
( 1,2 )
1 -1963,05
-3169,31 -3803,172
2 -1206,26
3 -1506,78
-2479,57 -2975,484
4 -972,79
5 -1715,33
-3062,09 -3674,508
6 -1346,76
7 -459,85 4,65
-142,39 -170,868
8 -27,69 340,5
9 -107,3 203,03
777,22 932,664
10 -8,78 690,27
11 -210,12 191,65
101,07 121,284
12 -132,85 252,39
13 981,16
2738,84 3286,608
14 1757,68
15 1675,08
3838,88 4606,656
16 2163,8
17 1308,21
2491,08 2989,296
18 1182,87
-9657,56 10751,29
Ł
Ł
Ł
Ł
3 3
ŁW := -9657.56�"m ŁN := 10751.29�"m
2
<
ŁW + ŁN = 1093730 L 9�"a �""Ho = 1093747.2 L
4
3. Optymalizacja przemieszczania mas ziemnych
W1 W2 W3
N1
W4 N2
N3 N4 N5
N1 N2 N3 N4 N5
KWADRAT
Ł
Ł
Ł
Ł
777,22 101,07 2738,84 3838,88 2491,08
W1 3169,31 572,86 2596,45 3169,31
W2 2479,57 204,36 2275,21 2479,57
W3 3062,09 101,07 1563,67 1397,35 3062,09
W4 142,39 142,39 142,39
Ł 777,22 101,07 2738,84 3838,88 1397,35
Ł
Ł
Ł
3 3
Dowóz:
2491.08�"m - 1397.35�"m = 1093730 L
5
Ho := 474.0m
H11 := 476.3621m h11 := - - Ho
(H )
11
H12 := 475.7500m h12 := - - Ho
(H )
12
H13 := 475.7826m h13 := - - Ho
(H )
13
H14 := 476.3250m h14 := - - Ho
(H )
14
H21 := 475m h21 := - - Ho
(H )
21
H22 := 474.3913m h22 := - - Ho
(H )
22
H23 := 474.3594m h23 := - - Ho
(H )
23
H24 := 474.8228m h24 := - - Ho
(H )
24
H31 := 473.7941m h31 := - - Ho
(H )
31
H32 := 473m h32 := - - Ho
(H )
32
H33 := 472.8659m h33 := - - Ho
(H )
33
H34 := 474m h34 := - - Ho
(H )
34
H41 := 472.6508m h41 := - - Ho
(H )
41
H42 := 471.7719m h42 := - - Ho
(H )
42
H43 := 471.7273m h43 := - - Ho
(H )
43
H44 := 473.1923m h44 := - - Ho
(H )
44
H'o := Ceil
(H )"H := H'o - Ho Ho := H'o
o, 0.1�"m o
6
L
L
5
Vr = -4.552 � 10 L
5
Vr = 3.128 � 10 L
4
Vr = 9.573 � 10 L
7
5
Vr = 6.815 � 10 L
4
Vr = -1.847 � 10 L
5
Vr = 1.195 � 10 L
8