10 Civl235 Slope Stake 6v3h1j
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PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
Introduction One of the operations carried out during road construction is setting up slope stakes. These stakes at set to guide the construction process at every cross-section of the road and to provide data needed for earthwork calculations. This section discusses the theory and field procedure for slope stakes. Cross-sections are usually taken at the stations along the route and at other intermediate points that are essential for correct calculation of the earthwork. Stakes are set at each cross-section to specify the location of the centerline (centre stake), the shoulder lines (shoulder stakes), and the point where the side slopes of the route meet the ground (slope stakes). At each station, the engineer sets up the instrument at a convenient point where a back-sight to a benchmark is possible. The height of the instrument (H.I.) is then obtained from the rod reading at the location of the benchmark. The elevation of the grade at the cross-section is known from the route data. The difference between the H.I. and the grade elevation is known as the grade rod. In a way, grade rod represents the reading off the rod had it been set on the grade level, as grade rod = H.I. – elevation of the grade. At any point of the cross-section, the reading of the rod is usually referred to as the ground rod. The difference between the ground rod and the grade rod is equal to the cut or fill at a specific point (figure 1).
H.I. Grade Rod
Ground Rod
Fill
Figure 1: Road cross-section in fill. Figure 1 shows a cross-section in fill. In practice, the cross-sections can be entirely in cut, in fill, or be in a combination of the two. The cross-section that es from cut to fill is usually referred to as side-hill section. Between two consecutive cut and fill cross-sections, a transition line usually marks the intersection of the grade and the natural ground (figure 2)
Page 1 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
Figure 2: Cross-section in transition area. [1] The cut (c) or fill (f) at the centerline and the shoulder stakes can be easily calculated from the known grade rod and the measured ground rod. The field method of finding the location of the slope stakes is based on trial and error. From the geometry of the cut (or fill) section, the following relationship can be derived:
d=
w + cs 2
for cut sections
d=
w + fs 2
for fill sections
where d is the distance from the centerline to the slope stake, w is the width of the road, and s is the sideslope ratio. The steps involved in setting the slope stakes are illustrated in the following example (taken from [1]): Example: Let w=7 m, side slopes 2:1, grade elevation at 32+00 = 240.36 m, centerline elevation = 239.25 m. Find the slope stakes for the cross-section of figure 3 in fill.
Figure 3: Slope stakes for a cross-section in fill. [1]
Page 2 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
A back-sight on a B.M. gives the H.I. of 241.90 m. The rod reading on centerline is 2.65 m, which verifies the given centerline elevation. The grade rod = H.I. – grade elevation = 241.90 – 240.36 = 1.54 m. In order to set the right slope stake, the rod is held as a first trial at point 1, where the ground rod = 3.23. Thus, f1 = grade rod – ground rod = 1.54 – 3.23 = -1.69 m, where the negative sign indicates a fill. The computed distance for the absolute value of f1 by equation d =
w + fs is 3.5 + (1.69)(2) = 6.88 m. The measured value 2
for d1 is 6.2 m, so that the rod must be moved farther from the centerline. A second trial is made at point 2, where the ground rod is 3.62, f2 = 1.54 – 3.62 = -2.08 m, and the computed distance to f2 is 3.5 + (2.08)(2) = 7.66 m. Since the measured distance d2 is 8.2 m, the rod is out too far. Eventually, by trial, the rod is held at 3, where the ground rod = 3.40, fr = 1.54-3.40 = -1.86 m, and the computed distance is 3.5 + (1.86)(2) = 7.22 m. This distance agrees with the measured distance dr; hence, point 3 is the correct location for the slope stake. The notes for this final cross-section are: H.I. 241.90 32 + 00
f 0.65 4.62
f 1.11 0
f 1.86 7.22
Areas of cross-sections Total area of a cross-section can be calculated based on the recorded field data. The easiest method of calculating the total area of a cross-section is to sum up all the sub-areas between shoulder stakes and the slope or centerline stakes (figure 4). In other words:
ATotal = ∑ Ai i
A1
A2 w/2
A3
A4
w
Figure 4: Sub-areas are used to calculate the total area. Page 3 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
Volume of Earthwork Volume of the earthwork is usually calculated using one of the two methods: Average end area method, Prismoidal method. The average end area method is based on the assumption that the volume between two successive cross-sections is equal to the average area multiplied by the distance between them:
V =
A1 + A2 ×l 2
where V is the volume, A1 and A2 are the cross-sectional areas at stations 1 and 2 respectively, and l is the distance between the two stations. It should be noted that this method is exact when A1=A2. The error in this approximation increases when running from cut to fill or for the side-hill work, and can be as high as 50% In the prismoidal method, the volume is calculated using the two end areas and a middle area obtained from the average of linear dimensions (note: Am is obtained by averaging the dimensions and not the areas). The following formula gives the volume of a prismoid based on the end and middle areas:
V=
l ( A1 + 4 Am + A2 ) 6
Page 4 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
Field Exercise The purpose of the exercise is to lay out the centerline, shoulder lines and the slope stakes for a road. You are responsible to set up cross-sections for five consecutive stations. The location of the centerline of the first station is specified in the field by a stake, and a second stake provided for the direction of the road, both placed in the field in advance. Follow the procedure outlined below: 1. Using the letter on the first stake, look up the elevation of the ground and road grade at centerline from the table below. Note that the ground elevations are assumed and not related to each other. Party
Ground Elevation (m)
Grade Elevation (m)
A
95.51
92.59
B
94.22
91.36
C
93.15
90.07
D
92.07
89.22
E
91.26
88.15
F
90.47
87.37
G
89.34
86.66
H
88.56
85.25
I
87.25
84.39
J
86.43
83.67
K
85.32
82.11
L
84.72
81.83
M
83.18
80.52
N
82.27
79.39
O
81.42
78.31
P
80.33
77.78
The starting stake is for the station STA 600 + 90.00 (this provides the location of the station with respect to the beginning of the road). 2. Set up the centerline and shoulder stakes for all five stations following STA 600 + 90.00. The stations are 10.00 m apart and the distance between the centerline and the shoulder stakes is 3.00 m. Make sure that the plane of each station is perpendicular to the direction of the road and confirm it with your TA. 3. Use your Level to find the elevation of the ground at all the centerline and shoulder stakes. Note that you have to set up a table showing your readings and elevations similar to the leveling exercise. At this point you can ask your TA to specify the slope of the road grade (the TA would set the grade elevation 1-2 m higher than the ground elevation at the last centerline and ensure that the road slope is non-zero). Calculate the elevation of the grade at each station. Page 5 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
4. Set up the slope stakes using the trial and error method discussed in class. Assume that the side-slope ratio is 1:1.5. to specify the cut and fill for all the stakes using the format specified in the example. Shoulder Stake
Centerline Stake
1 1.5 Road Grade
Slope Stake
3.00 m
3.00 m Natural Ground
Figure 5: Road details and the stakes. 5. Set up the transition points along the centerline and the shoulder lines. Get approval for the fieldwork from your TA. Make sure that you have all the information for calculating the volume of earthwork. 6. Each party member should calculate the end areas for one road segment (between two consecutive crosssections). Calculate the volume of cut or fill for the same segment from the average end area method and the prismoidal method. 7. Calculate the total volume of cut and fill for all the segments (obtain the other segment volumes from your partners). 8. Make sure that your field books include all of the following: !
Leveling notes.
!
Location sketch of the proposed road.
!
The centerline profile of the ground and the road grade showing the elevations at each station.
!
A plan view of the road layout showing all the stakes.
!
Cut and fill information for two adjacent stations.
!
Cross-section sketches and calculations for end areas at the above two stations, plus the crosssection and area for a section mid-way between them.
!
Volume calculation for the above segment of the road.
!
Volumes for the other sections of the road (from your partners).
!
Volumes and the total quantities for the entire road.
Page 6 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
References 1. R. E. Davis, F. S. Foote, J. M. Anderson, E. M. Mikhail, “Surveying: Theory and Practice”, McGraw Hill Inc., 1981, pp. 723-727.
Page 7 of 7
Plane Surveying – Slope and Stake Civil Engineering 235
Department of Civil Engineering, UBC
Objective:
A road is to be laid out in a straight line, starting at a stake defined in the field, and heading in the direction defined by an end stake, also placed in the field in advance. At the starting stake, a ground elevation and road grade elevation are give on the attached page (one for each group) and the slope of the road grade has to be discussed in the field with the TA. Field staking and measurements permit construction to proceed because the slope stakes define the area affected and the cut or fill to be constructed between them. Field notes permit calculations of quantities to be completed for contract payment and post control purposes.
Field: 1. Set out centerline, shoulder, and slope stakes for 5 stations, i.e. the start point, and four additional stations along the centerline defined by the start and end stakes placed in the field in advance. Stations are to be 10m apart along the centerline. 2. Determine the cut and fill values at each station and mark these on the stakes. 3. Determine the location of the transition point from cut to fill of centerline and shoulder stakes. 4. Acquire enough data to accurately calculate cut and fill quantities (volumes) between stations.
Office: 1. Calculate cut and/or fill end areas at each of the five stations. 2. Calculate the cut and fill quantities between adjacent stations using: a. average end area method b. prismoidal formula Each student should calculate at least one of the end areas, and then obtain the data from the others in the group so that each student can calculate one cut of fill volume. Results of the calculations should then be shared so that each field book has the complete results.
Field Book:
Each person’s field book should contain: 1. 2. 3. 4. 5. 6.
Levelling notes for this exercise. A location sketch of the proposed road. The centerline profile of the ground and the road grade showing the elevations at each station. A plan view of the road layout showing all the stakes. The leveling notes for 2 adjacent stations, i.e. the cut and fill values at two adjacent stations. Cross-section sketches and calculations for end areas at the above two stations, plus the cross-section and end area for a section mid-way between them. 7. Volume calculations for the above section of road. 8. Volumes for the other sections of the road (copied from your partners). 9. Volumes and total quantities for the entire piece of work.
Page 1 of 2
Plane Surveying – Slope and Stake Civil Engineering 235
Department of Civil Engineering, UBC
Starting data for road layout: The starting stake is found near the edge of the roadway. The ground elevations given are assumed and are not related to each other. Each party should first lay out the road centerline stakes (lined up towards the end stake at 10m intervals, and then determine the elevations of the 5 stations from the first station (STA 800 + 7.00). you may then choose a roadway elevations at station 900+ 10.00) such that the roadway is 1 to 2 meter above the ground elevations at that station. You can then CALCULATE a suitable road grade (slope). This should be approved by the instructor in the field. Note the result on this sheet and show the calculation and result in the filed books. Starting Stake Data (STA 800 + 70.00) PARTY A B C D E F G H I J K L M N O P
GROUND ELEVATION (m) 95.51 94.22 93.15 92.07 91.26 90.47 89.34 88.56 87.25 86.43 85.32 84.72 83.18 82.27 81.42 80.33
ROAD GRADE ELEVATION 92.59 91.36 90.07 89.22 88.15 87.37 86.66 85.25 84.39 83.67 82.11 81.83 80.52 79.39 78.31 77.78
Page 2 of 2
Department of Civil Engineering, UBC
Introduction One of the operations carried out during road construction is setting up slope stakes. These stakes at set to guide the construction process at every cross-section of the road and to provide data needed for earthwork calculations. This section discusses the theory and field procedure for slope stakes. Cross-sections are usually taken at the stations along the route and at other intermediate points that are essential for correct calculation of the earthwork. Stakes are set at each cross-section to specify the location of the centerline (centre stake), the shoulder lines (shoulder stakes), and the point where the side slopes of the route meet the ground (slope stakes). At each station, the engineer sets up the instrument at a convenient point where a back-sight to a benchmark is possible. The height of the instrument (H.I.) is then obtained from the rod reading at the location of the benchmark. The elevation of the grade at the cross-section is known from the route data. The difference between the H.I. and the grade elevation is known as the grade rod. In a way, grade rod represents the reading off the rod had it been set on the grade level, as grade rod = H.I. – elevation of the grade. At any point of the cross-section, the reading of the rod is usually referred to as the ground rod. The difference between the ground rod and the grade rod is equal to the cut or fill at a specific point (figure 1).
H.I. Grade Rod
Ground Rod
Fill
Figure 1: Road cross-section in fill. Figure 1 shows a cross-section in fill. In practice, the cross-sections can be entirely in cut, in fill, or be in a combination of the two. The cross-section that es from cut to fill is usually referred to as side-hill section. Between two consecutive cut and fill cross-sections, a transition line usually marks the intersection of the grade and the natural ground (figure 2)
Page 1 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
Figure 2: Cross-section in transition area. [1] The cut (c) or fill (f) at the centerline and the shoulder stakes can be easily calculated from the known grade rod and the measured ground rod. The field method of finding the location of the slope stakes is based on trial and error. From the geometry of the cut (or fill) section, the following relationship can be derived:
d=
w + cs 2
for cut sections
d=
w + fs 2
for fill sections
where d is the distance from the centerline to the slope stake, w is the width of the road, and s is the sideslope ratio. The steps involved in setting the slope stakes are illustrated in the following example (taken from [1]): Example: Let w=7 m, side slopes 2:1, grade elevation at 32+00 = 240.36 m, centerline elevation = 239.25 m. Find the slope stakes for the cross-section of figure 3 in fill.
Figure 3: Slope stakes for a cross-section in fill. [1]
Page 2 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
A back-sight on a B.M. gives the H.I. of 241.90 m. The rod reading on centerline is 2.65 m, which verifies the given centerline elevation. The grade rod = H.I. – grade elevation = 241.90 – 240.36 = 1.54 m. In order to set the right slope stake, the rod is held as a first trial at point 1, where the ground rod = 3.23. Thus, f1 = grade rod – ground rod = 1.54 – 3.23 = -1.69 m, where the negative sign indicates a fill. The computed distance for the absolute value of f1 by equation d =
w + fs is 3.5 + (1.69)(2) = 6.88 m. The measured value 2
for d1 is 6.2 m, so that the rod must be moved farther from the centerline. A second trial is made at point 2, where the ground rod is 3.62, f2 = 1.54 – 3.62 = -2.08 m, and the computed distance to f2 is 3.5 + (2.08)(2) = 7.66 m. Since the measured distance d2 is 8.2 m, the rod is out too far. Eventually, by trial, the rod is held at 3, where the ground rod = 3.40, fr = 1.54-3.40 = -1.86 m, and the computed distance is 3.5 + (1.86)(2) = 7.22 m. This distance agrees with the measured distance dr; hence, point 3 is the correct location for the slope stake. The notes for this final cross-section are: H.I. 241.90 32 + 00
f 0.65 4.62
f 1.11 0
f 1.86 7.22
Areas of cross-sections Total area of a cross-section can be calculated based on the recorded field data. The easiest method of calculating the total area of a cross-section is to sum up all the sub-areas between shoulder stakes and the slope or centerline stakes (figure 4). In other words:
ATotal = ∑ Ai i
A1
A2 w/2
A3
A4
w
Figure 4: Sub-areas are used to calculate the total area. Page 3 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
Volume of Earthwork Volume of the earthwork is usually calculated using one of the two methods: Average end area method, Prismoidal method. The average end area method is based on the assumption that the volume between two successive cross-sections is equal to the average area multiplied by the distance between them:
V =
A1 + A2 ×l 2
where V is the volume, A1 and A2 are the cross-sectional areas at stations 1 and 2 respectively, and l is the distance between the two stations. It should be noted that this method is exact when A1=A2. The error in this approximation increases when running from cut to fill or for the side-hill work, and can be as high as 50% In the prismoidal method, the volume is calculated using the two end areas and a middle area obtained from the average of linear dimensions (note: Am is obtained by averaging the dimensions and not the areas). The following formula gives the volume of a prismoid based on the end and middle areas:
V=
l ( A1 + 4 Am + A2 ) 6
Page 4 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
Field Exercise The purpose of the exercise is to lay out the centerline, shoulder lines and the slope stakes for a road. You are responsible to set up cross-sections for five consecutive stations. The location of the centerline of the first station is specified in the field by a stake, and a second stake provided for the direction of the road, both placed in the field in advance. Follow the procedure outlined below: 1. Using the letter on the first stake, look up the elevation of the ground and road grade at centerline from the table below. Note that the ground elevations are assumed and not related to each other. Party
Ground Elevation (m)
Grade Elevation (m)
A
95.51
92.59
B
94.22
91.36
C
93.15
90.07
D
92.07
89.22
E
91.26
88.15
F
90.47
87.37
G
89.34
86.66
H
88.56
85.25
I
87.25
84.39
J
86.43
83.67
K
85.32
82.11
L
84.72
81.83
M
83.18
80.52
N
82.27
79.39
O
81.42
78.31
P
80.33
77.78
The starting stake is for the station STA 600 + 90.00 (this provides the location of the station with respect to the beginning of the road). 2. Set up the centerline and shoulder stakes for all five stations following STA 600 + 90.00. The stations are 10.00 m apart and the distance between the centerline and the shoulder stakes is 3.00 m. Make sure that the plane of each station is perpendicular to the direction of the road and confirm it with your TA. 3. Use your Level to find the elevation of the ground at all the centerline and shoulder stakes. Note that you have to set up a table showing your readings and elevations similar to the leveling exercise. At this point you can ask your TA to specify the slope of the road grade (the TA would set the grade elevation 1-2 m higher than the ground elevation at the last centerline and ensure that the road slope is non-zero). Calculate the elevation of the grade at each station. Page 5 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
4. Set up the slope stakes using the trial and error method discussed in class. Assume that the side-slope ratio is 1:1.5. to specify the cut and fill for all the stakes using the format specified in the example. Shoulder Stake
Centerline Stake
1 1.5 Road Grade
Slope Stake
3.00 m
3.00 m Natural Ground
Figure 5: Road details and the stakes. 5. Set up the transition points along the centerline and the shoulder lines. Get approval for the fieldwork from your TA. Make sure that you have all the information for calculating the volume of earthwork. 6. Each party member should calculate the end areas for one road segment (between two consecutive crosssections). Calculate the volume of cut or fill for the same segment from the average end area method and the prismoidal method. 7. Calculate the total volume of cut and fill for all the segments (obtain the other segment volumes from your partners). 8. Make sure that your field books include all of the following: !
Leveling notes.
!
Location sketch of the proposed road.
!
The centerline profile of the ground and the road grade showing the elevations at each station.
!
A plan view of the road layout showing all the stakes.
!
Cut and fill information for two adjacent stations.
!
Cross-section sketches and calculations for end areas at the above two stations, plus the crosssection and area for a section mid-way between them.
!
Volume calculation for the above segment of the road.
!
Volumes for the other sections of the road (from your partners).
!
Volumes and the total quantities for the entire road.
Page 6 of 7
PLANE SURVEYING – Slope Stake Civil Engineering 235
Department of Civil Engineering, UBC
References 1. R. E. Davis, F. S. Foote, J. M. Anderson, E. M. Mikhail, “Surveying: Theory and Practice”, McGraw Hill Inc., 1981, pp. 723-727.
Page 7 of 7
Plane Surveying – Slope and Stake Civil Engineering 235
Department of Civil Engineering, UBC
Objective:
A road is to be laid out in a straight line, starting at a stake defined in the field, and heading in the direction defined by an end stake, also placed in the field in advance. At the starting stake, a ground elevation and road grade elevation are give on the attached page (one for each group) and the slope of the road grade has to be discussed in the field with the TA. Field staking and measurements permit construction to proceed because the slope stakes define the area affected and the cut or fill to be constructed between them. Field notes permit calculations of quantities to be completed for contract payment and post control purposes.
Field: 1. Set out centerline, shoulder, and slope stakes for 5 stations, i.e. the start point, and four additional stations along the centerline defined by the start and end stakes placed in the field in advance. Stations are to be 10m apart along the centerline. 2. Determine the cut and fill values at each station and mark these on the stakes. 3. Determine the location of the transition point from cut to fill of centerline and shoulder stakes. 4. Acquire enough data to accurately calculate cut and fill quantities (volumes) between stations.
Office: 1. Calculate cut and/or fill end areas at each of the five stations. 2. Calculate the cut and fill quantities between adjacent stations using: a. average end area method b. prismoidal formula Each student should calculate at least one of the end areas, and then obtain the data from the others in the group so that each student can calculate one cut of fill volume. Results of the calculations should then be shared so that each field book has the complete results.
Field Book:
Each person’s field book should contain: 1. 2. 3. 4. 5. 6.
Levelling notes for this exercise. A location sketch of the proposed road. The centerline profile of the ground and the road grade showing the elevations at each station. A plan view of the road layout showing all the stakes. The leveling notes for 2 adjacent stations, i.e. the cut and fill values at two adjacent stations. Cross-section sketches and calculations for end areas at the above two stations, plus the cross-section and end area for a section mid-way between them. 7. Volume calculations for the above section of road. 8. Volumes for the other sections of the road (copied from your partners). 9. Volumes and total quantities for the entire piece of work.
Page 1 of 2
Plane Surveying – Slope and Stake Civil Engineering 235
Department of Civil Engineering, UBC
Starting data for road layout: The starting stake is found near the edge of the roadway. The ground elevations given are assumed and are not related to each other. Each party should first lay out the road centerline stakes (lined up towards the end stake at 10m intervals, and then determine the elevations of the 5 stations from the first station (STA 800 + 7.00). you may then choose a roadway elevations at station 900+ 10.00) such that the roadway is 1 to 2 meter above the ground elevations at that station. You can then CALCULATE a suitable road grade (slope). This should be approved by the instructor in the field. Note the result on this sheet and show the calculation and result in the filed books. Starting Stake Data (STA 800 + 70.00) PARTY A B C D E F G H I J K L M N O P
GROUND ELEVATION (m) 95.51 94.22 93.15 92.07 91.26 90.47 89.34 88.56 87.25 86.43 85.32 84.72 83.18 82.27 81.42 80.33
ROAD GRADE ELEVATION 92.59 91.36 90.07 89.22 88.15 87.37 86.66 85.25 84.39 83.67 82.11 81.83 80.52 79.39 78.31 77.78
Page 2 of 2
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