Lesson Note On Digital Terrain Model (DTM)

Digital Terrain Model (DTM)

A digital terrain model (DTM) is a mathematical model of a project surface that becomes a three- dimensional representation (3D) of existing and proposed ground surface features. Critical calculations and processes based on the DTM include contouring, cross sections and quantities, drainage models, watersheds, hydraulics, water catchment areas, and cross sections sheets.

A DTM is created through the construction of a Triangulated Irregular Network (TIN) and is based on modeling the terrain surface as a network of triangular facets that are created by simply connecting each data point to its nearest neighboring points. Each data point (having x, y and z coordinates) is the vertices of 2 or more triangles. The advantage of the TIN method is its mathematical simplicity- all DTM calculations are either linear or planar.

The processes and the resulting DTM offer many advantages over a topographic survey. Field data for a DTM is collected in a way that allows TxDOT to use the latest in automated survey technology. Traditional data collection (for a topographic survey) involves taking cross sections, typically every 100 feet, along a horizontal control line or in a grid pattern. Digital terrain modeling has virtually eliminated this practice.

Data points (shots) are taken at every break in elevation with no particular pattern being required. The emphasis is on identifying all features and changes in elevation within project limits. Data is collected using an electronic data collector with an electronic total station. The data points are assigned feature codes, attributes, descriptions, comments, and connectivity linking codes to add intelligence to a point at the time of data entry into data collector.

Information is downloaded from the data collector to a computer, either in the field or later in an office, and is processed using AASHTOWare^® Survey Data Management System^®(SDMS) software. A SDMS^® calculated file is generated for importation into CAiCE^™ or GEOPAK Survey^™ for further review. The file is then imported into GEOPAK^® for project design.

Digital Terrain Model (DTM)

A digital terrain model (DTM) is a mathematical model of a project surface that becomes a three- dimensional representation (3D) of existing and proposed ground surface features. Critical calculations and processes based on the DTM include contouring, cross sections and quantities, drainage models, watersheds, hydraulics, water catchment areas, and cross sections sheets.

A DTM is created through the construction of a Triangulated Irregular Network (TIN) and is based on modeling the terrain surface as a network of triangular facets that are created by simply connecting each data point to its nearest neighboring points. Each data point (having x, y and z coordinates) is the vertices of 2 or more triangles. The advantage of the TIN method is its mathematical simplicity- all DTM calculations are either linear or planar.

Table 4.4 TSPS Manual of Practice Chart for Tolerances for Conditions
Condition	I	II
	Urban Business, District Urban, Suburban & Industrial	Rural & Broad Area General Mapping	Remarks & Formulae
Error in Traverse Closure	1:10,000	1:7500	System Control Loop
Unadjusted Level Loop Closure (ft.)	.04	.08	System Control Loop M=Miles
Secondary Traverse Closure	1:7500	1:5000	Between System Control Points
Secondary Level Loop Closure (ft.)	.05	0.2	Between System Control Points
Positional Error of Any Primary Monument (horizontal)	1:15000	1:10000	For monuments used for Triangulation or Radial Surveying in respect to another
Positional Error of Any Primary Monument (vertical)	± .03 ft.	± 0.15 ft.	For permanent bench marks
*Contour Interval	2 ft.	10 ft.	Or as needed by the State
Contour Accuracy	± ½ Contour Interval	± ½ Contour Interval
Positional error of any Photo Control Point (horizontal and/or vertical)	0.50 ft.	2 ft.	Or as recommended by Photogrammetrist
Location of Improvements, Structures, and Facilities during survey	± 0.05 ft. ± 0.50 ft.	± 0.1 ft. ± 1 ft.	Vertical (inverts, flow lines) Horizontal
Plotted location of Improvements, etc.	± 1/40 in.	± 1/40 in.	Symbols may be used for large scale maps indicating Center point
Scale of maps sufficient to show detail, but no less than	1'' – 200'	1'' – 2000'	Drawings are to show location of survey monuments and bench marks

The processes and the resulting DTM offer many advantages over a topographic survey. Field data for a DTM is collected in a way that allows TxDOT to use the latest in automated survey technology. Traditional data collection (for a topographic survey) involves taking cross sections, typically every 100 feet, along a horizontal control line or in a grid pattern. Digital terrain modeling has virtually eliminated this practice.

Data points (shots) are taken at every break in elevation with no particular pattern being required. The emphasis is on identifying all features and changes in elevation within project limits. Data is collected using an electronic data collector with an electronic total station. The data points are assigned feature codes, attributes, descriptions, comments, and connectivity linking codes to add intelligence to a point at the time of data entry into data collector.

Information is downloaded from the data collector to a computer, either in the field or later in an office, and is processed using AASHTOWare^® Survey Data Management System^®(SDMS) software. A SDMS^® calculated file is generated for importation into CAiCE^™ or GEOPAK Survey^™ for further review. The file is then imported into GEOPAK^® for project design.

LESSON NOTE ON STRESSES IN PRESTRESSED CYLINDER

STRESSES IN PRESTRESSED CYLINDER

A steel ring having an internal diameter of 8.99 in (228.346 mm) and a thickness of % in

(6.35 mm) is heated and allowed to shrink over an aluminum cylinder having an external

diameter of 9.00 in (228.6 mm) and a thickness of 1A in (12.7 mm). After the steel cools,

the cylinder is subjected to an internal pressure of 800 lb/in2 (5516 kPa). Find the stresses

in the two materials. For aluminum, E = 10 x 106 lb/in2 (6.895 x 107 kPa).

Calculation Procedure:

1. Compute the radial pressure caused by prestressing

Use the relation;? = 2ϕD/{LD²[l/(t_aE_a) + l/t_sE_s)]}, where/? = radial pressure resulting

from prestressing, lb/in² (kPa), with other symbols the same as in the previous calculation

procedure and the subscripts a and s referring to aluminum and steel, respectively. Thus,

p = 2(0.01)/{9²[1/(0.5 x l 0 x 10⁶) + 1/(0.25 >( 30 x 106)]) = 741 lb/in2 (5109.2 kPa).

2. Compute the corresponding prestresses

Using the subscripts 1 and 2 to denote the stresses caused by prestressing and internal

pressure, respectively, we find s_a1 = pD/(2t_a), where the symbols are the same as in the

previous calculation procedure. Thus, s_a1 = 741(9)/[2(0.5)] = 6670-lb/in² (45,989.7-kPa)

compression. Likewise, s_s1 = 741(9)/[2(0.25)] = 13,340-lb/in2 (91,979-kPa) tension.

3. Compute the stresses caused by internal pressure

Use the relation s s²lsa² = E_s/Ea or, for this cylinder, s_s²ls_a² = (30 x 10⁶)/(10 x 10⁶) = 3.

Next, compute s_a² from t_a² t_sS_s² = pD/2, or sa² = 800(9)/[2(0.5 + 0.25 x 3)] = 2880-

lb/in2 (19,857.6-kPa) tension. Also, s_s² = 3(2880) - 8640-lb/in² (59,572.8-kPa) tension.

4. Compute the final stresses

Sum the results in steps 2 and 3 to obtain the final stresses: sa³ = 6670 - 2880 = 3790-

lb/in² (26,132.1-kPa) compression; ss3 = 13,340 + 8640 = 21,980-lb/in² (151,552.1-kPa)

tension.

5. Check the accuracy of the results

Ascertain whether the final diameters of the steel ring and aluminum cylinder are equal.

Thus, setting s' = 0 in ϕ/E> = (D/E)(s - vs') we find ϕDa = -3790(9)7(10 x 10⁶) = -0.0034

in (-0.0864 mm), D0 = 9.0000 - 0.0034 = 8.9966 in (228.51 mm). Likewise, ϕDs =

21,980(9)7(30 x io6) = 0.0066 in (0.1676 mm), Ds = 8.99 + 0.0066 = 8.9966 in (228.51

mm). Since the computed diameters are equal, the results are valid.

Lesson Note On GPS

What is GPS?

 The Global Positioning System (GPS) is a satellite-based navigation system made up of a network of 24 satellites placed into orbit by the U.S. Department of Defense. GPS was originally intended for military applications, but in the 1980s, the US government made the system available for civilian use. Prior to 1990, GPS signals were deteriorated so a user could not achieve accuracy better than 10 meters. However, this has been changed and now any standard GPS unit can provide a precision of 4 to5 meters or 12- 15 feet. GPS works in any weather conditions, anywhere in the world, 24 hours a day. There are no subscription fees or setup charges to use GPS. 

However, tall building s or thick forest cover may block the GPS signal and result in a less precise accuracy. 

The 24 satellites that make up the GPS space segment are orbiting the earth about 12,000 miles above us. They are constantly moving, making two complete orbits in less than 24 hours. These satellites are traveling at speeds of roughly 7,000 miles an hour. GPS satellites circle the earth twice a day in a very precise orbit and transmit signal information to earth. GPS receivers take this information and use triangulation to calculate the user's exact location. Essentially, the GPS receiver compares the time a signal was transmitted by a satellite with the time it was received. 

The time difference tells the GPS receiver how far away the satellite is. Now, with distance measurements from a few more satellites, the receiver can determine the user's position and display it on the unit's electronic map. 

As GPS receivers track satellites and calculate your position this process is referred to as Triangulation. Any organization or agency that requires accurate location information can benefit from the efficiency and productivity provided by GPS technology. GPS units are used to collect point, line or polygon data on program activities by recording the latitude and longitude of activity sites, or tacking roads or walking/driving perimeter locations. 

The type of GPS unit used by USAID/Malawi does not provide data measurements necessary for land tenure processes and data collected should not be used for any legal purposes or land dispute as it is not to the required accuracy.

Lesson Note On PROFILE LEVELING

PROFILE LEVELING

DEFINITION OF PROFILE LEVELING

The process of determining the elevations of a series of points at measured intervals along a line such as the centerline of a proposed ditch or road or the centerline of a natural feature such as a stream bed.
Normally we will assign an elevation of 100.00 to the datum rather using the mean sea level elevation.

AN EXTENSION OF DIFFERENTIAL LEVELING

·  Elevations are determined in the same manner.

·  The same definitions define the concepts and terms involved.

·  The same types of mistakes and errors are possible.

·  A page check should always be done.

·  A closure check should be done if the profile line runs between bench marks.

ACCURACY OF ROD READINGS

The backsights, foresights, and elevations of benchmarks and turning points should be recorded to the nearest 0.01 ft. Profile elevations of intermediate points are determined from "ground readings" and thus the foresight readings and subsequent elevations should be recorded to the nearest 0.1 ft.

THEORY

Add rod readings (BS) to benchmark or known turning point elevations to get the elevation of the line of sight (HI).
Subtract rod readings (FS) from the line of sight to establish elevations of unknown points.
Take any number of intermediate FS readings at points along the line until it is necessary to establish a turning point to move the level.
Repeat as required.

LOCATION OF INTERMEDIATE POINTS

A foresight is taken on a bench mark to establish the height of instrument.
A foresight is taken on the stations as required (such as every 100 ft).
Foresights are also taken at breaks in the ground surface and at critical points.
This is repeated until the limit of accurate sighting is reached, at which point a turning point is established and the level is moved.

SCHEMATIC

The level is usually set up off the center line.

PROFILE CROSS SECTIONS

Cross sections are lines of levels or short profiles made perpendicular to the center line of the project. (For example, taking a cross section profile of a stream bed while doing a profile survey of the stream.)
Cross sections are usually taken at regular intervals and at sudden changes in the center-line profile.

CROSS SECTION SCHEMATIC

CROSS SECTIONS

The cross sections must extend a sufficient distance on each side of the center line to provide a view of the surrounding terrain.
Rod readings should be taken at equal intervals on both sides of the center line and at significant changes in the terrain.
Example: for a stream cross section, rod readings could be taken at 15, 30, 45, and 60 ft on each side of the center line as well as the edge of the stream and the top of bank of the stream.

CROSS SECTION FIELD NOTES

·  Field notes for a cross section should include:

an elevation or difference in elevation from the center line
horizontal distance from the center line