Coursework – Assessment Brief
UBGMW9-15-3 Computational Civil Engineering
Preamble
All assessments on this module are individual work. The work you submit must be your own work. Submitting work that is copied in part or whole from another student with or without their permission is an assessment offence.
You must fully attribute/reference all sources of information used during the completion of your submission, failure to do so constitutes plagiarism, which is an assessment offence.
If you are not familiar with the definitions of plagiarism and collusion, more information can be found here: http://www1.uwe.ac.uk/students/academicadvice/assessments/ assessmentoffences.aspx
Please ensure you are familiar with assessment procedures and policies, which can be found here: http://www1.uwe.ac.uk/students/academicadvice/assessments/ assessmentsguide.aspx
Structure of assessments
This module is assessed by two components, A and B:
• Component A is a one hour written exam and is weighted as 25 % of the final mark.
• Component B is a coursework portfolio and is weighted as 75 % of the final mark. The coursework portfolio described here asks you to consider two problems entitled:
1. Structural analysis under variable loads (worth 37.5 % of the final module mark) 2. Geotechnical slope stability (worth 37.5 % of the final module mark)
The final report on your coursework portfolio must include ele a
code
routines
developed
for
both
ments
in
text
selectable
form
(no
images
or
1
screenshots
will b
e
accepted).
Online blackboard submission due on the 23 April 2020.
The following two sections describe the problems you are to develop computer programs to solve. In each section, specific details of the tasks and outputs to feed in to your report are described. An overall summary of the assessment criteria is provided at the end of this docu- ment.
Structural analysis under variable loads – 37.5 %
When dealing with variable loads the internal forces or reactions that a structure generates will vary according to a probability distribution. Then, the design of a structure is based on an output value of this distribution which has a small probability, on an absolute basis, of being exceeded. A workflow of this process is shown in Fig. 1.
1 – Generate samples for input variable UDL
2 – Compute output reactions/internal forces
3 – Plot outputs histograms
and estimate the 5% threshold
output value
–
V
p ∼ N(μp,σp) +
500
450
400
350
300
250
200
150
100
50
MV
+
M
0 -40 -35 -30 -25
800
700
600
500
400
300
200
100
V [kN]
0-500 0
Diagram of computational analysis for a simply supported beam subjected to a
500 10001500 M [kNm]
Figure 1:
variable uniformly distributed load (UDL).
Consider the isostatic structures shown in Figs. 2, 3, 4, 5, and the output reactions/internal forces presented in Table 1. You are asked to assess the variability of one these structures’ outputs when subjected to the shown loads. Each of the loads is assumed to follow a nor- mal distribution, e.g. for a uniform distributed load assume p ∼ N (μp , σp ) with mean μp and standard deviation σp.
Using MATLAB or other programming language generate 10000 data points for each load, according to its distribution parameters, and compute the corresponding output reactions/ internal forces.
Your report should include
Dr Andre Jesus & Dr Richard Sandford 2 University of the West of England
p
A
1 2
34 P2
5
C
ab
P1
c
B
d
2
Figure2: Structure1 aaaa
P1 P2 P3 6 345
1
cp
Figure3: Structure2 M
b
P
f
Figure4: Structure3
• A description of the equations and histograms for each output reaction/internal force.
• Anestimateofthe5%thresholdoutputvalue,whichisdefinedhereasthevaluewhich is exceeded, on an absolute basis, by only 5 % of the load combination realizations.
• A pseudocode or flowchart of the algorithm that underlies your analysis.
Dr Andre Jesus & Dr Richard Sandford 3 University of the West of England
p
1
46578
23
abcde
p
2
abc
P
d e
f
1
35 4
Figure5: Structure4
Structure
Outputs
1
Bending moment at section C, bending mo- ment at section 5 and axial force at section 2
2
Axial force at bar 1-2 and shear force along sec- tion 2-3
3
Horizontal reaction at 2 and bending moment at 7 towards 5
4
Vertical reaction at 1 and bending moment at 4 towards 3
Table 1: Output reactions and internal forces
The structure and numerical values that each student has to consider are made avail- able on Blackboard Learning Materials > Coursework > Coursework values html file, or by following the URL https://blackboard.uwe.ac.uk/bbcswebdav/ pid-7216458-dt-content-rid-16362959_2/courses/UBGMW9-15-3_19jan_ 1/my_values.html
Furthermore, the results of validation tests against which you can test if your program is func- tioning correctly can be found here:
https://blackboard.uwe.ac.uk/bbcswebdav/pid-7318412-dt-content-rid-17299225_ 2/courses/UBGMW9-15-3_19jan_1/my_ex1_results%281%29.html
Geotechnical slope stability – 37.5 %
An important task in geotechnical engineering is to assess the propensity for a slope to col-
lapse. It is common to analyse the stability of cohesive soil slopes by considering limiting Dr Andre Jesus & Dr Richard Sandford 4 University of the West of England
plastic equilibrium. To carry out a limiting plastic equilibrium analysis, it is first necessary to define the failure mechanism, which is specified by the geometry of the failure surface. The mass of soil bounded by this failure surface is assumed to move over this surface as a free body in equilibrium. The forces and moments acting to induce failure are then compared with the resistance to slip that is mobilised along the assumed failure surface.
A variety of different failure surfaces can be considered, but a common choice is a circular seg- ment in two-dimensions. An important analysis case is that relevant to short-term conditions, immediately after a cutting is made or an embankment is built. In the short-term, there is in- sufficient time for excess pore water pressures to dissipate; such conditions are referred to as undrained. The shear strength, τ, along a failure surface in undrained conditions is constant and denoted as cu. The difficulty in carrying out a limiting equilibrium analysis is the choice of failure surface. The key task is therefore to find the critical failure surface, that is the failure surface along which failure is most likely to occur and, hence, gives the lowest factor of safety.
Figure 6: Example of the slope stability problem
Figure 6 is an example of the class of problem that you are to address. The figure shows a two-dimensional slope of constant inclination. The soil consists of a cohesive homogeneous soil of undrained strength, cu, and unit weight, γ. The slope overlies a stiff strata. The ge- ometry and material parameters shown in Figure 6 are an example for illustration – you have been assigned an individual problem, with a set of geometric and material properties that are individual to you and can be downloaded from: Blackboard Learning Materials > Course- work > Coursework values html file, or by following the URL https://blackboard. uwe.ac.uk/bbcswebdav/pid-7216458-dt-content-rid-16362959_2/courses/
Dr Andre Jesus & Dr Richard Sandford 5 University of the West of England
UBGMW9-15-3_19jan_1/my_values.html.
Your task is to determine the safety factor against collapse for the slope geometry and ma- terials to which you have been assigned. The material properties (γ and cu) relevant to your individual problem are given on the diagram together with your slope geometry (which can be read-off from the scale). You are to consider only rotational failure along circular slip surfaces, but are to vary the radius and centre coordinates of the failure surface in order to find the min- imum safety factor against collapse. A bounding box, termed the ’search area’, is provided to limit the bounds on the search of your circle centre coordinates. The approach to minimising the safety factor by varying the location of the slip circle centre and its radius is your choice, although recommendations and possibilities will be discussed in the lectures and tutorials.
For a particular choice of circular slip surface, the safety factor, SF is calculated as: SF = resisting moment
disturbing moment where the disturbing moment is given as:
disturbing moment = W d
and the resisting moment due to shear along the slip plane is given as:
resisting moment = cuR2θ
(0.1)
(0.2)
(0.3)
In these equations, W is the weight of the soil bounded within the failure surface, d is the horizontal distance from the slip circle centre to the centre of gravity of the soil mass bounded within the failure surface, R is the slip-circle radius and θ is the angle subtended by the slip surface (see Figure 7). Note that W and d are typically found by dividing the soil bounded with the failure surface into slices or rectangular segments and then taking area-moments about a convenient point. Substitution of Equations 0.2 and 0.3 into Equation 0.1 gives:
SF = resisting moment = cuR2θ (0.4) disturbing moment W d
To aid the validation of the computer program you will develop, a particular slope geometry is shown in Figure 8. For the particular circular slip line shown (i.e. the given circle centre position and radius), and for γ=18.5kN/m3 and cu=40kPa, the safety factor against collapse is 1.44 (correct to 2 decimal places). Demonstrating that your computer program can correctly calculate this safety factor is a valuable task and one you should document in your report. [You might find it valuable to note that for this problem: θ=84.06◦, R=17.43m and d=6.54m].
Note that to consider a variety of different combinations of the circle centre positions and circle radii in a time-efficient manner, it is necessary to implement a test as to whether a par- ticular slip circle intersects the inclined or horizontal portions of the slope surface. To assist
Dr Andre Jesus & Dr Richard Sandford 6 University of the West of England
with carrying out this test, you may find the following resource useful: http://mathworld. wolfram.com/Circle-LineIntersection.html.
Figure 7: Parameters involved in the calculation of the safety factor
Figure 8: Validation problem geometry
Your report should include:
1. A description of the mathematical equations needed to find the safety factor against col- lapse.
2. The results of a validation case to demonstrate that your code can calculate the safety factor correctly for a particular choice of circle centre coordinates, slip circle radius and parameters that specify the geometry and strength of the slope.
Dr Andre Jesus & Dr Richard Sandford 7 University of the West of England
3. Justificationofyourapproachtofindthecriticalslipcircleradiusandcentrecoordinates.
4. Pseudocodeoraflowchartshowingyourapproachto(i)findthesafetyfactorforagiven combination of slip-circle centre coordinates and slip-circle radius, and (ii) optimise the slip circle centre coordinates and slip-circle radius to find the critical safety factor.
5. A graphical presentation of the dependence of the safety factor on the slip circle centre coordinates.
6. Your calculation of the critical safety factor (as well as the circle centre coordinates and slip-circle radius that generated the critical safety factor).
Assessment criteria
Your report should contain the following and you will be assessed according to the criteria described in Table 2.
• Problem description: A summary of the problem you are attempting to solve, to include the assumptions needed to obtain a solution and any mathematical elaboration of the equations that are used within your computer program. (15%)
• Program development: The pseudocode or flowchart used to solve the problem, to- gether with an explanation and justification for your chosen numerical approach to solve the problem. Note that you are also required to submit, as part of your report, the code used to generate your results. (25%)
• Presentation of the results: To include plots showing the outputs from your work and accompanying text to describe their meaning. This section should include the outcomes of any validation exercises you undertake to demonstrate the correct functioning of the programs you develop. (50%)
• Concluding comments: To explain how your computer program could be extended or generalised for increased functionality. (10%)
%
Descriptor
Problem description (15%)
Program de- velopment (25%)
Presentation of results (50%)
Concluding comments (10%)
Dr Andre Jesus & Dr Richard Sandford 8 University of the West of England
80-100
Outstanding
Problem descriptions stated with outstanding clarity, with complete mathemati- cal treatment
Outstanding program de- velopment, with com- plete and thorough justification for chosen approach
Outstanding clarity of presentation with fully annotated plots, com- plete and fully cor- rect results and vali- dation test outcomes
Outstanding clarity of comments on the generalisa- tion of the computer program
70-79
Excellent
Problem descriptions stated with excellent clarity, with comprehen- sive math- ematical treatment
Excellent program de- velopment, with clear justification for chosen approach
Excellent clarity of presentation with well annotated plots, com- plete and fully cor- rect results and vali- dation test outcomes
Excellent clarity of comments on the generalisa- tion of the computer program
60-69
Very good: 65-69 Good: 60-64
Problem descrip- tions stated with clarity, with mostly complete mathemati- cal treatment
Program de- velopment presented that ad- dresses the main aims of the task with clear justification
Very good/good clarity of presentation with well annotated plots, mostly complete and correct results and some vali- dation test outcomes
Very good/good clarity of comments on the generalisa- tion of the computer program
Dr Andre Jesus & Dr Richard Sandford 9 University of the West of England
50-59
Competent: 55-59 Adequate: 50-54
Problem descriptions stated with adequate clarity, with basic math- ematical treatment
Program de- velopment presented that ad- dresses some as- pects of the task with partial justification
Competent/ adequate clarity of presenta- tion with plots, some complete and correct results and limited val- idation test outcomes
Competent/ adequate clarity of comments on the generalisa- tion of the computer program
40-49
Weak
Problem descriptions lacking clar- ity, with minimal or only par- tially correct mathemati- cal treatment
Program de- velopment presented that ad- dresses limited as- pects of the task with limited justification
Limited clarity of presenta- tion with few plots, incomplete results and limited val- idation test outcomes
Limited clarity of comments on the generalisa- tion of the computer program
30-39
Poor (FAIL)
Problem descriptions unclear, with incomplete or incorrect mathemati- cal treatment
Program develop- ment that is incom- plete with very limited justification
Poor clarity of presen- tation with very few plots, in- complete and incor- rect results and limited validation test out- comes
Poor clarity of com- ments on the generalisa- tion of the computer program
Dr Andre Jesus & Dr Richard Sandford 10 University of the West of England
<30 Very poor (FAIL) Problem descriptions very un- clear, with no math- ematical treatment Program de- velopment that to the and justification fails address brief lacks Very poor clarity presenta- tion lacking plots, in- complete and incor- rect results and very limited val- idation test outcomes of Very poor clarity comments on the generalisa- tion of the computer program of Table 2: Assessment Criteria Dr Andre Jesus & Dr Richard Sandford 11 University of the West of England