Analysis of stability and dimensioning of retaining wall

1. Introduction

The program Analysis of stability and dimensioning of supporting walls is one of the many programs that deals with supporting walls, but holds advantages of similar programs in its wholeness. Input data encompass all possible types and directions of supporting wall loads, and types of walls can be from classic to massive. Besides, after entering input parameters printout of the document is practically a complete project because it provides: Analysis of stability, reinforcement design, specification of reinforcement, moment bending diagram and expenses of the construction.
Program is fully compliant with all of the changes (up to end of 2012) of Eurocode2. Eurocode7 and Eurocode8, as is with Croatian norms HRN EN 1997-1:2012/NA.
Unlike other programs, for the first time, by using the special algorithm, the program enables calculation of supporting wall stability even in case when the angle of backfill steepness behind the wall is higher than inner friction of the soil.
Textual part of the program, related to coast estimate, unlike other parts of the program, is possible to change and adjust to specific needs, or not print it if it is not necessary.
Even though the program Analysis of stability and dimensioning of retaining walls is a result of the multiple years’ work and has been tested on all possible types and directions of supporting wall loads, and types of walls and wall types there are always possibilities for improvements.
Author will be thankful to everybody who has a constructive criticism or supplement to the program in other to improve it.


2. Input data
2.1. Soil properties

In the Form Soil properties entry of data about angle of the internal friction (φ), cohesion (c), height and angle of the layers and slope angle behind and beneath the wall. Because of rotation of the foundation, it is anticipated /required entering of average soil Ms beneath foundation. Rotation of the foundation and angle of top of the wall (assuming rigid wall) are resulting from subsidence in characteristically points of foundation.


2.2. Actions

In the Form Action all data regarding acting forces and their position – loads on the wall, like: traffic load, foundation load or for example special vehicle, linear loading, spot loading, ground water behind the wall and seismic load with amax (YES or NO).
If earthquake is factored in the calculation then earthquake pressure coefficient “K” is defined – determined according to Mononobe & Okabe.
If earthquake is not factored in the calculation than active pressure coefficient “Ka” is defined according to Coulomb – Poncelet.


2.3. Wall Geometry

2.3.1. General

Data on wall measures (blue numbers) is inputted by the designer and other data (black numbers) are dependent on the inputted data. It is possible to check the result after each data input by pressing the Calculation button – values of degree utilization (U %) for turning over, sliding and bearing resistance in Form 3. Calculation checking can be done unlimited number of times. If some of the values are higher than 100%, it is required to change unfitting dimension of the wall (width and/or height of foundation foot, angle of the wall, extend the cantilever or increase anchor forces) in order to achieve value below 100%.


2.3.2. Revetment Wall

Revetment wall is done in places where the slope is abrupt and relatively stable, with thin backfill or no backfill between the wall and the ground. In that case active sliding surface is fits to slopes of the terrain (e.g. in case of loess almost vertical), and that steepness of sliding surface can be calculated by fictive angle of internal friction as is explained in user manual.
Not everybody will agree with this approach of soil parameters selection, but it is rather simple to do a cross-check on rollover stability by minimally adjusting fictive angle of internal friction and observe that by the increase of internal friction angle usage is increased U (%), and by reduction of that angle, usage is decreased as well (roll-over safety factor is increased).

2.3.3. Gravity wall

Gravity wall in this program is formed like the classic gravity wall, where measures of the wall depend on height of the wall and width in the wall crown. After setting those values and pressing the Calculate button, the program calculates all other measures of classic gravity wall.
That data has to be entered in Form 3, in appropriate cells in the left column (from the given example, instead of hB =1.2 in the left column input hB = 2.24 from the right column, etc.). Instead of those values, any other values can be inputted, but then it would not be a classic form of supporting wall. Since height of the wall H is equal to sum of soil layers heights, it is required in Form 1 – “Soil properties”, to reduce one of those upper two layers. Note that height of the third layer in this program is always equal to height of foundation foot by the ground.
Gravity walls consisting shown reinforcements only anchors from foundation are required (Pos.5).


2.4. Anchors and cantilever

2.4.1. Anchors

If the wall has anchors (0-5 anchors in one column), in Form – Anchors and cantilever (Fig. 4) in the row „Anchors”“ click “YES”, in case of no anchors click “NO”. Data about anchors are inputted in the table in Form 4.
If an anchor is too short there will be a note about minimal length, and then the value has to be changed. Bearing capacity of the anchor is achieved by adjusting anchor bond length, therefore by choosing proper bond length of the anchor; spacing between the anchors can be regulated. It is recommended that spacing of anchor rows be equal also from aesthetic reasons (e.g. 2m). Given force in the anchor is the anchor pre-stressing force per m’ of the wall.


2.4.2. Cantilever

If the wall has cantilever, in the Form – Anchors and Cantilever in the row cantilever, click “YES” it has not, click “NO”. Cantilever design ensures much more economical wall, due to the fact that cantilever considerably reduces bending moment in the section wall – foundation. Increase of the wall stability can be achieved only if the width of the cantilever is bigger than the width of the foundation at the ground.
Cantilever is extremely efficient at increasing stability of the wall in case border of the cantilever is in contact with the sliding surface (active wedge) since active pressure beneath the cantilever in that case starts from 0 (zero).

When determining console width “bk”, one has to be mind that console is not too wide, because with increased width of the console drag zone beneath the console might extend all the way to wall foundation junction. In that case, during the wall build phase – until the console main armature (reinforcement) does not cover the drag zone which is at that moment on the side of the wall by the ground. In the anchors from foundation are long enough than that drag zone is also covered by reinforcement.


2.4.3. Counterforts

If the counterfort is foreseen, in Form 5.  counterfort , choose “YES” and if there is no counterfort, choose “NO”.

Using counterforts can save on wall concretes,  reducing the cross-sectional height in the crown and in contact with the foundation, but when constructing the counterforts, account should be taken of the costs of concrete, plating and counterforts work.

So, In my opinion, from this point of view, a more detailed cost analysis should be made when deciding on using counterforts .

With the extension of the foundation at the counterforts , it is possible to increase the stability of the wall effectively without the need to increase the base width “B” throughout the length of the wall. This is especially true for foundations in rocky terrain because in this case the costs of rock excavation are significantly reduced (excavation only for the foundation of the counterforts).

Even with this kind of performance (as far as the length of the counterforts foundation), it should not be exaggerated because in that case the seismic force increases considerably. (if the wall accounts for the seismic forces) . A satisfactory result is obtained by extending the counterforts foundation for about 1 m (as in the original of this program).


2.5. Material properties

By entering values in Form 5 through drop-down menus , the program enables choosing category of concrete, kind of reinforcement (rebar for the foundation, rebar and reinforcement mesh for wall and cantilever), profile and distances main reinforcement and distribution reinforcement, protection layer and cracks limitation (Fig. 5)


2.6. Terrain profile

In order to calculate excavation, backfill material and soakaways in the Form 6, it is necessary to enter five coordinates of the terrain (blue number) and inclination of the temporary excavation – for time wall execution (Fig.6).