DCP and DSN800: definitions, calculations and applicability

A thin band should not disappear in the average

One penetration number is convenient. A depth record is more interesting.

TRH12 is the rehabilitation research starting point in the official manual catalogue. Its applicable DCP method and limits must be checked before using a derived parameter for design. (Department of Transport, n.d.)

Take the difference between consecutive readings

Governing relationship: DN = Δdepth / Δblows [mm/blow].

z: cumulative depth (mm); N: cumulative blows. Use differences, not z/N at every point.

Intervals: 10, 15, 30 and 45 blows produce 100, 100, 200 and 400 mm.

The film first plots blows per interval, then follows the calculation and plots dn (mm/blow). The last interval gives 8.89 mm/blow. The overall 800/100 = 8.00 conceals the changes between intervals.

Incremental test record

Penetration as a measured profile

This replays an assumed record; it does not predict cone resistance or CBR.

Download example data (CSV)

Model, calculations and transcriptEquations, worked steps, source notes and a timed reading guide

Understand the model

The local slope of the cumulative penetration record measures millimetres of penetration per blow over a particular interval.

Work through the inputs and equations below, then compare the calculated output with the film. All numerical inputs in this study are synthetic.

Inputs and symbol key

zj; Nj

Cumulative penetration depth (mm) and cumulative blows at reading j.

DNj

Incremental penetration per blow over interval j (mm/blow).

Values used in this film

• z: cumulative depth (mm); N: cumulative blows. Use differences, not z/N at every point.
• Intervals: 10, 15, 30 and 45 blows produce 100, 100, 200 and 400 mm.

The mathematical relationships

1. Equation 1

   Source and scope
   $$DN_j=\frac{z_j-z_{j-1}}{N_j-N_{j-1}}$$

   Use increments of depth and blows between successive readings. Cumulative depth divided by cumulative blows answers a different question.

2. Equation 2

   Source and scope
   $$DN_4=(800-400)/(100-55)=8.89\ \mathrm{mm/blow}$$

   The last 400 mm requires 45 blows, giving 8.89 mm/blow. The full-profile average conceals those interval changes.

Work through the example

Use the relationships above with consistent units. These substitutions are our worked example, not values quoted from the source.

1. Depth increments

   100, 100, 200, 400

   mm

2. Blow increments

   10, 15, 30, 45

   blows

3. Interval rates

   10, 6.6667, 6.6667, 8.8889

   mm/blow

4. Weighted identity

   Σ(DNj × ΔNj) / ΣΔNj = 800 / 100 = 8

   mm/blow

Read the output

The last interval gives 8.89 mm/blow. The overall 800/100 = 8.00 conceals the changes between intervals.

Check your understanding

Require increasing cumulative blows and nondecreasing penetration. A zero blow increment cannot be divided into a rate; flag it for review. Retain refusal and missing intervals explicitly instead of replacing them with zero penetration resistance.

Assumptions and limits

This replays an assumed record; it does not predict cone resistance or CBR.

Return to the full references and method notes to check the cited edition and its applicability.

Timestamped film transcript 28 short entries · select a time to revisit the film

1. 0:00

   Penetration as a measured profile. Cumulative blows 0, 10, 25, 55, 100; depth 0–800 mm.

2. 0:01

   MATHEMATICS · define the relationship and the meaning of each symbol before calculating.

3. 0:07

   z: cumulative depth (mm); N: cumulative blows. Use differences, not z/N at every point. Intervals: 10, 15, 30 and 45 blows produce 100, 100, 200 and 400 mm.

4. 0:14

   INPUT · blow increments · read the axis units and the numerical values.

5. 0:23

   Interval 1: (100 − 0) / (10 − 0) = 10.00 mm/blow.

6. 0:27

   Interval 2: (200 − 100) / (25 − 10) = 6.67 mm/blow.

7. 0:31

   Interval 3: (400 − 200) / (55 − 25) = 6.67 mm/blow.

8. 0:35

   Interval 4: (800 − 400) / (100 − 55) = 8.89 mm/blow.

9. 0:43

   OUTPUT · incremental penetration rates · read the axis units and the numerical values.

10. 0:52

    The last interval gives 8.89 mm/blow. The overall 800/100 = 8.00 conceals the changes between intervals.

11. 0:59

    CALCULATION · substitute the defined inputs; keep units through each intermediate step.

12. 1:05

    Depth increments: 100, 100, 200, 400 mm

13. 1:08

    Blow increments: 10, 15, 30, 45 blows

14. 1:11

    Interval rates: 10, 6.6667, 6.6667, 8.8889 mm/blow

15. 1:14

    Weighted identity: Σ(DNj × ΔNj) / ΣΔNj = 800 / 100 = 8 mm/blow

16. 1:17

    SENSITIVITY · change one declared input · read the axis units and the numerical values.

17. 1:26

    40 last blows: 10 mm/blow last interval. Last 400 mm divided by 40 blows; other intervals unchanged.

18. 1:29

    45 last blows: 8.88889 mm/blow last interval. Reference last interval, 400 mm over 45 blows.

19. 1:33

    50 last blows: 8 mm/blow last interval. Last 400 mm divided by 50 blows.

20. 1:36

    Check: Require increasing cumulative blows and nondecreasing penetration. A zero blow increment cannot be divided into a rate; flag it for review. Retain refusal and missing intervals explicitly instead of replacing them with zero penetration resistance.

21. 1:42

    ONE ROW · One penetration number is convenient. A depth record is more interesting.

22. 2:00

    PARAMETER MAP · 12261 evaluated cells. The colour limits stay fixed across every row.

23. 2:10

    Begin with the interval penetration values from the worked record, then prescribe a 15% spatial modulation along a 2 km corridor. DN₀ is 10 from the surface to less than 200 mm,

24. 2:22

    6.6666667 from 200 to below 400 mm, and 8.8888889 from 400 mm onward. Read each column as a depth profile. Bands are prescribed layers in the teaching dataset, not detected field

25. 2:33

    interfaces.

26. 2:38

    VALUE LANDSCAPE · Height and colour encode Prescribed DN (mm/blow). This is a graph over the two input axes, not automatically a physical pavement shape.

27. 2:50

    This synthetic response field does not convert DN to CBR, capacity or DSN800. A real sounding has discrete blows, depth resolution and possible refusal; smooth chainage variation is an imposed assumption.

28. 2:58

    This replays an assumed record; it does not predict cone resistance or CBR.

Download the timed captions (VTT)

The transcript records the on-screen wording. Formula provenance and interpretation are explained in the source note above.

Preserve the field record

Our suggested data record stores cumulative blows, cumulative depth, units, test location, date and material observations. Derived values should not replace the original measurements. Mark interruptions and refusal explicitly rather than interpolate through them silently.

Check a penetration increment

In a synthetic interval, depth increases from 120 to 160 mm over five blows. The interval penetration rate is 40/5 = 8 mm per blow. This arithmetic is not itself DSN800 and is not a strength or remaining-life estimate.

Check the method before converting penetration

Do not extrapolate a shallow test to 800 mm without the selected method permitting it. Soil, moisture and method applicability require engineering assessment.

What DSN800 means in the source

Draft TRH12 describes DSN800 as the total number of blows required to penetrate the pavement layers to a depth of 800 mm. It discusses a bearing-capacity interpretation for a reasonably balanced pavement; that qualification matters. The parameter is a blow count, unlike an interval penetration rate expressed in mm/blow. (Department of Transport, 1997)

A synthetic record reaching 800 mm after 100 cumulative blows would therefore record 100 blows to that depth, subject to the applicable test and interpretation conventions. The earlier example of 8 mm/blow describes only one interval. It cannot by itself establish the total blow count through the entire profile.

If a test stops at 600 mm, record that fact. Do not label its final count DSN800 merely because the reporting column expects a number. Check the selected method, test conditions and material applicability before making an empirical interpretation.

Calculate the intervals before interpreting the profile

Use the cumulative synthetic record below. Each row preserves an observation; each interval calculation is derived from two adjacent rows.

Cumulative blows	Cumulative depth (mm)	Interval penetration (mm/blow)
0	0	—
10	100	(100 − 0) / (10 − 0) = 10.00
25	200	(200 − 100) / (25 − 10) = 6.67
55	400	(400 − 200) / (55 − 25) = 6.67
100	800	(800 − 400) / (100 − 55) = 8.89

The total count to 800 mm is 100 blows in this invented record. The whole-depth average penetration is 800 / 100 = 8 mm/blow. That average does not preserve the variation between intervals, and it is not interchangeable with the DSN800 blow count.

Case review

The total hides the intervals that produced it

What changes through the 800 mm penetration record?

0–100 · 10 DN (mm/blow)

The discriminating check

Inspect the original blow/depth record, interval lengths, material changes and any refusal or incomplete penetration.

Evidence supports the comparison

With a complete record, calculate the specified descriptor using its own definition and applicability rules.

Evidence is missing or incompatible

With an incomplete or refused sounding, retain that state; do not extend the profile by assumption.

What you can conclude. Moving from DN to a strength or capacity estimate requires a separately verified applicable relationship.

Original worked case. Read the source editions and method notes.

Draft TRH12 describes the use of the total blows to 800 mm for a reasonably balanced pavement in its discussion of the DCP method. The qualification belongs with the parameter; a count alone does not establish applicability or remaining life. (Department of Transport, 1997)

The chart preserves the unequal blow intervals on its horizontal axis, with depth increasing downward. To calculate an interval rate, use the differences in the table. Connecting lines guide the eye between observations; they do not establish the unmeasured detail between those observations.

A record that terminates at 600 mm should say so. Refusal, interruption and incomplete depth coverage are information, not values to interpolate away so that a report has no empty fields. Before empirical interpretation, inspect the test record and the selected method's conditions.

The useful engineering discussion is therefore layered: what did the instrument record, what arithmetic was applied, and what interpretation is justified? Keeping those questions separate makes a compact parameter easier to use responsibly.

Calculation laboratory

Why is the whole-profile rate not the average of interval rates?

Calculation step	Substitution or result	Units and interpretation
Depth increments	100, 100, 200, 400	mm
Blow increments	10, 15, 30, 45	blows
Interval rates	10, 6.6667, 6.6667, 8.8889	mm/blow
Weighted identity	Σ(DNj × ΔNj) / ΣΔNj = 800 / 100 = 8	mm/blow

The cumulative depth curve carries the raw sequence. Its local slope over an interval is penetration per blow, so it must use differences in both coordinates. Dividing each cumulative depth by cumulative blows instead yields an average from the starting point and progressively mixes the material encountered earlier into the new value.

The arithmetic mean of the four interval rates is 8.0556 mm/blow, whereas the global rate is 8.0000. The difference arises because the intervals have unequal blow counts. Weighting each local rate by its blow count reconstructs total penetration exactly. Neither summary preserves the location of a rapid change; retain the profile before deciding whether and how to divide it into layers.

A count to a specified depth and a penetration rate have different dimensions. Reaching 800 mm at 100 blows in this synthetic record does not by itself authorise a particular DSN800 capacity correlation. Equipment, starting datum, refusal handling, material applicability and the selected published method must be established first. No CBR conversion or remaining-life relationship is inferred here. The investigation framework calls for evidence appropriate to the pavement situation, rather than choosing a correlation solely because a depth appears in its name. (Department of Transport, 1997)

Controlled sensitivity experiment

Controlled case	Calculated output	What changes
40 last blows	10.000000 mm/blow last interval	Last 400 mm divided by 40 blows; other intervals unchanged.
45 last blows	8.888889 mm/blow last interval	Reference last interval, 400 mm over 45 blows.
50 last blows	8.000000 mm/blow last interval	Last 400 mm divided by 50 blows.

CALCULATION LABORATORY

Why is the whole-profile rate not the average of interval rates?

Compare the cases on a fixed scale. Select a case to inspect its input change and calculated output.

Sensitivity case1. 40 last blows2. 45 last blows3. 50 last blows

40 last blows: 10 mm/blow last interval. Last 400 mm divided by 40 blows; other intervals unchanged.

Reproduce and challenge the result

Require increasing cumulative blows and nondecreasing penetration. A zero blow increment cannot be divided into a rate; flag it for review. Retain refusal and missing intervals explicitly instead of replacing them with zero penetration resistance.

These are original synthetic calculations. The sensitivity cases vary the stated input while retaining the other assumptions; they are not field observations or treatment thresholds. The film’s calculation and sensitivity chapters use the same numerical cases as this table.

Unroll the soundings along the corridor

Begin with the interval penetration values from the worked record, then prescribe a 15% spatial modulation along a 2 km corridor. DN₀ is 10 from the surface to less than 200 mm, 6.6666667 from 200 to below 400 mm, and 8.8888889 from 400 mm onward. Read each column as a depth profile. Bands are prescribed layers in the teaching dataset, not detected field interfaces.

Reproduce the experiment. DN(x,z) = DN₀(z)[1 + 0.15 sin(2πx/700)]. The downloadable table contains 12,261 evaluated cells, with the two input coordinates and output value retained on every row. These are parameter combinations, not that many independent field observations. The equation extends the worked example above; it is original teaching arithmetic, not a new standard or calibrated prediction.

Computed parameter atlas · 12,261 cells

A thin band should not disappear in the average

One penetration number is convenient. A depth record is more interesting.

Download every calculated cell (CSV) · Open full-size explorer · Equation source and tests (ZIP)

This synthetic response field does not convert DN to CBR, capacity or DSN800. A real sounding has discrete blows, depth resolution and possible refusal; smooth chainage variation is an imposed assumption.

References and method notes

1. Department of Transport (n.d.). Roads: Engineering Standard Guidelines and Manuals. Official catalogue; accessed 5 September 2026. Original source (Accessed: 5 September 2026).TMH22 V8b Draft; TRH12; TRH15; TRH24 catalogue entries
2. Department of Transport (1997). TRH12: Flexible Pavement Rehabilitation Investigation and Design. Draft TRH12, Pretoria: Department of Transport for COLTO. Original source (Accessed: 5 September 2026).Chapter 1: rehabilitation design process; investigation, evaluation, analysis and economic appraisal

Use the source edition and project requirements that apply to your work. Educational examples are not site-specific design advice.