Highway 73 · Southern Stockholm

Observe. Update. Decide.

A clay foundation is settling beneath a future highway. Every week, one noisy measurement reshapes the digital state—and may change the next construction action.

550 m embankment15.5 m soft clay72-week horizonWeekly settlement data

Run the twin ↓What has value?

Terminology: the paper presents a Probabilistic Digital Twin. The branching view below is a decision visual—not a separate “Probability Tree Twin.”

01 · Field simulation

Move through construction

Drag the week slider or play the sequence. The site, posterior belief, risk and recommended action update together.

Physical twin

Embankment on soft clay

Paper p.11

Observed zₛ(t)No reading yet

Digital state dₜPrior · σ 0.18 m

Construction clockWeek 0 / 72

BuildWeek 16 reviewUnload decision

MODELOBSERVEUPDATEACT

Paper scenarioFigure 8

Initial surcharge h₀1.09 m

Measurement error σₑ0.05 m

Risk threshold Pₜₕ0.43

Stop threshold covₜₕ0.05

72-week settlement1.18 m

95% interval · 0.83–1.53 m

OCR at week 721.08

Paper requirement: OCR ≥ 1.10

Probability of missing target—

Waiting for observations

Uncertainty reduction0%

Simulated variance reduction—not formal VoI

Current recommendationBuild the initial probabilistic model

The engineer remains the approving decision maker.

Posterior prediction

Settlement S(t)

Live simulation

95% intervalPosterior meanObservation1.27 m target

02 · Information value

Which information actually matters?

The twin does not assign “value” to every number equally. It values information through the decision it can improve.

Initial evidence

Soil-property data Z_prop

Samples across depth initialise X_soil: stresses, moduli, unit weights, water content and consolidation coefficients.

Main sequential information

Weekly settlement z_s(t)

This is the new field information that is repeatedly assimilated. Its usefulness depends on both the reading and its measurement error σ_ε.

Updated knowledge

Posterior digital state d_t

The particle filter turns observations into a tighter probability distribution over the hidden physical state.

Decision-relevant outputs

S(72), OCR(72), risk and cost

The posterior is projected into target compliance, lifecycle cost, and the choice to hold or add surcharge.

Important boundary. In the paper, weekly monitoring is fixed in advance; the information-collection decision e_t is not optimised. Therefore this page reports posterior uncertainty reduction. A strict value-of-information study would compare optimal expected cost with and without an additional measurement.

03 · Decision branch

From belief to action

Branch width is replaced by clear mobile cards. Each branch carries a probability and a simulated expected cost.

Current posterior beliefdₜ · σ = 0.18 m

OPTION A

Hold surcharge

—

Probability of missing the settlement target

Expected cost—

RECOMMENDED

Add surcharge

—

Residual probability after the simulated action

Expected cost—

04 · Influence diagram

How the PDT is wired

Tap a node. The mobile layout preserves the dependency logic of the paper’s Figure 7 without forcing a wide desktop graph.

CAUSAL FLOW · OBSERVATION FEEDS BACK THROUGH BAYESIAN UPDATING

Paper pp.11–12

Physical state X_t

A probabilistic description of geometry, surcharge height, soil properties, long-term settlement and degree of consolidation—not merely a static BIM object.

05 · People in the loop

A human decision chain

The PDT changes the information flow; it does not erase engineering responsibility.

SurveyorRecords weekly settlement with known measurement error.

→

Probabilistic digital twinUpdates the hidden state and forecasts S(72) and OCR(72).

→

Geotechnical engineerReviews posterior risk, cost and model assumptions.

→

Construction crewHolds or adds surcharge, changing the next state.

↺

06 · Paper evidence

Paper facts vs simulation

Everything is labelled so readers can see what came from the article and what was added for interaction.

Case geometry and monitoring

Highway 73, southern Stockholm; 550 m road embankment.
0.3 m dry crust over 15.5 m soft clay; target embankment height 1.2 m.
PVD design is fixed. Weekly settlement is the sequential behaviour data.

Source: PDF pp.11–12.

Decision targets and Figure 8

Maximum project time: 72 weeks.
Settlement target: 1.27 m; OCR target: 1.10.
Figure 8 example: h₀=1.09 m, covₜₕ=0.05, Pₜₕ=0.43; measurements stop and the surcharge is raised at week 16.

Source: PDF pp.15–17.

Table 2 parameter presets

σₑ	h₀	COVₜₕ	Pₜₕ	Cost*
0.05 m	0.98 m	0.50	0.62	6.42
0.10 m	0.99 m	0.50	0.47	6.51
0.15 m	1.06 m	0.49	0.40	6.88

* Expected cost in 10⁶ SEK. Source: PDF p.18, Table 2.

Simulation and interpretation limits

The live trajectories use a simplified normal Bayesian demonstration, not the paper’s full particle filter, Monte Carlo and cross-entropy optimisation.
Instant branch probabilities, action size, live OCR and branch costs are explanatory simulations.
Equation (10) writes S(tmax) ≤ starget, while the Figure 8 narrative moves settlement upward after added surcharge. This page follows the operational Figure 8 narrative and flags the tension.

Open the paper DOI ↗

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