1. Square-root – time curve fitting method

1. Plot the dial reading and square root of time i.e T for a pressure increment as shown in figure.

In this initial step, you begin by constructing a plot that represents two important variables: the dial reading and the square root of time (denoted as T) relative to a specific increase in pressure. The dial reading may represent some measured value in a testing process that changes as pressure is applied, while plotting the square root of time helps visualize how the process evolves over time. This step is crucial as it allows you to see the relationship between these variables in a graphical format, which is essential for further analysis.

Imagine you're tracking how long it takes for a sponge to absorb water. In this scenario, the dial reading represents the amount of water absorbed, while the square root of time indicates how long it has been soaking. By plotting these two values on a graph, you can visually assess the efficiency of absorption over time.

2. Draw a tangent PQ to the initial portion of the plot as shown in fig.

Once the plot is created, the next step is to draw a tangent line (denoted as line PQ) to the initial portion of the curve. This tangent line represents the instantaneous rate of change at the start of the plot. The slope of this tangent line provides important information about how rapidly the dial reading is changing in response to time during the initial phases of the pressure application, which is crucial for understanding the behavior of the system under study.

Think of a car accelerating from a stop light; initially, the speed increases rapidly. By drawing a tangent at the moment the light turns green, you can see how fast the car is speeding up at that exact moment. This tangent similarly helps us understand the rate of change in our graph during the early stages.

3. Draw a line PR such that OR=1.15OQ.

After establishing the tangent line, the next instruction requires you to draw another line (identified as PR) such that its length relation to the previously drawn tangent line PQ indicates that OR is 1.15 times the length of OQ. This step is significant as it adjusts the slope of the line PR in a specific manner, which can be used to predict or analyze future data points on the curve. This adjustment plays a vital role in curve fitting and influences the accuracy in estimating how the system behaves under varying conditions.

Imagine you are scaling a model; you want the new model (PR) to be slightly larger than the original proportion (PQ). If PQ represents the original, adjusting PR to be 1.15 times larger allows you to see how the model behaves under slightly modified conditions, giving you insights into potential changes in performance or behavior.

4. The intersection of the line PR with the second portion of the curve i.e point S is marked.

In the final step of this procedure, you are tasked with finding where the line PR intersects with the second part of the curve (this intersection is labeled as point S). The significance of this point lies in its importance for subsequent analysis or calculations regarding the consolidation process. Marking this point gives a key reference that can help determine how well the model fits the observed data, informing future forecasting or adjustments.

Consider a mountain climbing scenario where you place a marker (point S) at the intersection of two different trails. This marker not only helps guide you in selecting paths in the future but reinforces your understanding of the terrain. Similarly, point S indicates a critical juncture in your measurements that will be vital for future comparisons or assessments.

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