Through the test, the settlement value S under various loads P can be measured, and the P-S relationship curve can be drawn (Figure 2-2). However, the measured deformation values are not all generated under the corresponding load, and truly reflect the P-S law of foundation soil.
In the test, due to the interference of various factors, the measured deformation value is different from the real deformation value. The task of settlement data correction is to eliminate these errors. Generally speaking, there are the following correction methods:
Correction of 1. inflection point P-S curve
Figure 2-2 Measured P-S Curve and Corrected P-S Curve
Most of these curves reflect the overall failure of soil, with obvious proportional limit point P0 and limit point Pu. With P0 and Pu as the boundary, the deformation stage of soil is divided into three stages (Figure 2-2): Zone I-compaction and linear strain stage (elastic deformation) of foundation soil under load; Zone Ⅱ-shear deformation stage under load (elastic-plastic deformation); Zone ⅲ-failure stage under load (plastic deformation). P-S curve is straight before the proportional limit point P0. In the test, the starting point of the measured curve often deviates from the origin, and curve correction is to find out the measurement error S0 value deviating from the origin of coordinates and the slope c of the straight line segment before the proportional limit point (Figure 2-2).
Method 1: Linear relation method (also known as graphic method and straight line segment calculation method) is suitable for the correction of inflection point P-S curve.
Find the proportional limit point P0 on the P-S relation curve drawn according to the original test data, and draw a straight line from the proportional limit point along the observation data to the original point, so that the settlement point before the proportional limit is as close as possible to the straight line, and the intercept of the intersection of the straight line and the ordinate is S0, so that the slope c determined by this straight line can be obtained. On this straight line, we can find two characteristic points (0, S0) and (P 1, 0) where the straight line intersects with the vertical axis and the horizontal axis of the coordinate, and any point (Pk, Sk) on the straight line. According to the equal slope relationship between two points on the same straight line, there is the following relationship:
Soil in-situ testing and engineering investigation
Method 2: Least square method (straight line segment calculation method) is suitable for the correction of inflection point P-S curve.
According to the principle of least square method, the square of the difference between the observed deformation value S'i and the settlement value (S0+CPi) on the initial straight line segment of the P-S curve should be the minimum value, namely:
∑[S'i-(S0+CPi)]2= minimum value, which must have:
Soil in-situ testing and engineering investigation
Soil in-situ testing and engineering investigation
Solve the above two differential equations and get two equations of the least square method:
NS0+C∑P-∑S=0 (2-4)
S0∑P+C∑P2-∑PS=0 (2-5)
Where: n is the loading times of the straight line segment.
Then solve the above two equations of the least square method to obtain the expressions of the settlement correction value S0 and the slope c of the S-P curve:
Soil in-situ testing and engineering investigation
Soil in-situ testing and engineering investigation
After finding S0 and c by linear relation method or least square method, the point before the proportional limit can be corrected according to formula (2-8) to obtain the settlement correction value S':
s′= C P(-8)
For each point after the proportional limit, it can be corrected by Formula (2-9) according to the measured settlement values S and S0:
s′= Si′-S0(2-9)
That is, a corrected P-S curve can be obtained by subtracting S0 from each point of the measured P-S curve along the ordinate.
In order to conveniently find out S0 and c by formulas (2-6) and (2-7), the correlation values of S0 and c calculated by least square method when the load interval at all levels is 3. 125 ~ 100 kPa are given, as shown in Table 2-4.
Method 3: Non-inflection point P-S curve correction
The shapes of P-S curves of foundation soils with different genetic types and different stress histories are also quite different during the plate load test, which comprehensively reflects the soil mechanical properties such as consolidation pressure in the early stage of excavation, soil structure, soil particle gradation and its mineral composition, and soil hydraulic properties under a certain load. It can be considered that the P-S curve of inflection point with obvious inflection point characteristics shows that the soil has a sudden change in mechanical properties at its mechanical boundary point, and finally shows the overall failure mode, which is generally low compressibility soil; If there is no obvious mechanical demarcation point on the P-S curve, it is a smooth P-S curve, and this kind of soil shows progressive failure or has certain creep characteristics, mainly medium-high compressibility soil.
Table 2-4 Correlation Values of S0 and C Calculated by Least Square Method
sequential
2. Correction of smooth P-S curve without inflection point
(1) equal increment correction method: the smooth P-S curve without inflection point (Figure 2-3) has the characteristics of equal increment of curve slope under equal load increment, namely:
Soil in-situ testing and engineering investigation
If the slope on the curve is k, the slopes K0, k01of the connecting line between two points can be calculated at the adjacent coordinate points with equal load increment on the curve;
Figure 2-3 P-S curve of steady load test
Soil in-situ testing and engineering investigation
Soil in-situ testing and engineering investigation
Soil in-situ testing and engineering investigation
Soil in-situ testing and engineering investigation
And:
k0-k 0 1 = k 0 1-k 12 = k 12-K23
These include:
P0 = P0-p 1 = p 1-P2 = P2-P3(2- 14)
Combined with the above formula, it is concluded that:
S0=3S 1-3S2+S3 (2- 15)
Or:
Soil in-situ testing and engineering investigation
If S0 is found, the settlement value of the non-inflection point smooth P-S curve can be corrected as follows:
Si=S0+Sc (2- 17)
Where: Si is the corrected settlement value on the smooth P-S curve; S0 is the settlement correction value; Sc is the measured value of settlement.
(2) Data conversion method: According to the convergence speed difference of some functions, we can also appropriately convert the non-inflection point type smooth P-S curve in P-S coordinates, so that the curve can be converted into inflection point type curve, and the proportional limit P0 of the curve can be obtained more intuitively.
Commonly used methods are: lgP—lgS curve method; P-δ S/δ P curve method
Example: Determining Proportional Limit P0 by lgP-lgS Curve Method
Some data of in-situ load test of shallow fine sand slab in geotechnical practice base of School of Civil Engineering and Architecture of Jilin University are selected and converted into lgP—lgS coordinate curve by P-S curve. The proportional limit point P0 is easy to determine (Table 2-5 and Figure 2-4).
It should be pointed out that not all P-S curves can become inflection points with intuitive proportional limit P0 after lgP—lgS and P-δ S/δ P conversion. In the work, it is necessary to deal with the specific conditions of foundation soil.
Table 2-5 Record Sheet of In-situ Test of Shallow Plate Load
Fig. 2-4 Schematic diagram of transforming non-inflection point smooth P-S curve into inflection point curve
A. The data in Table 2-5 shows a smooth P-S curve in P and S coordinates, and there is no obvious proportional boundary point P0; B. The data in Table 2-5 has obvious proportional demarcation point P0 in lgP—lgS coordinates.