DE102020133929B3 - Method for the laboratory determination of the earth pressure behavior at rest of an earth-moist, non-cohesive loose rock under load, taking into account the overconsolidation number - Google Patents

Abstract

The invention relates to a method for the laboratory determination of the earth pressure behavior at rest of an earth-moist loose rock under load, taking into account the overconsolidation number, in which consolidation tests are carried out on loose rock samples produced from the loose rock in the static triaxial device or in the one-dimensional compression device with lateral pressure measurement.

Description

The field of application of the invention is in soil physics, the laboratory measurement of the pore fraction n, the vertical principal stress σ ₁ and the overconsolidation number OCR-dependent resting earth pressure behavior of earth-moist, non-cohesive loose rock. Soft rock is defined as earth-moist here, in which the water contained can develop cohesive effects. Loose rock is understood to be almost completely saturated here, in which the gas fractions that are still present are no longer connected to the atmosphere. This method cannot be used for loose rock that is completely or almost completely saturated with water.

bei welchem die relative Längendeformation in Richtung der größten Hauptspannung σ₁ gleich der relativen Volumendeformation ist. Damit ist die relative Längendeformation in Richtung der kleinsten Hauptspannung σ₃ = 0. Der Porenanteil n ist das Verhältnis der gasförmigen und flüssigen Phase eines Lockergesteins zu dessen Gesamtvolumen. Die Überkonsolidierungszahl OCR ist das Verhältnis des Größtwertes σ_1max der größten Hauptspannung σ₁, der das Lockergestein während seiner Genese jemals ausgesetzt war, zur aktuellen größten Hauptspannung σ₁ (Gleichung (2)). $$OCR=\frac{{\sigma }_{1\text{max}}}{{\sigma }_1}$$

The earth pressure coefficient at rest K ₀ of loose rock is the ratio of the smallest principal stress σ ₃ to the largest principal stress σ ₁ (equation (1)), $${\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_0=\frac{{\mathrm{<figure-callout\; id="3"\; label="\sigma "\; filenames="DE102020133929B3\_0027.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_3}{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}$$

where the relative length deformation in the direction of the greatest principal stress σ ₁ is equal to the relative volume deformation. The relative length deformation in the direction of the smallest principal stress is σ ₃ = 0. The porosity n is the ratio of the gaseous and liquid phase of loose rock to its total volume. The overconsolidation number OCR is the ratio of the maximum value σ _1max of the greatest principal stress σ ₁ that the soft rock was ever exposed to during its genesis to the current greatest principal stress σ ₁ (equation (2)). $$OCR=\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_{1\text{Max}}}{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}$$

The measurement of the earth pressure coefficient K ₀ at rest using this method and the test apparatus are state of the art.

The static triaxial device is used as a test apparatus for measuring the earth pressure coefficient at rest, whereby the method can only be used to measure the earth pressure coefficient under load, but not when unloaded.

Alternatively, a one-dimensional compression device with a sufficiently precise lateral pressure measurement can also be used to carry out the method.

In the triaxial test, the largest principal stress σ ₁ on the soil sample to be examined is increased and, at the same time, lateral expansion of the sample is prevented by controlling the smallest principal stress σ ₃ .

With this method and the test apparatus, the dependency of the earth pressure coefficient K ₀ at rest on the greatest principal stress σ ₁ can be measured for each installation state of the sample, which is characterized by the initial porosity n ₀ at a greatest principal stress σ ₁ ~ 0.

According to this invention, the pore fraction n ₁ is the pore fraction of the earth-moist loose rock, which thus differs from the initial pore fraction n ₀ in the (almost) stress-free state and from the pore fraction n ₂ of an almost water-saturated, non-cohesive or a completely water-saturated, non-cohesive loose rock.

In the pamphlet DE 199 19 351 C1 a method for determining the earth pressure coefficient at rest has already been described. In this method, the earth pressure coefficient at rest is determined in a known manner as a function of the vertical principal stress σ ₁ and the proportion of pores n in the areas of vertical principal stress σ ₁ and proportion of pores n used for measuring the subsidence dimension.

From the preparatory consolidation phases of the subsidence tests, the coefficients of an equation (compare equation (17) there) of the earth pressure coefficient at rest for the earth-moist loose rock can be determined.

In other words, in print DE 199 19 351 C1 a determination of the earth pressure coefficient at rest for the earth-moist loose rock is described, which determines the earth pressure coefficient at rest as a function of the vertical principal stress σ ₁ and the pore fraction n at the areas of vertical principal stress σ ₁ and the pore fraction n used for measuring the subsidence dimension.

With the one in the pamphlet DE 199 19 351 C1 However, with the method explained above, an extrapolation beyond the ranges used there can disadvantageously lead to physically impossible values of the earth pressure coefficient K ₀ of <0 or greater than 1, as will be explained below.

• Es zeigt 1 ein K₀/σ₁-Diagramm mit Einzelversuchen zur Verdeutlichung der Abhängigkeiten zwischen dem Erdruhedruckbeiwert K₀ und der vertikalen Hauptspannung σ₁
• Es zeigt 2 ein K₀/n-Diagramm mit den Einzelversuchen zur Verdeutlichung der Abhängigkeiten zwischen dem Erdruhedruckbeiwert K₀ und dem Porenanteil n₁.

A further explanation of the existing level of knowledge is given on the basis of the following 1 and 2 .

• It shows 1 a K ₀ /σ ₁ diagram with individual tests to illustrate the dependencies between the earth pressure coefficient at rest K ₀ and the vertical principal stress σ ₁
• It shows 2 a K ₀ /n diagram with the individual tests to illustrate the dependencies between the earth pressure coefficient K ₀ and the porosity n ₁ .

1 shows some typical individual experiments I, I', II, II' and III as well as IV by means of which the dependencies in the K ₀ /σ ₁ diagram and in 2 be illustrated in the K ₀ /n diagram.

The overconsolidation number OCR (σ ₁ = σ _1max ) in the 1 and 2 , in the individual tests I, II, III and IV, characterized by the solid curve sections, is (equal) = 1, which means there is no overconsolidation. For each individual test I, II, III and IV (see the solid curves I, II, II, IV), the associated initial void fraction n ₀ is constant.

The overconsolidation number OCR (σ ₁ < σ _1max ) in the 1 and 2 , in the individual tests I' and II' belonging to the individual tests I and II, identified by the dashed curve sections, is (greater than) >1, which means that there is overconsolidation. For each individual test I', II', the associated initial porosity n ₀ (see the dashed curves I', II') corresponds to the initial porosity n ₀ from individual tests I, II.

Corresponding tests, in which there is overconsolidation, were carried out for the individual tests III and IV, but they are in the 1 and 2 not shown.

From the explanations it becomes clear that with the procedure according to the prior art, a separate triaxial test has to be carried out disadvantageously for each initial pore fraction n ₀ and for each overconsolidation number OCR in order to determine the corresponding earth pressure coefficients K ₀ at rest, taking into account the respective overconsolidation number OCR = 1 or OCR > 1 to measure.

In addition to the already explained method for determining the earth pressure coefficient K ₀ at rest according to the publication, the state of the art also includes the prior art DE 199 19 351 C1 a "Method for determining the stress-dependent limit storage condition of a preferably cohesive loose rock" according to the publication DE 195 35 210 C1 which will be discussed further below.

Based on this state of the art, the object of the invention is to create a method by means of which the earth pressure behavior at rest of an earth-moist, non- _cohesive loose rock under load, in particular can be determined while avoiding the above disadvantages.

The scope of the method according to the invention is limited to stress areas in which grain fragmentation does not yet occur and to moist loose rock.

The starting point of the invention is a method for the laboratory determination of the earth pressure behavior at rest of an earth-moist, non-cohesive loose rock under load, in which consolidation tests are carried out in the static triaxial device or in the one-dimensional compression device with lateral pressure measurement.

1. a) Durchführen der Konsolidierungsversuche und Erfassen von Parameter-Daten bei behinderter Seitendehnung bei verschiedenen, den Erdruhedruckbeiwert beeinflussenden Parametern, dazu zählen, der Porenanteil, die größte Hauptspannung und die Überkonsolidierungszahl.
2. b) Bestimmen der Koeffizienten des spannungsabhängigen Grenzlagerungszustands aus den Parameter-Daten der Konsolidierungsversuche.
3. c) Bilden von gemessenen Wertetripel und Transformieren der gemessenen Wertetripel in transformierte Wertequadrupel durch Transformation der unabhängigen Überkonsolidierungszahl in die Überkonsolidierungszahl, bei welcher der Porenanteil gleich dem Grenzporenanteil ist.
4. d) Berechnen materialspezifischen Koeffizienten des Erdruhedruckbeiwertes unter Verwendung der transformierten Wertequadrupel, welche die Abhängigkeit des Erdruhedruckbeiwertes von der größten Hauptspannung, dem Porenanteil und der transformierten Überkonsolidierungszahl repräsentieren.

According to the invention, the following steps are provided:

1. a) Carrying out the consolidation tests and recording parameter data in the case of restrained lateral strain for various parameters influencing the earth pressure coefficient at rest, including the porosity, the greatest principal stress and the overconsolidation number.
2. b) Determination of the coefficients of the stress-dependent boundary support state from the parameter data of the consolidation tests.
3. c) forming measured value triplets and transforming the measured value triplets into transformed value quadruples by transforming the independent overconsolidation number into the overconsolidation number, in which the void fraction is equal to the limit void fraction.
4. d) Calculation of material-specific coefficients of the earth pressure coefficient at rest using the transformed quadruples of values, which represent the dependence of the earth pressure coefficient at rest on the greatest principal stress, the proportion of pores and the transformed overconsolidation number.

Preferred refinements of the method are formulated in the dependent claims.

In the following, the invention will be explained in more detail by describing the path taken in developing the method.

As from those already described 1 and 2 As can be seen, there is a functional dependency K ₀ = f ( σ ₁ , n, OCR) between the earth pressure coefficient at rest K ₀ and the greatest principal stress σ ₁ , the porosity n and the overconsolidation number OCR.

In a known manner, the measurement of the earth pressure coefficient K ₀ at rest is only possible with an increasing maximum principal stress σ ₁ . In a known manner, the increase in stress causes a reduction in the porosity n ₁ .

The extent of this reduction in the porosity n ₁ is in turn dependent on the vertical principal stress σ ₁ .

The overconsolidation number OCR (σ ₁ = σ _1max ) only remains for OCR = 1 (compare the solid curve sections I, II, III, IV in the 1 and 2 ) constant with an increase in voltage.

The overconsolidation number OCR (σ ₁ < σ _1max ) for OCR > 1 (compare the dashed curve sections I', II' in the 1 and 2 ) changes with every change in voltage, reference being made again to equation (2). $$OCR=\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_{1\text{Max}}}{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}$$

Based on these explanations, it becomes clear that it is not possible to keep only one of the independent variables constant, namely the largest principal stress σ ₁ , the porosity n ₁ and the overconsolidation number OCR, and depending on the variable that is kept constant, the influences on the remaining ones to examine the dependent variables individually in the experiment.

If you compare, for example, in the 1 and 2 the measured earth pressure coefficients K ₀ at rest of a loose rock (which are represented by the various continuous curves I, II, II, IV) with the same greatest principal stress σ ₁ , the same porosity n ₁ and the same overconsolidation number OCR (OCR = 1), can - like from the 1 and 2 can be seen - large differences in the earth pressure coefficient K ₀ at rest.

Due to different material-defining parameters, such as grain size distribution, grain density, rounding, surface texture, a defined porosity n with a defined maximum principal stress σ ₁ can mean a rather loose bed for loose rock, which is characterized, for example, by a low stiffness modulus and low strength. In other words, for a different loose rock with different material-defining parameters, the same porosity n ₁ with the same maximum principal stress σ ₁ can mean a rather dense bed characterized by a different higher constrained modulus and a different higher strength.

For this reason, a loose rock-typical reference value for the proportion of pores and the tension is required first. The measurement of such a variable is - as already explained - from the publication in DE 195 35 210 C1 "Procedure for determining the stress-dependent limit storage condition of a preferably cohesive loose rock".

$$OC{R}_{gr}=\frac{{\sigma }_{1gr}}{{\sigma }_1}$$

According to the invention, an overconsolidation number OCR _gr (equation (4)) related to σ1 _gr can thus be defined using this stress-dependent loosest support (equation (3)). $$n_{G\mathrm{right}}=n_{G\mathrm{right}0}·e^{-\left({\left(\frac{{\sigma }_1}{E_{G\mathrm{right}}}\right)}^{C_{eG\mathrm{right}}}\right)}$$

$$OC{R}_{G\mathrm{right}}=\frac{{\sigma }_{1G\mathrm{<figure-callout\; id="1"\; label="right\; \sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">right</figure-callout>}}}{{\sigma }_{}}$$

The over-consolidation number OCR _gr related to σ1 _gr advantageously creates a stress-dependent relationship between the proportion of pores n ₁ and ngr (see equations (5.1 and 5.2)), as follows:

Equation (5.1) results from mathematical conversion of equation (3) to σ ₁ . $${\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1=E_{G\mathrm{right}}·{\left(-\text{ln}\left(\frac{n_{G\mathrm{right}}}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{C_{eG\mathrm{right}}}}$$

Replacing the porosity ngr in Equation (5.1) by the porosity n ₁ results in Equation (5.2). Equation (5.2) corresponds to steps iii and v given in 3 shown and explained below from OCR to OCR _gr . $${\sigma }_{1G\mathrm{right}}=E_{G\mathrm{right}}·{\left(-\text{ln}\left(\frac{n_1}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{C_{eG\mathrm{right}}}}$$

The general functional dependency of the hitherto customary earth pressure coefficient K ₀ =f(σ ₁ ,n ₁ ,OCR) is thus advantageously converted into a general dependency according to the invention of the form K ₀ =f(σ ₁ ,n ₁ ,OCR _gr ).

• • dem Porenanteil n₁ und der vertikalen Hauptspannung σ₁, sowie
• • dem Porenanteil n_gr0 und der Spannung σ_1gr, bei der die vertikale Hauptspannung σ₁, für die n₁ = ngr ist,

bei lockerster Lagerung des erdfeuchten Lockergestein beziehungsweise der Lockergesteinsproben.It shows 3 shows in a diagram the dependencies (ordinate) n ₁ of σ ₁ (abscissa) and (ordinate) ngr of σ _1gr (abscissa) of an exemplary individual attempt of the consolidation attempts to clarify the dependencies between

• • the porosity n ₁ and the vertical principal stress σ ₁ , and
• • the porosity n _gr0 and the stress σ _1gr , at which the vertical principal stress σ ₁ , for which n ₁ = ngr ,

in the case of very loose storage of the earth-moist loose rock or the loose rock samples.

It will be according to 3 proceeded as follows:

In 3 the characteristic Kn _gr of the stress-dependent limit storage state is shown.

Bedding states of the loose rock are only possible on or below this curve Kn _gr .

1. i. Es wird im Ausführungsbeispiel von dem Ausgangspunkt AP bei der Überkonsolidierungszahl OCR = 1, σ₁ ausgegangen.
2. ii. Anschließend wird mit der Gleichung (5.2) die Spannung σ_{1 gr} bei OCR = 1 ermittelt, sodass der Punkt ngr von AP auf den Kennlinie Kn_gr grafisch oder durch die Gleichung (5.2) gefunden wird.
3. iii. Anschließend wird mittels der Gleichung (4) der Wert OCR_gr für den Ausgangspunkt AP ermittelt, der stets > größer 1 ist.
4. iv. Danach wird das erdfeuchte, nichtbindige Lockergestein im Ausführungsbeispiel um 50% des Spannungswertes von σ₁ entlastet. Durch diese Entlastung erhöht sich der Porenanteil n₁ um einen geringen Betrag, wie in 3 durch den Pfeil, zwischen AP und EP verdeutlicht ist.
5. v. Analog zu dem Ausgangspunkt AP wird jetzt für den Entlastungspunkt EP mit der Gleichung (5.2) die Spannungσ_1gr bei OCR = 2 ermittelt, sodass der Punkt ngr von EP auf den Kennlinie Kn_gr grafisch oder durch die Gleichung (5.2) gefunden wird.
6. vi. Anschließend wird mittels der Gleichung (4) der Wert OCR_gr für den Entlastungspunkt EP ermittelt, der ebenfalls stets größer > 1 ist, und der im Vergleich zu dem OCR_gr des Ausgangspunktes AP (von ii) grösser ist, als der Wert OCR_gr des Ausgangspunktes AP. Durch diese Vorgehensweise ist sichergestellt, dass sich die ermittelten Werte für OCR_gr bei Entlastung in die gleiche Richtung entwickeln, wie die Ausgangswerte von OCR in Entlastung.

According to the invention, the independent overconsolidation number OCR, which is difficult to determine in the field, is transformed into the overconsolidation number OCR _gr , which is dependent on other parameters, as explained below.

1. i. In the exemplary embodiment, it is assumed that the starting point AP is the overconsolidation number OCR= ₁ , σ1.
2. ii. The stress σ _{1 gr} at OCR = 1 is then determined using equation (5.2), so that the point ngr of AP on the characteristic curve Kn _gr is found graphically or using equation (5.2).
3. iii. The value OCR _gr for the starting point AP, which is always >greater than 1, is then determined using equation (4).
4. IV. Then the earth-moist, non-cohesive loose rock is relieved by 50% of the stress value of σ ₁ in the exemplary embodiment. This relief increases the porosity n ₁ by a small amount, as shown in 3 by the arrow between AP and EP.
5. v. Analogously to the starting point AP, the stress _{σ 1gr} at OCR = 2 is now determined for the relief point EP using equation (5.2), so that the point ngr of EP on the characteristic curve Kn _gr is found graphically or using equation (5.2).
6. vi. Equation (4) is then used to determine the OCR _gr value for the relief point EP, which is also always greater than 1 and which, compared to the OCR _gr of the starting point AP (of ii), is greater than the OCR _gr des value starting point AP. This procedure ensures that the determined values for OCR _gr with relief develop in the same direction as the initial values of OCR with relief.

This means that the OCR values can be replaced by the OCR _gr values, ie they can be transformed. There is thus the possibility of replacing the independent variable OCR step by step with the variable OCR _gr , which is now dependent on the porosity n ₁ and the stress σ ₁ , in an advantageous qualitative manner using the transformation, as explained above.

By means of this changed general dependency of the variable OCR _gr , which is now dependent on other parameters, through the previously described transformation from OCR to OCR _gr , a concrete, advantageous form of the description of the earth pressure behavior at rest according to the invention of an earth-moist, non-cohesive loose rock under load that only still depends on the parameters pore fraction n ₁ and the stress σ ₁ and no longer on the overconsolidation number OCR, as is laid down in (equation (6)). $${\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_0={\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1·K_{Of}·\left(K_{OCR}+\frac{1}{OC{R}_{G\mathrm{right}}·\sqrt{K_{OCR}}}\right)+K_{wf}·\left(\left|{\mathrm{<figure-callout\; id="0"\; label="K\; w"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_w·e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}{{\sigma }_{Kw}}}-{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\right|+{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1-{\mathrm{<figure-callout\; id="0"\; label="K\; w"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_w·e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}{{\sigma }_{Kw}}}\right)$$

This equation (6) in conjunction with equations (1) to (5.1, 5.2) and the associated description lay down the method according to the invention, with which the at-rest earth pressure behavior of an earth-moist, non-cohesive loose rock under load can be determined in a laboratory.

Coming back to the 1 and 2 shows the at-rest earth pressure behavior of the method according to the invention with overconsolidation numbers OCR of >1 according to the dashed characteristic curves and an overconsolidation number OCR=1 according to the continuous characteristic curves with a pore fraction n ₀ of the sample, which is constant in each case.

A sufficiently small number—less than previously in the prior art—of measured data sets (Ko, σ ₁ , n ₁ ) now allows the coefficients of equation (6) to also be calculated if the coefficients of equation (3) are known.

It is thus possible to calculate the coefficients Egr and c _egr from Equation (3) with an additional measurement, i.e. a determination of the so-called pore fraction n _gr0 , the pore fraction in the loosest storage of the earth-moist, non-cohesive loose rock. $$n_{G\mathrm{right}}=n_{G\mathrm{right}0}·e^{-\left({\left(\frac{{\sigma }_1}{E_{G\mathrm{right}}}\right)}^{C_{eG\mathrm{right}}}\right)}$$

• An einem mit einem Wassergehalt von 0,1 verkippten schwach schluffigen Sand, somit eines erdfeuchten, nichtbindigen Lockergesteins, soll das Erdruhedruckverhalten, insbesondere der Erdruhedruckbeiwert K₀ nach dem erfindungsgemäß Verfahren bestimmt werden.

The method is to be explained in more detail using the following exemplary embodiment:

• The at-rest earth pressure behavior, in particular the at-rest earth pressure coefficient K ₀ , is to be determined using the method according to the invention on slightly silty sand that has been tilted with a water content of 0.1, i.e. an earth-moist, non-cohesive loose rock.

For the classification of this sand, the following material-descriptive key figures were determined by the expert for the rough assessment of the properties of this sand, of which only the grain density is necessary as an auxiliary variable for the calculation of the porosity n, in particular n ₁ and the initial porosity n ₀ : fine grain content 10% fine sand content 16% proportion of medium sand 45% coarse sand content 21% fine gravel content 7% non-uniformity number 6.9 curvature number 1.7 grain density ^2.628 g/cm3 Number of pores with the loosest storage according to DIN 18126 0.810 Number of pores with dense storage according to DIN 18126 0.329

step a)

• Es zeigt 4 ein K₀/σ₁-Diagramm mit den Messwertepaaren Ko, σ₁ der Versuche A, B, C, D.
• Es zeigt 5 ein K₀/n₁-Diagramm mit den in den Versuchen A, B, C, D gemessenen Messwertetripel Ko, σ₁, n₁.

Performing Consolidation Attempts in Impeded Lateral Extension:

• It shows 4 a K ₀ /σ ₁ diagram with the measured value pairs Ko, σ ₁ of experiments A, B, C, D.
• It shows 5 a K ₀ /n ₁ diagram with the measured value triplets Ko, σ ₁ , n ₁ measured in experiments A, B, C, D.

For example, four triaxial tests with different built-in porosity n ₀ are carried out with this sand, which were loaded as follows with restricted lateral expansion: Try A _n0 = 0.558 loaded up to σ ₁ = 85 kPa attempt B _n0 = 0.423 loaded up to σ ₁ = 205 kPa Attempt C _n0 = 0.517 loaded up to σ ₁ = 305 kPa Try D _n0 = 0.469 loaded up to σ ₁ = 705 kPa

The result of these consolidation attempts A to D are, with an overconsolidation number OCR=1, the parameter data present as value triples [K ₀ , n ₁ , σ ₁ ].

step b)

Apply the method according to the publication DE 195 35 210 C1 as part of this process:

The coefficients of the stress-dependent limit support state are determined according to equation (3), with the consolidation tests A, B, C, D according to step a) being used for this purpose. $$n_{G\mathrm{right}}=n_{G\mathrm{right}0}·e^{-\left({\left(\frac{{\sigma }_1}{E_{G\mathrm{right}}}\right)}^{C_{eG\mathrm{right}}}\right)}$$

As a result, the coefficients n _gr0 , Egr, c _egr of the stress-dependent limit state according to equation (3) are available, which result in the exemplary embodiment as follows: n _gr0 = 0.584 = proportion of pores in the loosest bedding of an earth-moist loose rock at σ ₁ = 0 Egr = 88810 kPa = equation coefficient of equation (3) _Cegr = 0.1592 = equation coefficient of equation (3)

step c)

Transform:

Transforming the measured value triples [K ₀ , σ ₁ , n ₁ ] into value quadruples [K ₀ , σ ₁ , n ₁ , OCR _gr ] according to the transformation of the independent overconsolidation number OCR into the σ ₁ and n ₁ dependent overconsolidation number OCR _gr , like previously in the transformation steps (compare 3 ) explained in points i to vi:

step d)

• Aus diesen transformierten Wertequadrupel [K₀, σ₁, n₁, OCR_gr] werden die Koeffizienten K_0f, K_OCR, K_wf, K_w0, σ_Kw von Gleichung (6) als - Schätzwerte - wie folgt berechnet: $${\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_0={\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1·K_{of}·\left(K_{OCR}+\frac{1}{OC{R}_{gr}·\sqrt{K_{OCR}}}\right)+K_{wf}·\left(\left|{\mathrm{<figure-callout\; id="0"\; label="K\; w"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_w·e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}{{\sigma }_{Kw}}}-{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\right|+{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1-{\mathrm{<figure-callout\; id="0"\; label="K\; w"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_w·e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}{{\sigma }_{Kw}}}\right)$$
  

K_0f = 0,02636 = Koeffizient K_OCR = 40,96 = Koeffizient K_wf = 0,2974 = Koeffizient K_w0 = 0,4362 = Koeffizient σ_Kw = 2436,6 kPa = Koeffizient Calculate the material specific coefficients using equation (6):

• From these transformed quadruples of values [K ₀ , σ ₁ , n ₁ , OCR _gr ], the coefficients K _0f , K _OCR , K _wf , K _w0 , σ _Kw of equation (6) are calculated as - estimated values - as follows: $$K_0=n_1·K_{Of}·\left(K_{OCR}+\frac{1}{OC{R}_{G\mathrm{right}}·\sqrt{K_{OCR}}}\right)+K_{wf}·\left(\left|K_{w0}·e^{-\frac{{\sigma }_1}{{\sigma }_{Kw}}}-n_1\right|+n_1-K_{w0}·e^{-\frac{{\sigma }_1}{{\sigma }_{Kw}}}\right)$$
  

K _0f = 0.02636 = coefficient K _OCR = 40.96 = coefficient K _wf = 0.2974 = coefficient K _w0 = 0.4362 = coefficient σ _kW = 2436.6kPa = coefficient

The Pearson correlation coefficient between the measured K ₀ values and the K ₀ values estimated using equation (6) is 0.967, so the standard deviation is only 0.004.

The calculated using equation (6) - estimated values - according to the standard deviation are in the 4 and 5 shown.

As a result of the procedure shows 6 a family of characteristics K ₀ = f (σ ₁ ) for constant initial pore fractions n ₀ according to the tests A to D carried out and according to a further initial pore fraction n ₀ = 0.49 of the unconsolidated rock, which advantageously through the method according to the invention - without real experiment - can be determined.

It shows 6 a K ₀ /σ ₁ diagram with a family of characteristics K ₀ = f (σ ₁ ) with the characteristics K _A , K _B , Kc, K _D for constant initial pore fractions n ₀ of the loose rock based on the tests A, B , C, D measured measured values K ₀ , σ ₁ , n ₁ and for at least one other exemplary constant initial pore fraction n ₀ = 0.49 of the unconsolidated rock according to the characteristic K _E , which can be determined based on the method - without further testing.

7 shows an n ₁ /σ ₁ diagram with a family of characteristics for constant initial pore fractions n ₀ of the characteristics K _A , _{KB , K C ,} K _D , _KE according to 6 . At every point in 6 one dot belongs in each 7 .

The pore fractions n ₁ resulting from the respective initial pore fractions n ₀ and the stress σ ₁ can be calculated from the in 7 mapped characteristic curves K _A , K _B , K _C , K _D , K _E of the family of characteristics can be read.

It shows 8th an OCR _gr /σ ₁ diagram with a family of characteristics for constant initial pore fractions n ₀ according to the characteristics K _A , K _B , K _C , K _D , K _E 6 . At every point in 6 one dot belongs in each 8th .

The overconsolidation numbers OCR _gr resulting from the porosity n ₁ and the stress σ ₁ can be derived from the in 8th mapped characteristics K _A , K _B , Kc, K _D , K _E of the family of characteristics can be read.

Advantageously, with the method explained, physically impossible values of the earth pressure coefficient K ₀ at rest can no longer occur.

In addition, the procedure according to the invention - in contrast to the procedure according to the prior art - advantageously makes it possible for each initial porosity n ₀ and for each overconsolidation number OCR, without having to carry out a separate triaxial test for each of these initial porosity n ₀ in order to be able to determine the corresponding earth pressure coefficients K ₀ at rest.

We based on the characteristics K _A , K _B , K _C , K _D , K _E in the 6 , 7 and 8th is made clear, the method according to the invention makes it possible in relation to the investigated earth-moist loose rock to determine the pore fraction n ₁ , - the greatest principal stress σ ₁ and - the overconsolidation number OCR, without having to carry out further triaxial tests.

The results can thus be transferred to the in situ conditions sought without having to carry out repeated triaxial tests.

In dumps in particular, parameters that describe the state of the earth pressure behavior at rest, in particular the porosity n ₁ , are subject to local fluctuations.

In addition, the state of stress that can be described by the largest principal stress σ ₁ and the overconsolidation number OCR changes, and thus its influence on the earth pressure behavior at rest, depending on the history and geometry of the tip.

These changes are taken into account in the procedure according to the invention.

In the case of earth-moist loose rock, if the proportion of pores n ₁ and the greatest principal stress σ ₁ are known, the overconsolidation factors OCR _gr and the earth pressure coefficients K ₀ at rest can be determined for a specific tip without having to carry out further triaxial tests, which is advantageous.

$$OCR=\frac{{\sigma }_{1\text{max}}}{{\sigma }_1}$$

$$n_{gr}=n_{gr0}·e^{-\left({\left(\frac{{\sigma }_1}{E_{gr}}\right)}^{C_{egr}}\right)}$$

$$OC{R}_{gr}=\frac{{\sigma }_{1gr}}{{\sigma }_1}$$

$${\sigma }_1=E_{gr}·{\left(-\text{ln}\left(\frac{n_{gr}}{n_{gr0}}\right)\right)}^{\frac{1}{C_{egr}}}$$

$${\sigma }_{1gr}=E_{gr}·{\left(-\text{ln}\left(\frac{n_1}{n_{gr0}}\right)\right)}^{\frac{1}{C_{egr}}}$$

$$K_0=n_1·K_{of}·\left(K_{OCR}+\frac{1}{OC{R}_{gr}·\sqrt{K_{OCR}}}\right)+K_{wf}·\left(\left|K_{w0}·e^{-\frac{{\sigma }_1}{{\sigma }_{Kw}}}-n_1\right|+n_1-K_{w0}·e^{-\frac{{\sigma }_1}{{\sigma }_{Kw}}}\right)$$

Compilation of the equations used: $${\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_0=\frac{{\mathrm{<figure-callout\; id="3"\; label="\sigma "\; filenames="DE102020133929B3\_0027.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_3}{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}$$

$$OCR=\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_{1\text{<figure-callout id="1" label="Max σ" filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png" state="{{state}}">Max</figure-callout>}}}{{\sigma }_{}}$$

$$n_{G\mathrm{right}}=n_{G\mathrm{right}0}·e^{-\left({\left(\frac{{\sigma }_1}{E_{G\mathrm{right}}}\right)}^{C_{eG\mathrm{right}}}\right)}$$

$$OC{R}_{G\mathrm{right}}=\frac{{\sigma }_{1G\mathrm{<figure-callout\; id="1"\; label="right\; \sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">right</figure-callout>}}}{{\sigma }_{}}$$

$${\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1=E_{G\mathrm{right}}·{\left(-\text{ln}\left(\frac{n_{G\mathrm{right}}}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{C_{eG\mathrm{right}}}}$$

$${\sigma }_{1G\mathrm{right}}=E_{G\mathrm{right}}·{\left(-\text{ln}\left(\frac{n_1}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{C_{eG\mathrm{right}}}}$$

$${\mathrm{<figure-callout\; id="0"\; label="K"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_0={\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1·K_{Of}·\left(K_{OCR}+\frac{1}{OC{R}_{G\mathrm{right}}·\sqrt{K_{OCR}}}\right)+K_{wf}·\left(\left|{\mathrm{<figure-callout\; id="0"\; label="K\; w"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_w·e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}{{\sigma }_{Kw}}}-{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\right|+{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">n</figure-callout>}}_1-{\mathrm{<figure-callout\; id="0"\; label="K\; w"\; filenames="DE102020133929B3\_0023.png,DE102020133929B3\_0025.png"\; state="\{\{state\}\}">K</figure-callout>}}_w·e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="\sigma "\; filenames="DE102020133929B3\_0021.png,DE102020133929B3\_0022.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_1}{{\sigma }_{Kw}}}\right)$$

Reference List

K0

earth pressure coefficient

σ1

in situ greatest principal stress, in the triaxial test vertical principal stress

σ3

in situ smallest principal stress, in the triaxial test horizontal principal stress

n

porosity

n0

Initial porosity in (almost) stress-free condition

n1

Percentage of pores in the earth-moist loose rock

OCR

overconsolidation number

σ1 max

Maximum value of σ ₁ that the unconsolidated rock has ever been exposed to

σ1gr

Stress σ ₁ for which n = ngr

OCRgr

overconsolidation number related to σ1 _gr

no

Limit pore fraction, largest pore fraction for a vertical principal stress σ ₁

ngr0

Equation coefficient of Equation (3), proportion of pores in the loosest bedding of an earth-moist loose rock at σ ₁ = 0

Egr

Equation coefficient reference stiffness modulus of equation (3)

cegr

Equation coefficient stress-free boundary storage state of Equation 3) (material constant)

c0f

Equation coefficient of Equation (6)

KOCR

Equation coefficient of Equation (6)

kwf

Equation coefficient of Equation (6)

wk0

Equation coefficient of Equation (6)

σKw

Equation coefficient of Equation (6)

AP

starting point

EP

relief point

royal

Characteristic of the limit void fraction, largest void fraction for a vertical principal stress σ ₁

KA

Characteristic curves from experiment A

KB

Characteristic curves from test B

KC

Characteristic curves from experiment C

KD

Characteristics from experiment D

KE

Characteristics independent of the test

Claims (5)

Method for the laboratory determination of the earth pressure behavior at rest of an earth-moist, non-cohesive loose rock under load, in which consolidation tests (A, B, C, D) are carried out on loose rock samples produced from the loose rock in the static triaxial device or in the one-dimensional compression device with lateral pressure measurement, with the steps: a) Carrying out the consolidation tests (A, B, C, D) on the loose rock samples and recording parameter data (n ₁ , σ ₁ , OCR) in the case of restricted lateral expansion with various parameters influencing the earth pressure coefficient (K ₀ ) at rest, including - the void fraction (n ₁ ), - the greatest principal stress (σ ₁ ) and - the overconsolidation number (OCR), b) determination of coefficients of the stress-dependent boundary support state from the parameter data (n ₁ , σ ₁ , OCR) of the consolidation tests (A, B, C, D), c) forming measured value triplets [K ₀ , σ ₁ , n ₁ ] and transforming the measured value triplets [K ₀ , σ ₁ , n ₁ ] into transformed value quadruples (K ₀ , σ ₁ , n ₁ , OCR _gr ), by transformation the independent overconsolidation number (OCR) into the overconsolidation number (OCR _gr ) at which the void fraction (n ₁ ) equals the limiting void fraction (ngr) using equations (4) and (5.2) $$OC{R}_{G\mathrm{right}}=\frac{{\sigma }_{1G\mathrm{right}}}{{\sigma }_1}\text{and}{\sigma }_1=E_{G\mathrm{right}}·{\left(-\text{ln}\left(\frac{n_1}{n_{G\mathrm{right}0}}\right)\right)}^{\frac{1}{C_{eG\mathrm{right}}}}$$

d) Calculation of material-specific coefficients (K _0f , K _OCR , K _wf , K _w0 , σ _Kw ) of the earth pressure coefficient (K ₀ ) at rest using the transformed quadruples of values [K ₀ , σ ₁ , n ₁ , OCR _gr ], which express the dependency the earth pressure coefficient at rest (K ₀ = f (σ ₁ , n ₁ , OCR _gr )) from the greatest principal stress (σ ₁ ), the porosity (n ₁ ) and the transformed overconsolidation number (OCR _gr ) according to equation (6) $$K_0=n_1·K_{Of}·\left(K_{OCR}+\frac{1}{OC{R}_{G\mathrm{right}}·\sqrt{K_{OCR}}}\right)+K_{wf}·\left(\left|K_{w0}·e^{-\frac{{\sigma }_1}{{\sigma }_{Kw}}}-n_1\right|+n_1-K_{w0}·e^{-\frac{{\sigma }_1}{{\sigma }_{Kw}}}\right)$$

represent. procedure according to claim 1 , characterized in that instead of the proportion of pores (n ₁ ), parameters which also describe the state of storage of the loose rock, such as the number of pores, density or dry density, are used. procedure according to claim 1 , characterized in that the consolidation attempts (A, B, C, D) are carried out at a constant over-consolidation number (OCR)=1. procedure according to claim 1 , characterized in that the consolidation attempts (A, B, C, D) are carried out with different over-consolidation numbers (OCR)>1. Procedure according to claims 1 and 3 or 1 and 4 , characterized in that the overconsolidation number (OCR _gr ) dependent on the parameters pore fraction (n ₁ ) and greatest principal stress (σ ₁ ) transformed in step c) is transformed by steps i) to vi), i.) forming a starting point ( AP) at the overconsolidation number (OCR =1, OCR >1) and ii.) finding the stress (σ _1gr ), at the overconsolidation number (OCR = 1) using equation (5.2), and iii.) finding the value of the overconsolidation number (OCR _gr ) for the starting point (AP) using equation (4), and iv.) relieving the loose rock by a predeterminable stress value (σ ₁ ), and v.) determining the stress (σ1 _gr ) in the starting point (AP ) associated relief point (EP) with equation (5.2) the stress (σ1 _gr ), and vi.) determining the value of the overconsolidation number (OCR _gr ) for the relief point (EP) with equation (4).

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